diff --git a/changelog b/changelog index 37c8d26..fac4fd5 100644 --- a/changelog +++ b/changelog @@ -1,3 +1,6 @@ +20100609 tpd src/axiom-website/patches.html 20100609.01.tpd.patch +20100609 tpd src/input/Makefile rule-based trig integration +20100609 tpd src/input/richtrig100-199.input rule-based trig integration 20100608 tpd src/axiom-website/patches.html 20100608.04.tpd.patch 20100608 tpd src/input/unittest1.input add David Parnas to credits 20100608 tpd books/bookvol5 add David Parnas to credits diff --git a/src/axiom-website/patches.html b/src/axiom-website/patches.html index 61516bf..78263f3 100644 --- a/src/axiom-website/patches.html +++ b/src/axiom-website/patches.html @@ -2866,6 +2866,8 @@ books/bookvolbib add Lecerf[Le96], Dewar[Dew94], Brunelli[Bru09]
src/input/richtrig000-099.input rule-based trig integration
20100608.04.tpd.patch books/bookvol5 add David Parnas to credits
+20100609.01.tpd.patch +src/input/richtrig100-199.input rule-based trig integration
diff --git a/src/input/Makefile.pamphlet b/src/input/Makefile.pamphlet index 5b11f0d..94587b0 100644 --- a/src/input/Makefile.pamphlet +++ b/src/input/Makefile.pamphlet @@ -377,6 +377,7 @@ REGRES= ackermann.regress \ richexponential.regress \ richrational.regress \ richtrig000-099.regress \ + richtrig100-199.regress \ robidoux.regress \ roman.regress roots.regress ruleset.regress rules.regress \ rubey.regress sae.regress spline.regress \ @@ -697,6 +698,7 @@ FILES= ${OUT}/ackermann.input \ ${OUT}/richexponential.input \ ${OUT}/richrational.input \ ${OUT}/richtrig000-099.input \ + ${OUT}/richtrig100-199.input \ ${OUT}/robidoux.input ${OUT}/roman.input ${OUT}/roots.input \ ${OUT}/ruleset.input ${OUT}/rules.input ${OUT}/rubey.input \ ${OUT}/sae.input \ @@ -1046,6 +1048,7 @@ DOCFILES= \ ${DOC}/richexponential.input.dvi \ ${DOC}/richrational.input.dvi \ ${DOC}/richtrig000-099.input.dvi \ + ${DOC}/richtrig100-199.input.dvi \ ${DOC}/rk4draw.input.dvi \ ${DOC}/robidoux.input.dvi ${DOC}/roman.input.dvi \ ${DOC}/romnum.as.dvi ${DOC}/roots.input.dvi \ diff --git a/src/input/richtrig100-199.input.pamphlet b/src/input/richtrig100-199.input.pamphlet new file mode 100644 index 0000000..7e563eb --- /dev/null +++ b/src/input/richtrig100-199.input.pamphlet @@ -0,0 +1,19497 @@ +\documentclass{article} +\usepackage{axiom} +\begin{document} +\title{\$SPAD/src/input richtrig100-199.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f richtrig100-199.output +)spool richtrig100-199.output +)set message test on +)set message auto off +)clear all + +--S 1 of 504 +t0100:= x*sin(a+b*log(c*x^n))^2 +--R +--R +--R n 2 +--R (1) x sin(b log(c x ) + a) +--R Type: Expression Integer +--E 1 + +--S 2 of 504 +--Rr0100:= -1/4*x^2*(-b^2*n^2+2*b*n*cos(a+b*log(c*x^n))*sin(a+b*log(c*x^n))-2+2*cos(a+b*log(c*x^n))^2)/(1+b^2*n^2) +--R +--R +--R (2) +--R 2 n n +--R - 2b n x cos(b log(c x ) + a)sin(b log(c x ) + a) +--R + +--R 2 n 2 2 2 2 +--R - 2x cos(b log(c x ) + a) + (b n + 2)x +--R / +--R 2 2 +--R 4b n + 4 +--R Type: Expression Integer +--R +--E 2 + +--S 3 of 504 +--Ra0100:= integrate(t0100,x) +--R +--R +--R (3) +--R 2 +--R - 2b n x cos(b n log(x) + b log(c) + a)sin(b n log(x) + b log(c) + a) +--R + +--R 2 2 2 2 2 +--R - 2x cos(b n log(x) + b log(c) + a) + (b n + 2)x +--R / +--R 2 2 +--R 4b n + 4 +--R Type: Union(Expression Integer,...) +--R +--E 3 + +--S 4 of 504 +--Rm0100:= a0100-r0100 +--R +--R +--R (4) +--R 2 n n 2 n 2 +--R b n x cos(b log(c x ) + a)sin(b log(c x ) + a) + x cos(b log(c x ) + a) +--R + +--R 2 +--R - b n x cos(b n log(x) + b log(c) + a)sin(b n log(x) + b log(c) + a) +--R + +--R 2 2 +--R - x cos(b n log(x) + b log(c) + a) +--R / +--R 2 2 +--R 2b n + 2 +--R Type: Expression Integer +--R +--E 4 + +--S 5 of 504 +--Rd0100:= D(m0100,x) +--R +--R +--R (5) +--R 2 2 2 n - 1 n 2 +--R - b n x x sin(b log(c x ) + a) +--R + +--R n 2 n - 1 n n +--R (2b n x x - 2b n x x )cos(b log(c x ) + a)sin(b log(c x ) + a) +--R + +--R n 2 2 2 n - 1 n 2 +--R (2x x + b n x x )cos(b log(c x ) + a) +--R + +--R 2 2 n 2 +--R b n x x sin(b n log(x) + b log(c) + a) +--R + +--R 2 2 n 2 +--R (- b n - 2)x x cos(b n log(x) + b log(c) + a) +--R / +--R 2 2 n +--R (2b n + 2)x +--R Type: Expression Integer +--R +--E 5 + +--S 6 of 504 +--Rt0101:= x^2*sin(a+b*log(c*x^n))^2 +--R +--R +--R 2 n 2 +--R (6) x sin(b log(c x ) + a) +--R Type: Expression Integer +--R +--E 6 + +--S 7 of 504 +--Rr0101:= -1/3*x^3*(-2*b^2*n^2+6*b*n*cos(a+b*log(c*x^n))*sin(a+b*log(c*x^n))-9+9*cos(a+b*log(c*x^n))^2)/(9+4*b^2*n^2) +--R +--R +--R (7) +--R 3 n n +--R - 6b n x cos(b log(c x ) + a)sin(b log(c x ) + a) +--R + +--R 3 n 2 2 2 3 +--R - 9x cos(b log(c x ) + a) + (2b n + 9)x +--R / +--R 2 2 +--R 12b n + 27 +--R Type: Expression Integer +--R +--E 7 + +--S 8 of 504 +--Ra0101:= integrate(t0101,x) +--R +--R +--R (8) +--R 3 +--R - 6b n x cos(b n log(x) + b log(c) + a)sin(b n log(x) + b log(c) + a) +--R + +--R 3 2 2 2 3 +--R - 9x cos(b n log(x) + b log(c) + a) + (2b n + 9)x +--R / +--R 2 2 +--R 12b n + 27 +--R Type: Union(Expression Integer,...) +--R +--E 8 + +--S 9 of 504 +--Rm0101:= a0101-r0101 +--R +--R +--R (9) +--R 3 n n +--R 2b n x cos(b log(c x ) + a)sin(b log(c x ) + a) +--R + +--R 3 n 2 +--R 3x cos(b log(c x ) + a) +--R + +--R 3 +--R - 2b n x cos(b n log(x) + b log(c) + a)sin(b n log(x) + b log(c) + a) +--R + +--R 3 2 +--R - 3x cos(b n log(x) + b log(c) + a) +--R / +--R 2 2 +--R 4b n + 9 +--R Type: Expression Integer +--R +--E 9 + +--S 10 of 504 +--Rd0101:= D(m0101,x) +--R +--R +--R (10) +--R 2 2 3 n - 1 n 2 +--R - 2b n x x sin(b log(c x ) + a) +--R + +--R 2 n 3 n - 1 n n +--R (6b n x x - 6b n x x )cos(b log(c x ) + a)sin(b log(c x ) + a) +--R + +--R 2 n 2 2 3 n - 1 n 2 +--R (9x x + 2b n x x )cos(b log(c x ) + a) +--R + +--R 2 2 2 n 2 +--R 2b n x x sin(b n log(x) + b log(c) + a) +--R + +--R 2 2 2 n 2 +--R (- 2b n - 9)x x cos(b n log(x) + b log(c) + a) +--R / +--R 2 2 n +--R (4b n + 9)x +--R Type: Expression Integer +--R +--E 10 + +--S 11 of 504 +--Rt0102:= sin(a+b*log(c*x^n))^2/x^2 +--R +--R +--R n 2 +--R sin(b log(c x ) + a) +--R (11) --------------------- +--R 2 +--R x +--R Type: Expression Integer +--R +--E 11 + +--S 12 of 504 +--Rr0102:= -1/(1+4*b^2*n^2)/x*(2*b^2*n^2+2*b*n*cos(a+b*log(c*x^n))*sin(a+b*log(c*x^n))+1-cos(a+b*log(c*x^n))^2) +--R +--R +--R (12) +--R n n n 2 +--R - 2b n cos(b log(c x ) + a)sin(b log(c x ) + a) + cos(b log(c x ) + a) +--R + +--R 2 2 +--R - 2b n - 1 +--R / +--R 2 2 +--R (4b n + 1)x +--R Type: Expression Integer +--R +--E 12 + +--S 13 of 504 +--Ra0102:= integrate(t0102,x) +--R +--R +--R (13) +--R - 2b n cos(b n log(x) + b log(c) + a)sin(b n log(x) + b log(c) + a) +--R + +--R 2 2 2 +--R cos(b n log(x) + b log(c) + a) - 2b n - 1 +--R / +--R 2 2 +--R (4b n + 1)x +--R Type: Union(Expression Integer,...) +--R +--E 13 + +--S 14 of 504 +--Rm0102:= a0102-r0102 +--R +--R +--R (14) +--R n n n 2 +--R 2b n cos(b log(c x ) + a)sin(b log(c x ) + a) - cos(b log(c x ) + a) +--R + +--R - 2b n cos(b n log(x) + b log(c) + a)sin(b n log(x) + b log(c) + a) +--R + +--R 2 +--R cos(b n log(x) + b log(c) + a) +--R / +--R 2 2 +--R (4b n + 1)x +--R Type: Expression Integer +--R +--E 14 + +--S 15 of 504 +--Rd0102:= D(m0102,x) +--R +--R +--R (15) +--R 2 2 n - 1 n 2 +--R - 2b n x x sin(b log(c x ) + a) +--R + +--R n n - 1 n n +--R (- 2b n x + 2b n x x )cos(b log(c x ) + a)sin(b log(c x ) + a) +--R + +--R n 2 2 n - 1 n 2 +--R (x + 2b n x x )cos(b log(c x ) + a) +--R + +--R 2 2 n 2 +--R 2b n x sin(b n log(x) + b log(c) + a) +--R + +--R 2 2 n 2 +--R (- 2b n - 1)x cos(b n log(x) + b log(c) + a) +--R / +--R 2 2 2 n +--R (4b n + 1)x x +--R Type: Expression Integer +--R +--E 15 + +--S 16 of 504 +--Rt0103:= x^m*sin(a+b*log(c*x^n))^2 +--R +--R +--R m n 2 +--R (16) x sin(b log(c x ) + a) +--R Type: Expression Integer +--R +--E 16 + +--S 17 of 504 +--Rr0103:= 2*b^2*n^2*x^(1+m)/(1+m)/((1+m)^2+4*b^2*n^2)-2*b*n*x^(1+m)*cos(a+b*log(c*x^n))*sin(a+b*log(c*x^n))/((1+m)^2+4*b^2*n^2)+(1+m)*x^(1+m)*sin(a+b*log(c*x^n))^2/((1+m)^2+4*b^2*n^2) +--R +--R +--R (17) +--R 2 m + 1 n 2 +--R (m + 2m + 1)x sin(b log(c x ) + a) +--R + +--R m + 1 n n 2 2 m + 1 +--R (- 2b m - 2b)n x cos(b log(c x ) + a)sin(b log(c x ) + a) + 2b n x +--R / +--R 2 2 2 3 2 +--R (4b m + 4b )n + m + 3m + 3m + 1 +--R Type: Expression Integer +--R +--E 17 + +--S 18 of 504 +--Ra0103:= integrate(t0103,x) +--R +--R +--R (18) +--R m log(x) +--R (- 2b m - 2b)n x cos(b n log(x) + b log(c) + a)%e +--R * +--R sin(b n log(x) + b log(c) + a) +--R + +--R 2 2 +--R (- m - 2m - 1)x cos(b n log(x) + b log(c) + a) +--R + +--R 2 2 2 +--R (2b n + m + 2m + 1)x +--R * +--R m log(x) +--R %e +--R / +--R 2 2 2 3 2 +--R (4b m + 4b )n + m + 3m + 3m + 1 +--R Type: Union(Expression Integer,...) +--R +--E 18 + +--S 19 of 504 +--Rm0103:= a0103-r0103 +--R +--R +--R (19) +--R 2 m + 1 n 2 +--R (- m - 2m - 1)x sin(b log(c x ) + a) +--R + +--R m + 1 n n +--R (2b m + 2b)n x cos(b log(c x ) + a)sin(b log(c x ) + a) +--R + +--R m log(x) +--R (- 2b m - 2b)n x cos(b n log(x) + b log(c) + a)%e +--R * +--R sin(b n log(x) + b log(c) + a) +--R + +--R 2 2 +--R (- m - 2m - 1)x cos(b n log(x) + b log(c) + a) +--R + +--R 2 2 2 +--R (2b n + m + 2m + 1)x +--R * +--R m log(x) +--R %e +--R + +--R 2 2 m + 1 +--R - 2b n x +--R / +--R 2 2 2 3 2 +--R (4b m + 4b )n + m + 3m + 3m + 1 +--R Type: Expression Integer +--R +--E 19 + +--S 20 of 504 +--Rd0103:= D(m0103,x) +--R +--R +--R (20) +--R 2 m n 2 2 m + 1 n - 1 n 2 +--R ((- m - 2m - 1)x x - 2b n x x )sin(b log(c x ) + a) +--R + +--R m n m + 1 n - 1 n +--R ((2b m + 2b)n x x + (- 2b m - 2b)n x x )cos(b log(c x ) + a) +--R * +--R n +--R sin(b log(c x ) + a) +--R + +--R 2 2 m + 1 n - 1 n 2 +--R 2b n x x cos(b log(c x ) + a) +--R + +--R 2 2 n m log(x) 2 +--R 2b n x %e sin(b n log(x) + b log(c) + a) +--R + +--R 2 2 2 n 2 +--R (- 2b n - m - 2m - 1)x cos(b n log(x) + b log(c) + a) +--R + +--R 2 2 2 n +--R (2b n + m + 2m + 1)x +--R * +--R m log(x) +--R %e +--R + +--R 2 2 m n +--R - 2b n x x +--R / +--R 2 2 2 n +--R (4b n + m + 2m + 1)x +--R Type: Expression Integer +--R +--E 20 + +--S 21 of 504 +--Rt0104:= sin(a+b*log(c*x^n))^3 +--R +--R +--R n 3 +--R (21) sin(b log(c x ) + a) +--R Type: Expression Integer +--R +--E 21 + +--S 22 of 504 +--Rr0104:= -6*b^3*n^3*x*cos(a+b*log(c*x^n))/(1+b^2*n^2)/(1+9*b^2*n^2)+6*b^2*n^2*x*sin(a+b*log(c*x^n))/(1+b^2*n^2)/(1+9*b^2*n^2)-3*b*n*x*cos(a+b*log(c*x^n))*sin(a+b*log(c*x^n))^2/(1+9*b^2*n^2)+x*sin(a+b*log(c*x^n))^3/(1+9*b^2*n^2) +--R +--R +--R (22) +--R 2 2 n 3 +--R (b n + 1)x sin(b log(c x ) + a) +--R + +--R 3 3 n n 2 +--R (- 3b n - 3b n)x cos(b log(c x ) + a)sin(b log(c x ) + a) +--R + +--R 2 2 n 3 3 n +--R 6b n x sin(b log(c x ) + a) - 6b n x cos(b log(c x ) + a) +--R / +--R 4 4 2 2 +--R 9b n + 10b n + 1 +--R Type: Expression Integer +--R +--E 22 + +--S 23 of 504 +--Ra0104:= integrate(t0104,x) +--R +--R +--R (23) +--R 2 2 2 2 2 +--R ((- b n - 1)x cos(b n log(x) + b log(c) + a) + (7b n + 1)x) +--R * +--R sin(b n log(x) + b log(c) + a) +--R + +--R 3 3 3 +--R (3b n + 3b n)x cos(b n log(x) + b log(c) + a) +--R + +--R 3 3 +--R (- 9b n - 3b n)x cos(b n log(x) + b log(c) + a) +--R / +--R 4 4 2 2 +--R 9b n + 10b n + 1 +--R Type: Union(Expression Integer,...) +--R +--E 23 + +--S 24 of 504 +--Rm0104:= a0104-r0104 +--R +--R +--R (24) +--R 2 2 n 3 +--R (- b n - 1)x sin(b log(c x ) + a) +--R + +--R 3 3 n n 2 +--R (3b n + 3b n)x cos(b log(c x ) + a)sin(b log(c x ) + a) +--R + +--R 2 2 n 3 3 n +--R - 6b n x sin(b log(c x ) + a) + 6b n x cos(b log(c x ) + a) +--R + +--R 2 2 2 2 2 +--R ((- b n - 1)x cos(b n log(x) + b log(c) + a) + (7b n + 1)x) +--R * +--R sin(b n log(x) + b log(c) + a) +--R + +--R 3 3 3 +--R (3b n + 3b n)x cos(b n log(x) + b log(c) + a) +--R + +--R 3 3 +--R (- 9b n - 3b n)x cos(b n log(x) + b log(c) + a) +--R / +--R 4 4 2 2 +--R 9b n + 10b n + 1 +--R Type: Expression Integer +--R +--E 24 + +--S 25 of 504 +--Rd0104:= D(m0104,x) +--R +--R +--R (25) +--R 2 2 n 4 4 2 2 n - 1 n 3 +--R ((- b n - 1)x + (- 3b n - 3b n )x x )sin(b log(c x ) + a) +--R + +--R 3 3 n 3 3 n - 1 n +--R ((3b n + 3b n)x + (- 3b n - 3b n)x x )cos(b log(c x ) + a) +--R * +--R n 2 +--R sin(b log(c x ) + a) +--R + +--R 4 4 2 2 n - 1 n 2 2 2 n +--R (6b n + 6b n )x x cos(b log(c x ) + a) - 6b n x +--R + +--R 4 4 n - 1 +--R - 6b n x x +--R * +--R n +--R sin(b log(c x ) + a) +--R + +--R 3 3 n 3 3 n - 1 n +--R (6b n x - 6b n x x )cos(b log(c x ) + a) +--R + +--R 3 3 n +--R (2b n + 2b n)x cos(b n log(x) + b log(c) + a) +--R * +--R 2 +--R sin(b n log(x) + b log(c) + a) +--R + +--R 4 4 2 2 n 2 +--R (- 9b n - 10b n - 1)x cos(b n log(x) + b log(c) + a) +--R + +--R 4 4 2 2 n +--R (9b n + 10b n + 1)x +--R * +--R sin(b n log(x) + b log(c) + a) +--R + +--R 3 3 n 3 +--R (2b n + 2b n)x cos(b n log(x) + b log(c) + a) +--R + +--R 3 3 n +--R (- 2b n - 2b n)x cos(b n log(x) + b log(c) + a) +--R / +--R 4 4 2 2 n +--R (9b n + 10b n + 1)x +--R Type: Expression Integer +--R +--E 25 + +--S 26 of 504 +--Rt0105:= x*sin(a+b*log(c*x^n))^3 +--R +--R +--R n 3 +--R (26) x sin(b log(c x ) + a) +--R Type: Expression Integer +--R +--E 26 + +--S 27 of 504 +--Rr0105:= -6*b^3*n^3*x^2*cos(a+b*log(c*x^n))/(4+b^2*n^2)/(4+9*b^2*n^2)+12*b^2*n^2*x^2*sin(a+b*log(c*x^n))/(4+b^2*n^2)/(4+9*b^2*n^2)-3*b*n*x^2*cos(a+b*log(c*x^n))*sin(a+b*log(c*x^n))^2/(4+9*b^2*n^2)+2*x^2*sin(a+b*log(c*x^n))^3/(4+9*b^2*n^2) +--R +--R +--R (27) +--R 2 2 2 n 3 +--R (2b n + 8)x sin(b log(c x ) + a) +--R + +--R 3 3 2 n n 2 +--R (- 3b n - 12b n)x cos(b log(c x ) + a)sin(b log(c x ) + a) +--R + +--R 2 2 2 n 3 3 2 n +--R 12b n x sin(b log(c x ) + a) - 6b n x cos(b log(c x ) + a) +--R / +--R 4 4 2 2 +--R 9b n + 40b n + 16 +--R Type: Expression Integer +--R +--E 27 + +--S 28 of 504 +--Ra0105:= integrate(t0105,x) +--R +--R +--R (28) +--R 2 2 2 2 2 2 2 +--R ((- 2b n - 8)x cos(b n log(x) + b log(c) + a) + (14b n + 8)x ) +--R * +--R sin(b n log(x) + b log(c) + a) +--R + +--R 3 3 2 3 +--R (3b n + 12b n)x cos(b n log(x) + b log(c) + a) +--R + +--R 3 3 2 +--R (- 9b n - 12b n)x cos(b n log(x) + b log(c) + a) +--R / +--R 4 4 2 2 +--R 9b n + 40b n + 16 +--R Type: Union(Expression Integer,...) +--R +--E 28 + +--S 29 of 504 +--Rm0105:= a0105-r0105 +--R +--R +--R (29) +--R 2 2 2 n 3 +--R (- 2b n - 8)x sin(b log(c x ) + a) +--R + +--R 3 3 2 n n 2 +--R (3b n + 12b n)x cos(b log(c x ) + a)sin(b log(c x ) + a) +--R + +--R 2 2 2 n 3 3 2 n +--R - 12b n x sin(b log(c x ) + a) + 6b n x cos(b log(c x ) + a) +--R + +--R 2 2 2 2 2 2 2 +--R ((- 2b n - 8)x cos(b n log(x) + b log(c) + a) + (14b n + 8)x ) +--R * +--R sin(b n log(x) + b log(c) + a) +--R + +--R 3 3 2 3 +--R (3b n + 12b n)x cos(b n log(x) + b log(c) + a) +--R + +--R 3 3 2 +--R (- 9b n - 12b n)x cos(b n log(x) + b log(c) + a) +--R / +--R 4 4 2 2 +--R 9b n + 40b n + 16 +--R Type: Expression Integer +--R +--E 29 + +--S 30 of 504 +--Rd0105:= D(m0105,x) +--R +--R +--R (30) +--R 2 2 n 4 4 2 2 2 n - 1 n 3 +--R ((- 4b n - 16)x x + (- 3b n - 12b n )x x )sin(b log(c x ) + a) +--R + +--R 3 3 n 3 3 2 n - 1 n +--R ((6b n + 24b n)x x + (- 6b n - 24b n)x x )cos(b log(c x ) + a) +--R * +--R n 2 +--R sin(b log(c x ) + a) +--R + +--R 4 4 2 2 2 n - 1 n 2 2 2 n +--R (6b n + 24b n )x x cos(b log(c x ) + a) - 24b n x x +--R + +--R 4 4 2 n - 1 +--R - 6b n x x +--R * +--R n +--R sin(b log(c x ) + a) +--R + +--R 3 3 n 3 3 2 n - 1 n +--R (12b n x x - 12b n x x )cos(b log(c x ) + a) +--R + +--R 3 3 n +--R (4b n + 16b n)x x cos(b n log(x) + b log(c) + a) +--R * +--R 2 +--R sin(b n log(x) + b log(c) + a) +--R + +--R 4 4 2 2 n 2 +--R (- 9b n - 40b n - 16)x x cos(b n log(x) + b log(c) + a) +--R + +--R 4 4 2 2 n +--R (9b n + 40b n + 16)x x +--R * +--R sin(b n log(x) + b log(c) + a) +--R + +--R 3 3 n 3 +--R (4b n + 16b n)x x cos(b n log(x) + b log(c) + a) +--R + +--R 3 3 n +--R (- 4b n - 16b n)x x cos(b n log(x) + b log(c) + a) +--R / +--R 4 4 2 2 n +--R (9b n + 40b n + 16)x +--R Type: Expression Integer +--R +--E 30 + +--S 31 of 504 +--Rt0106:= x^2*sin(a+b*log(c*x^n))^3 +--R +--R +--R 2 n 3 +--R (31) x sin(b log(c x ) + a) +--R Type: Expression Integer +--R +--E 31 + +--S 32 of 504 +--Rr0106:= -2/3*b^3*n^3*x^3*cos(a+b*log(c*x^n))/(1+b^2*n^2)/(9+b^2*n^2)+2*b^2*n^2*x^3*sin(a+b*log(c*x^n))/(1+b^2*n^2)/(9+b^2*n^2)-b*n*x^3*cos(a+b*log(c*x^n))*sin(a+b*log(c*x^n))^2/(3+3*b^2*n^2)+x^3*sin(a+b*log(c*x^n))^3/(3+3*b^2*n^2) +--R +--R +--R (32) +--R 2 2 3 n 3 +--R (b n + 9)x sin(b log(c x ) + a) +--R + +--R 3 3 3 n n 2 +--R (- b n - 9b n)x cos(b log(c x ) + a)sin(b log(c x ) + a) +--R + +--R 2 2 3 n 3 3 3 n +--R 6b n x sin(b log(c x ) + a) - 2b n x cos(b log(c x ) + a) +--R / +--R 4 4 2 2 +--R 3b n + 30b n + 27 +--R Type: Expression Integer +--R +--E 32 + +--S 33 of 504 +--Ra0106:= integrate(t0106,x) +--R +--R +--R (33) +--R 2 2 3 2 2 2 3 +--R ((- b n - 9)x cos(b n log(x) + b log(c) + a) + (7b n + 9)x ) +--R * +--R sin(b n log(x) + b log(c) + a) +--R + +--R 3 3 3 3 +--R (b n + 9b n)x cos(b n log(x) + b log(c) + a) +--R + +--R 3 3 3 +--R (- 3b n - 9b n)x cos(b n log(x) + b log(c) + a) +--R / +--R 4 4 2 2 +--R 3b n + 30b n + 27 +--R Type: Union(Expression Integer,...) +--R +--E 33 + +--S 34 of 504 +--Rm0106:= a0106-r0106 +--R +--R +--R (34) +--R 2 2 3 n 3 +--R (- b n - 9)x sin(b log(c x ) + a) +--R + +--R 3 3 3 n n 2 +--R (b n + 9b n)x cos(b log(c x ) + a)sin(b log(c x ) + a) +--R + +--R 2 2 3 n 3 3 3 n +--R - 6b n x sin(b log(c x ) + a) + 2b n x cos(b log(c x ) + a) +--R + +--R 2 2 3 2 2 2 3 +--R ((- b n - 9)x cos(b n log(x) + b log(c) + a) + (7b n + 9)x ) +--R * +--R sin(b n log(x) + b log(c) + a) +--R + +--R 3 3 3 3 +--R (b n + 9b n)x cos(b n log(x) + b log(c) + a) +--R + +--R 3 3 3 +--R (- 3b n - 9b n)x cos(b n log(x) + b log(c) + a) +--R / +--R 4 4 2 2 +--R 3b n + 30b n + 27 +--R Type: Expression Integer +--R +--E 34 + +--S 35 of 504 +--Rd0106:= D(m0106,x) +--R +--R +--R (35) +--R 2 2 2 n 4 4 2 2 3 n - 1 n 3 +--R ((- 3b n - 27)x x + (- b n - 9b n )x x )sin(b log(c x ) + a) +--R + +--R 3 3 2 n 3 3 3 n - 1 n +--R ((3b n + 27b n)x x + (- 3b n - 27b n)x x )cos(b log(c x ) + a) +--R * +--R n 2 +--R sin(b log(c x ) + a) +--R + +--R 4 4 2 2 3 n - 1 n 2 2 2 2 n +--R (2b n + 18b n )x x cos(b log(c x ) + a) - 18b n x x +--R + +--R 4 4 3 n - 1 +--R - 2b n x x +--R * +--R n +--R sin(b log(c x ) + a) +--R + +--R 3 3 2 n 3 3 3 n - 1 n +--R (6b n x x - 6b n x x )cos(b log(c x ) + a) +--R + +--R 3 3 2 n +--R (2b n + 18b n)x x cos(b n log(x) + b log(c) + a) +--R * +--R 2 +--R sin(b n log(x) + b log(c) + a) +--R + +--R 4 4 2 2 2 n 2 +--R (- 3b n - 30b n - 27)x x cos(b n log(x) + b log(c) + a) +--R + +--R 4 4 2 2 2 n +--R (3b n + 30b n + 27)x x +--R * +--R sin(b n log(x) + b log(c) + a) +--R + +--R 3 3 2 n 3 +--R (2b n + 18b n)x x cos(b n log(x) + b log(c) + a) +--R + +--R 3 3 2 n +--R (- 2b n - 18b n)x x cos(b n log(x) + b log(c) + a) +--R / +--R 4 4 2 2 n +--R (3b n + 30b n + 27)x +--R Type: Expression Integer +--R +--E 35 + +--S 36 of 504 +--Rt0107:= sin(a+b*log(c*x^n))^3/x^2 +--R +--R +--R n 3 +--R sin(b log(c x ) + a) +--R (36) --------------------- +--R 2 +--R x +--R Type: Expression Integer +--R +--E 36 + +--S 37 of 504 +--Rr0107:= -6*b^3*n^3*cos(a+b*log(c*x^n))/(1+b^2*n^2)/(1+9*b^2*n^2)/x-6*b^2*n^2*sin(a+b*log(c*x^n))/(1+b^2*n^2)/(1+9*b^2*n^2)/x-3*b*n*cos(a+b*log(c*x^n))*sin(a+b*log(c*x^n))^2/(1+9*b^2*n^2)/x-sin(a+b*log(c*x^n))^3/(1+9*b^2*n^2)/x +--R +--R +--R (37) +--R 2 2 n 3 +--R (- b n - 1)sin(b log(c x ) + a) +--R + +--R 3 3 n n 2 +--R (- 3b n - 3b n)cos(b log(c x ) + a)sin(b log(c x ) + a) +--R + +--R 2 2 n 3 3 n +--R - 6b n sin(b log(c x ) + a) - 6b n cos(b log(c x ) + a) +--R / +--R 4 4 2 2 +--R (9b n + 10b n + 1)x +--R Type: Expression Integer +--R +--E 37 + +--S 38 of 504 +--Ra0107:= integrate(t0107,x) +--R +--R +--R (38) +--R 2 2 2 2 2 +--R ((b n + 1)cos(b n log(x) + b log(c) + a) - 7b n - 1) +--R * +--R sin(b n log(x) + b log(c) + a) +--R + +--R 3 3 3 +--R (3b n + 3b n)cos(b n log(x) + b log(c) + a) +--R + +--R 3 3 +--R (- 9b n - 3b n)cos(b n log(x) + b log(c) + a) +--R / +--R 4 4 2 2 +--R (9b n + 10b n + 1)x +--R Type: Union(Expression Integer,...) +--R +--E 38 + +--S 39 of 504 +--Rm0107:= a0107-r0107 +--R +--R +--R (39) +--R 2 2 n 3 +--R (b n + 1)sin(b log(c x ) + a) +--R + +--R 3 3 n n 2 +--R (3b n + 3b n)cos(b log(c x ) + a)sin(b log(c x ) + a) +--R + +--R 2 2 n 3 3 n +--R 6b n sin(b log(c x ) + a) + 6b n cos(b log(c x ) + a) +--R + +--R 2 2 2 2 2 +--R ((b n + 1)cos(b n log(x) + b log(c) + a) - 7b n - 1) +--R * +--R sin(b n log(x) + b log(c) + a) +--R + +--R 3 3 3 +--R (3b n + 3b n)cos(b n log(x) + b log(c) + a) +--R + +--R 3 3 +--R (- 9b n - 3b n)cos(b n log(x) + b log(c) + a) +--R / +--R 4 4 2 2 +--R (9b n + 10b n + 1)x +--R Type: Expression Integer +--R +--E 39 + +--S 40 of 504 +--Rd0107:= D(m0107,x) +--R +--R +--R (40) +--R 2 2 n 4 4 2 2 n - 1 n 3 +--R ((- b n - 1)x + (- 3b n - 3b n )x x )sin(b log(c x ) + a) +--R + +--R 3 3 n 3 3 n - 1 n +--R ((- 3b n - 3b n)x + (3b n + 3b n)x x )cos(b log(c x ) + a) +--R * +--R n 2 +--R sin(b log(c x ) + a) +--R + +--R 4 4 2 2 n - 1 n 2 2 2 n +--R (6b n + 6b n )x x cos(b log(c x ) + a) - 6b n x +--R + +--R 4 4 n - 1 +--R - 6b n x x +--R * +--R n +--R sin(b log(c x ) + a) +--R + +--R 3 3 n 3 3 n - 1 n +--R (- 6b n x + 6b n x x )cos(b log(c x ) + a) +--R + +--R 3 3 n +--R (- 2b n - 2b n)x cos(b n log(x) + b log(c) + a) +--R * +--R 2 +--R sin(b n log(x) + b log(c) + a) +--R + +--R 4 4 2 2 n 2 +--R (- 9b n - 10b n - 1)x cos(b n log(x) + b log(c) + a) +--R + +--R 4 4 2 2 n +--R (9b n + 10b n + 1)x +--R * +--R sin(b n log(x) + b log(c) + a) +--R + +--R 3 3 n 3 +--R (- 2b n - 2b n)x cos(b n log(x) + b log(c) + a) +--R + +--R 3 3 n +--R (2b n + 2b n)x cos(b n log(x) + b log(c) + a) +--R / +--R 4 4 2 2 2 n +--R (9b n + 10b n + 1)x x +--R Type: Expression Integer +--R +--E 40 + +--S 41 of 504 +--Rt0108:= x^m*sin(a+b*log(c*x^n))^3 +--R +--R +--R m n 3 +--R (41) x sin(b log(c x ) + a) +--R Type: Expression Integer +--R +--E 41 + +--S 42 of 504 +--Rr0108:= -6*b^3*n^3*x^(1+m)*cos(a+b*log(c*x^n))/((1+m)^2+b^2*n^2)/((1+m)^2+9*b^2*n^2)+6*b^2*(1+m)*n^2*x^(1+m)*sin(a+b*log(c*x^n))/((1+m)^2+b^2*n^2)/((1+m)^2+9*b^2*n^2)-3*b*n*x^(1+m)*cos(a+b*log(c*x^n))*sin(a+b*log(c*x^n))^2/((1+m)^2+9*b^2*n^2)+(1+m)*x^(1+m)*sin(a+b*log(c*x^n))^3/((1+m)^2+9*b^2*n^2) +--R +--R +--R (42) +--R 2 2 2 3 2 m + 1 n 3 +--R ((b m + b )n + m + 3m + 3m + 1)x sin(b log(c x ) + a) +--R + +--R 3 3 2 m + 1 n +--R (- 3b n + (- 3b m - 6b m - 3b)n)x cos(b log(c x ) + a) +--R * +--R n 2 +--R sin(b log(c x ) + a) +--R + +--R 2 2 2 m + 1 n 3 3 m + 1 n +--R (6b m + 6b )n x sin(b log(c x ) + a) - 6b n x cos(b log(c x ) + a) +--R / +--R 4 4 2 2 2 2 2 4 3 2 +--R 9b n + (10b m + 20b m + 10b )n + m + 4m + 6m + 4m + 1 +--R Type: Expression Integer +--R +--E 42 + +--S 43 of 504 +--Ra0108:= integrate(t0108,x) +--R +--R +--R (43) +--R 2 2 2 3 2 2 +--R ((- b m - b )n - m - 3m - 3m - 1)x cos(b n log(x) + b log(c) + a) +--R + +--R 2 2 2 3 2 +--R ((7b m + 7b )n + m + 3m + 3m + 1)x +--R * +--R m log(x) +--R %e sin(b n log(x) + b log(c) + a) +--R + +--R 3 3 2 3 +--R (3b n + (3b m + 6b m + 3b)n)x cos(b n log(x) + b log(c) + a) +--R + +--R 3 3 2 +--R (- 9b n + (- 3b m - 6b m - 3b)n)x cos(b n log(x) + b log(c) + a) +--R * +--R m log(x) +--R %e +--R / +--R 4 4 2 2 2 2 2 4 3 2 +--R 9b n + (10b m + 20b m + 10b )n + m + 4m + 6m + 4m + 1 +--R Type: Union(Expression Integer,...) +--R +--E 43 + +--S 44 of 504 +--Rm0108:= a0108-r0108 +--R +--R +--R (44) +--R 2 2 2 3 2 m + 1 n 3 +--R ((- b m - b )n - m - 3m - 3m - 1)x sin(b log(c x ) + a) +--R + +--R 3 3 2 m + 1 n +--R (3b n + (3b m + 6b m + 3b)n)x cos(b log(c x ) + a) +--R * +--R n 2 +--R sin(b log(c x ) + a) +--R + +--R 2 2 2 m + 1 n +--R (- 6b m - 6b )n x sin(b log(c x ) + a) +--R + +--R 3 3 m + 1 n +--R 6b n x cos(b log(c x ) + a) +--R + +--R 2 2 2 3 2 2 +--R ((- b m - b )n - m - 3m - 3m - 1)x cos(b n log(x) + b log(c) + a) +--R + +--R 2 2 2 3 2 +--R ((7b m + 7b )n + m + 3m + 3m + 1)x +--R * +--R m log(x) +--R %e sin(b n log(x) + b log(c) + a) +--R + +--R 3 3 2 3 +--R (3b n + (3b m + 6b m + 3b)n)x cos(b n log(x) + b log(c) + a) +--R + +--R 3 3 2 +--R (- 9b n + (- 3b m - 6b m - 3b)n)x cos(b n log(x) + b log(c) + a) +--R * +--R m log(x) +--R %e +--R / +--R 4 4 2 2 2 2 2 4 3 2 +--R 9b n + (10b m + 20b m + 10b )n + m + 4m + 6m + 4m + 1 +--R Type: Expression Integer +--R +--E 44 + +--S 45 of 504 +--Rd0108:= D(m0108,x) +--R +--R +--R (45) +--R 2 2 2 2 2 4 3 2 m n +--R ((- b m - 2b m - b )n - m - 4m - 6m - 4m - 1)x x +--R + +--R 4 4 2 2 2 2 2 m + 1 n - 1 +--R (- 3b n + (- 3b m - 6b m - 3b )n )x x +--R * +--R n 3 +--R sin(b log(c x ) + a) +--R + +--R 3 3 3 3 2 m n +--R ((3b m + 3b )n + (3b m + 9b m + 9b m + 3b)n)x x +--R + +--R 3 3 3 3 2 m + 1 n - 1 +--R ((- 3b m - 3b )n + (- 3b m - 9b m - 9b m - 3b)n)x x +--R * +--R n n 2 +--R cos(b log(c x ) + a)sin(b log(c x ) + a) +--R + +--R 4 4 2 2 2 2 2 m + 1 n - 1 n 2 +--R (6b n + (6b m + 12b m + 6b )n )x x cos(b log(c x ) + a) +--R + +--R 2 2 2 2 2 m n 4 4 m + 1 n - 1 +--R (- 6b m - 12b m - 6b )n x x - 6b n x x +--R * +--R n +--R sin(b log(c x ) + a) +--R + +--R 3 3 3 m n 3 3 3 m + 1 n - 1 n +--R ((6b m + 6b )n x x + (- 6b m - 6b )n x x )cos(b log(c x ) + a) +--R + +--R 3 3 3 3 2 n +--R ((2b m + 2b )n + (2b m + 6b m + 6b m + 2b)n)x +--R * +--R m log(x) 2 +--R cos(b n log(x) + b log(c) + a)%e sin(b n log(x) + b log(c) + a) +--R + +--R 4 4 2 2 2 2 2 4 3 2 n +--R (- 9b n + (- 10b m - 20b m - 10b )n - m - 4m - 6m - 4m - 1)x +--R * +--R 2 +--R cos(b n log(x) + b log(c) + a) +--R + +--R 4 4 2 2 2 2 2 4 3 2 n +--R (9b n + (10b m + 20b m + 10b )n + m + 4m + 6m + 4m + 1)x +--R * +--R m log(x) +--R %e sin(b n log(x) + b log(c) + a) +--R + +--R 3 3 3 3 2 n +--R ((2b m + 2b )n + (2b m + 6b m + 6b m + 2b)n)x +--R * +--R 3 +--R cos(b n log(x) + b log(c) + a) +--R + +--R 3 3 3 3 2 n +--R ((- 2b m - 2b )n + (- 2b m - 6b m - 6b m - 2b)n)x +--R * +--R cos(b n log(x) + b log(c) + a) +--R * +--R m log(x) +--R %e +--R / +--R 4 4 2 2 2 2 2 4 3 2 n +--R (9b n + (10b m + 20b m + 10b )n + m + 4m + 6m + 4m + 1)x +--R Type: Expression Integer +--R +--E 45 + +--S 46 of 504 +--Rt0109:= sin(log(9+17*x)) +--R +--R +--R (46) sin(log(17x + 9)) +--R Type: Expression Integer +--R +--E 46 + +--S 47 of 504 +--Rr0109:= -1/34*(9+17*x)*(cos(log(9+17*x))-sin(log(9+17*x))) +--R +--R +--R (17x + 9)sin(log(17x + 9)) + (- 17x - 9)cos(log(17x + 9)) +--R (47) --------------------------------------------------------- +--R 34 +--R Type: Expression Integer +--R +--E 47 + +--S 48 of 504 +--Ra0109:= integrate(t0109,x) +--R +--R +--R (17x + 9)sin(log(17x + 9)) + (- 17x - 9)cos(log(17x + 9)) +--R (48) --------------------------------------------------------- +--R 34 +--R Type: Union(Expression Integer,...) +--R +--E 48 + +--S 49 of 504 +--Rm0109:= a0109-r0109 +--R +--R +--R (49) 0 +--R Type: Expression Integer +--R +--E 49 + +--S 50 of 504 +--Rd0109:= D(m0109,x) +--R +--R +--R (50) 0 +--R Type: Expression Integer +--R +--E 50 + +--S 51 of 504 +--Rt0110:= cos(a+b*x)^(1/2) +--R +--R +--R +------------+ +--R (51) \|cos(b x + a) +--R Type: Expression Integer +--R +--E 51 + +--S 52 of 504 +--Rr0110:= 2*EllipticE(1/2*a+1/2*b*x,2)/b +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Polynomial Fraction Integer +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--R +--E 52 + +--S 53 of 504 +--Ra0110:= integrate(t0110,x) +--R +--R +--R x +--R ++ +-------------+ +--R (52) | \|cos(%H b + a) d%H +--R ++ +--R Type: Union(Expression Integer,...) +--R +--E 53 + +--S 54 of 504 +--Rm0110:= a0110-r0110 +--R +--R +--R x +--R ++ +-------------+ +--R (53) | \|cos(%H b + a) d%H - r0110 +--R ++ +--R Type: Expression Integer +--R +--E 54 + +--S 55 of 504 +--Rd0110:= D(m0110,x) +--R +--R +--R +------------+ +--R (54) \|cos(b x + a) +--R Type: Expression Integer +--R +--E 55 + +--S 56 of 504 +--Rt0111:= cos(a+b*x)^(3/2) +--R +--R +--R +------------+ +--R (55) cos(b x + a)\|cos(b x + a) +--R Type: Expression Integer +--R +--E 56 + +--S 57 of 504 +--Rr0111:= 2/3*(EllipticF(1/2*a+1/2*b*x,2)+cos(a+b*x)^(1/2)*sin(a+b*x))/b +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Polynomial Fraction Integer +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--R +--E 57 + +--S 58 of 504 +--Ra0111:= integrate(t0111,x) +--R +--R +--R x +--R ++ +-------------+ +--R (56) | cos(%H b + a)\|cos(%H b + a) d%H +--R ++ +--R Type: Union(Expression Integer,...) +--R +--E 58 + +--S 59 of 504 +--Rm0111:= a0111-r0111 +--R +--R +--R x +--R ++ +-------------+ +--R (57) | cos(%H b + a)\|cos(%H b + a) d%H - r0111 +--R ++ +--R Type: Expression Integer +--R +--E 59 + +--S 60 of 504 +--Rd0111:= D(m0111,x) +--R +--R +--R +------------+ +--R (58) cos(b x + a)\|cos(b x + a) +--R Type: Expression Integer +--R +--E 60 + +--S 61 of 504 +--Rt0112:= cos(a+b*x)^(5/2) +--R +--R +--R 2 +------------+ +--R (59) cos(b x + a) \|cos(b x + a) +--R Type: Expression Integer +--R +--E 61 + +--S 62 of 504 +--Rr0112:= 2/5*(3*EllipticE(1/2*a+1/2*b*x,2)+cos(a+b*x)^(3/2)*sin(a+b*x))/b +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Polynomial Fraction Integer +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--R +--E 62 + +--S 63 of 504 +--Ra0112:= integrate(t0112,x) +--R +--R +--R x +--R ++ 2 +-------------+ +--R (60) | cos(%H b + a) \|cos(%H b + a) d%H +--R ++ +--R Type: Union(Expression Integer,...) +--R +--E 63 + +--S 64 of 504 +--Rm0112:= a0112-r0112 +--R +--R +--R x +--R ++ 2 +-------------+ +--R (61) | cos(%H b + a) \|cos(%H b + a) d%H - r0112 +--R ++ +--R Type: Expression Integer +--R +--E 64 + +--S 65 of 504 +--Rd0112:= D(m0112,x) +--R +--R +--R 2 +------------+ +--R (62) cos(b x + a) \|cos(b x + a) +--R Type: Expression Integer +--R +--E 65 + +--S 66 of 504 +--Rt0113:= 1/cos(a+b*x)^(1/2) +--R +--R +--R 1 +--R (63) --------------- +--R +------------+ +--R \|cos(b x + a) +--R Type: Expression Integer +--R +--E 66 + +--S 67 of 504 +--Rr0113:= 2*EllipticF(1/2*a+1/2*b*x,2)/b +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Polynomial Fraction Integer +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--R +--E 67 + +--S 68 of 504 +--Ra0113:= integrate(t0113,x) +--R +--R +--R x +--R ++ 1 +--R (64) | ---------------- d%H +--R ++ +-------------+ +--R \|cos(%H b + a) +--R Type: Union(Expression Integer,...) +--R +--E 68 + +--S 69 of 504 +--Rm0113:= a0113-r0113 +--R +--R +--R x +--R ++ 1 +--R (65) | ---------------- d%H - r0113 +--R ++ +-------------+ +--R \|cos(%H b + a) +--R Type: Expression Integer +--R +--E 69 + +--S 70 of 504 +--Rd0113:= D(m0113,x) +--R +--R +--R 1 +--R (66) --------------- +--R +------------+ +--R \|cos(b x + a) +--R Type: Expression Integer +--R +--E 70 + +--S 71 of 504 +--Rt0114:= 1/cos(a+b*x)^(3/2) +--R +--R +--R 1 +--R (67) --------------------------- +--R +------------+ +--R cos(b x + a)\|cos(b x + a) +--R Type: Expression Integer +--R +--E 71 + +--S 72 of 504 +--Rr0114:= -2*EllipticE(1/2*a+1/2*b*x,2)/b+2*sin(a+b*x)/b/cos(a+b*x)^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Polynomial Fraction Integer +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--R +--E 72 + +--S 73 of 504 +--Ra0114:= integrate(t0114,x) +--R +--R +--R x +--R ++ 1 +--R (68) | ----------------------------- d%H +--R ++ +-------------+ +--R cos(%H b + a)\|cos(%H b + a) +--R Type: Union(Expression Integer,...) +--R +--E 73 + +--S 74 of 504 +--Rm0114:= a0114-r0114 +--R +--R +--R x +--R ++ 1 +--R (69) | ----------------------------- d%H - r0114 +--R ++ +-------------+ +--R cos(%H b + a)\|cos(%H b + a) +--R Type: Expression Integer +--R +--E 74 + +--S 75 of 504 +--Rd0114:= D(m0114,x) +--R +--R +--R 1 +--R (70) --------------------------- +--R +------------+ +--R cos(b x + a)\|cos(b x + a) +--R Type: Expression Integer +--R +--E 75 + +--S 76 of 504 +--Rt0115:= 1/cos(a+b*x)^(5/2) +--R +--R +--R 1 +--R (71) ---------------------------- +--R 2 +------------+ +--R cos(b x + a) \|cos(b x + a) +--R Type: Expression Integer +--R +--E 76 + +--S 77 of 504 +--Rr0115:= 2/3*EllipticF(1/2*a+1/2*b*x,2)/b+2/3*sin(a+b*x)/b/cos(a+b*x)^(3/2) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Polynomial Fraction Integer +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--R +--E 77 + +--S 78 of 504 +--Ra0115:= integrate(t0115,x) +--R +--R +--R x +--R ++ 1 +--R (72) | ------------------------------ d%H +--R ++ 2 +-------------+ +--R cos(%H b + a) \|cos(%H b + a) +--R Type: Union(Expression Integer,...) +--R +--E 78 + +--S 79 of 504 +--Rm0115:= a0115-r0115 +--R +--R +--R x +--R ++ 1 +--R (73) | ------------------------------ d%H - r0115 +--R ++ 2 +-------------+ +--R cos(%H b + a) \|cos(%H b + a) +--R Type: Expression Integer +--R +--E 79 + +--S 80 of 504 +--Rd0115:= D(m0115,x) +--R +--R +--R 1 +--R (74) ---------------------------- +--R 2 +------------+ +--R cos(b x + a) \|cos(b x + a) +--R Type: Expression Integer +--R +--E 80 + +--S 81 of 504 +--Rt0116:= (a*cos(x))^(1/2) +--R +--R +--R +--------+ +--R (75) \|a cos(x) +--R Type: Expression Integer +--R +--E 81 + +--S 82 of 504 +--Rr0116:= 2*(a*cos(x))^(1/2)*EllipticE(1/2*x,2)/cos(x)^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Polynomial Fraction Integer +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--R +--E 82 + +--S 83 of 504 +--Ra0116:= integrate(t0116,x) +--R +--R +--R x +--R ++ +---------+ +--R (76) | \|a cos(%H) d%H +--R ++ +--R Type: Union(Expression Integer,...) +--R +--E 83 + +--S 84 of 504 +--Rm0116:= a0116-r0116 +--R +--R +--R x +--R ++ +---------+ +--R (77) | \|a cos(%H) d%H - r0116 +--R ++ +--R Type: Expression Integer +--R +--E 84 + +--S 85 of 504 +--Rd0116:= D(m0116,x) +--R +--R +--R +--------+ +--R (78) \|a cos(x) +--R Type: Expression Integer +--R +--E 85 + +--S 86 of 504 +--Rt0117:= (a*cos(x)^3)^(1/2) +--R +--R +--R +---------+ +--R | 3 +--R (79) \|a cos(x) +--R Type: Expression Integer +--R +--E 86 + +--S 87 of 504 +--Rr0117:= 2/3*(a*cos(x)^3)^(1/2)*(EllipticF(1/2*x,2)+cos(x)^(1/2)*sin(x))/cos(x)^(3/2) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Polynomial Fraction Integer +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--R +--E 87 + +--S 88 of 504 +--Ra0117:= integrate(t0117,x) +--R +--R +--R x +----------+ +--R ++ | 3 +--R (80) | \|a cos(%H) d%H +--R ++ +--R Type: Union(Expression Integer,...) +--R +--E 88 + +--S 89 of 504 +--Rm0117:= a0117-r0117 +--R +--R +--R x +----------+ +--R ++ | 3 +--R (81) | \|a cos(%H) d%H - r0117 +--R ++ +--R Type: Expression Integer +--R +--E 89 + +--S 90 of 504 +--Rd0117:= D(m0117,x) +--R +--R +--R +---------+ +--R | 3 +--R (82) \|a cos(x) +--R Type: Expression Integer +--R +--E 90 + +--S 91 of 504 +--Rt0118:= (a*cos(x))^(3/2) +--R +--R +--R +--------+ +--R (83) a cos(x)\|a cos(x) +--R Type: Expression Integer +--R +--E 91 + +--S 92 of 504 +--Rr0118:= 2/3*a^2*(cos(x)^(1/2)*EllipticF(1/2*x,2)+cos(x)*sin(x))/(a*cos(x))^(1/2) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Polynomial Fraction Integer +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--R +--E 92 + +--S 93 of 504 +--Ra0118:= integrate(t0118,x) +--R +--R +--R x +--R ++ +---------+ +--R (84) | a cos(%H)\|a cos(%H) d%H +--R ++ +--R Type: Union(Expression Integer,...) +--R +--E 93 + +--S 94 of 504 +--Rm0118:= a0118-r0118 +--R +--R +--R x +--R ++ +---------+ +--R (85) | a cos(%H)\|a cos(%H) d%H - r0118 +--R ++ +--R Type: Expression Integer +--R +--E 94 + +--S 95 of 504 +--Rd0118:= D(m0118,x) +--R +--R +--R +--------+ +--R (86) a cos(x)\|a cos(x) +--R Type: Expression Integer +--R +--E 95 + +--S 96 of 504 +--Rt0119:= (a*cos(x)^3)^(3/2) +--R +--R +--R +---------+ +--R 3 | 3 +--R (87) a cos(x) \|a cos(x) +--R Type: Expression Integer +--R +--E 96 + +--S 97 of 504 +--Rr0119:= 2/45*a*(a*cos(x)^3)^(1/2)*(21*EllipticE(1/2*x,2)+7*cos(x)^(3/2)*sin(x)+5*cos(x)^(7/2)*sin(x))/cos(x)^(3/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Polynomial Fraction Integer +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--R +--E 97 + +--S 98 of 504 +--Ra0119:= integrate(t0119,x) +--R +--R +--R x +----------+ +--R ++ 3 | 3 +--R (88) | a cos(%H) \|a cos(%H) d%H +--R ++ +--R Type: Union(Expression Integer,...) +--R +--E 98 + +--S 99 of 504 +--Rm0119:= a0119-r0119 +--R +--R +--R x +----------+ +--R ++ 3 | 3 +--R (89) | a cos(%H) \|a cos(%H) d%H - r0119 +--R ++ +--R Type: Expression Integer +--R +--E 99 + +--S 100 of 504 +--Rd0119:= D(m0119,x) +--R +--R +--R +---------+ +--R 3 | 3 +--R (90) a cos(x) \|a cos(x) +--R Type: Expression Integer +--R +--E 100 + +--S 101 of 504 +--Rt0120:= 1/(a*cos(x))^(1/2) +--R +--R +--R 1 +--R (91) ----------- +--R +--------+ +--R \|a cos(x) +--R Type: Expression Integer +--R +--E 101 + +--S 102 of 504 +--Rr0120:= 2*cos(x)^(1/2)*EllipticF(1/2*x,2)/(a*cos(x))^(1/2) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Polynomial Fraction Integer +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--R +--E 102 + +--S 103 of 504 +--Ra0120:= integrate(t0120,x) +--R +--R +--R x +--R ++ 1 +--R (92) | ------------ d%H +--R ++ +---------+ +--R \|a cos(%H) +--R Type: Union(Expression Integer,...) +--R +--E 103 + +--S 104 of 504 +--Rm0120:= a0120-r0120 +--R +--R +--R x +--R ++ 1 +--R (93) | ------------ d%H - r0120 +--R ++ +---------+ +--R \|a cos(%H) +--R Type: Expression Integer +--R +--E 104 + +--S 105 of 504 +--Rd0120:= D(m0120,x) +--R +--R +--R 1 +--R (94) ----------- +--R +--------+ +--R \|a cos(x) +--R Type: Expression Integer +--R +--E 105 + +--S 106 of 504 +--Rt0121:= 1/(a*cos(x)^2)^(1/2) +--R +--R +--R 1 +--R (95) ------------ +--R +---------+ +--R | 2 +--R \|a cos(x) +--R Type: Expression Integer +--R +--E 106 + +--S 107 of 504 +--Rr0121:= atanh(sin(x))*cos(x)/(a*cos(x)^2)^(1/2) +--R +--R +--R cos(x)atanh(sin(x)) +--R (96) ------------------- +--R +---------+ +--R | 2 +--R \|a cos(x) +--R Type: Expression Integer +--R +--E 107 + +--S 108 of 504 +--Ra0121:= integrate(t0121,x) +--R +--R +--R +---+ +-+ +--R sin(x) - cos(x) - 1 sin(x)\|- a \|a +--R log(-------------------) 2atan(----------------) +--R sin(x) + cos(x) + 1 a cos(x) + a +--R (97) [------------------------,- -----------------------] +--R +-+ +---+ +--R \|a \|- a +--R Type: Union(List Expression Integer,...) +--R +--E 108 + +--S 109 of 504 +--Rm0121a:= a0121.1-r0121 +--R +--R +--R +---------+ +--R sin(x) - cos(x) - 1 | 2 +-+ +--R log(-------------------)\|a cos(x) - cos(x)\|a atanh(sin(x)) +--R sin(x) + cos(x) + 1 +--R (98) -------------------------------------------------------------- +--R +---------+ +--R +-+ | 2 +--R \|a \|a cos(x) +--R Type: Expression Integer +--R +--E 109 + +--S 110 of 504 +--Rd0121a:= D(m0121a,x) +--R +--R +--R (99) +--R 4 2 2 2 +-+ +--R (2sin(x) + (2cos(x) + 2cos(x) - 2)sin(x) - 2cos(x) - 2cos(x))\|a +--R * +--R +---------+ +--R | 2 +--R \|a cos(x) +--R + +--R 2 2 4 3 2 +--R a cos(x) sin(x) - a cos(x) - 2a cos(x) - a cos(x) +--R / +--R 4 2 2 2 +--R a sin(x) + (- a cos(x) - 2a cos(x) - 2a)sin(x) + a cos(x) +--R + +--R 2a cos(x) + a +--R * +--R +---------+ +--R | 2 +--R \|a cos(x) +--R Type: Expression Integer +--R +--E 110 + +--S 111 of 504 +--Rm0121b:= a0121.2-r0121 +--R +--R +--R +---+ +-+ +---------+ +--R sin(x)\|- a \|a | 2 +---+ +--R - 2atan(----------------)\|a cos(x) - cos(x)\|- a atanh(sin(x)) +--R a cos(x) + a +--R (100) ----------------------------------------------------------------- +--R +---------+ +--R +---+ | 2 +--R \|- a \|a cos(x) +--R Type: Expression Integer +--R +--E 111 + +--S 112 of 504 +--Rd0121b:= D(m0121b,x) +--R +--R +--R (101) +--R 4 2 2 2 +-+ +--R (2sin(x) + (2cos(x) + 2cos(x) - 2)sin(x) - 2cos(x) - 2cos(x))\|a +--R * +--R +---------+ +--R | 2 +--R \|a cos(x) +--R + +--R 2 2 4 3 2 +--R a cos(x) sin(x) - a cos(x) - 2a cos(x) - a cos(x) +--R / +--R 4 2 2 2 +--R a sin(x) + (- a cos(x) - 2a cos(x) - 2a)sin(x) + a cos(x) +--R + +--R 2a cos(x) + a +--R * +--R +---------+ +--R | 2 +--R \|a cos(x) +--R Type: Expression Integer +--R +--E 112 + +--S 113 of 504 +--Rt0122:= 1/(a*cos(x)^3)^(1/2) +--R +--R +--R 1 +--R (102) ------------ +--R +---------+ +--R | 3 +--R \|a cos(x) +--R Type: Expression Integer +--R +--E 113 + +--S 114 of 504 +--Rr0122:= -2*cos(x)*(cos(x)^(1/2)*EllipticE(1/2*x,2)-sin(x))/(a*cos(x)^3)^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Polynomial Fraction Integer +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--R +--E 114 + +--S 115 of 504 +--Ra0122:= integrate(t0122,x) +--R +--R +--R x +--R ++ 1 +--R (103) | ------------- d%H +--R ++ +----------+ +--R | 3 +--R \|a cos(%H) +--R Type: Union(Expression Integer,...) +--R +--E 115 + +--S 116 of 504 +--Rm0122:= a0122-r0122 +--R +--R +--R x +--R ++ 1 +--R (104) | ------------- d%H - r0122 +--R ++ +----------+ +--R | 3 +--R \|a cos(%H) +--R Type: Expression Integer +--R +--E 116 + +--S 117 of 504 +--Rd0122:= D(m0122,x) +--R +--R +--R 1 +--R (105) ------------ +--R +---------+ +--R | 3 +--R \|a cos(x) +--R Type: Expression Integer +--R +--E 117 + +--S 118 of 504 +--Rt0123:= 1/(a+b*cos(c+d*x))^4 +--R +--R +--R (106) +--R 1 +--R / +--R 4 4 3 3 2 2 2 +--R b cos(d x + c) + 4a b cos(d x + c) + 6a b cos(d x + c) +--R + +--R 3 4 +--R 4a b cos(d x + c) + a +--R Type: Expression Integer +--R +--E 118 + +--S 119 of 504 +--Rr0123:= a*(2*a^2+3*b^2)*atan((a-b)*tan(1/2*c+1/2*d*x)/(a^2-b^2)^(1/2))/(a^2-b^2)^(7/2)/d-1/3*b*sin(c+d*x)/(a^2-b^2)/d/(a+b*cos(c+d*x))^3-5/6*a*b*sin(c+d*x)/(a^2-b^2)^2/d/(a+b*cos(c+d*x))^2-1/6*b*(11*a^2+4*b^2)*sin(c+d*x)/(a^2-b^2)^3/d/(a+b*cos(c+d*x)) +--R +--R +--R (107) +--R 5 3 3 3 2 4 4 2 2 +--R (18a b + 12a b )cos(d x + c) + (54a b + 36a b )cos(d x + c) +--R + +--R 3 3 5 4 2 6 +--R (54a b + 36a b)cos(d x + c) + 18a b + 12a +--R * +--R d x + c +--R (b - a)tan(-------) +--R 2 +--R atan(-------------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 5 2 3 2 4 3 2 5 +--R (4b + 11a b )cos(d x + c) + (3a b + 27a b )cos(d x + c) + 2b +--R + +--R 2 3 4 +--R - 5a b + 18a b +--R * +--R +---------+ +--R | 2 2 +--R sin(d x + c)\|- b + a +--R / +--R 9 2 7 4 5 6 3 3 +--R (6b - 18a b + 18a b - 6a b )d cos(d x + c) +--R + +--R 8 3 6 5 4 7 2 2 +--R (18a b - 54a b + 54a b - 18a b )d cos(d x + c) +--R + +--R 2 7 4 5 6 3 8 +--R (18a b - 54a b + 54a b - 18a b)d cos(d x + c) +--R + +--R 3 6 5 4 7 2 9 +--R (6a b - 18a b + 18a b - 6a )d +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R Type: Expression Integer +--R +--E 119 + +--S 120 of 504 +--Ra0123:= integrate(t0123,x) +--R +--R +--R (108) +--R [ +--R 5 3 3 3 2 4 4 2 2 +--R (9a b + 6a b )cos(d x + c) + (27a b + 18a b )cos(d x + c) +--R + +--R 3 3 5 4 2 6 +--R (27a b + 18a b)cos(d x + c) + 9a b + 6a +--R * +--R +-------+ +--R | 2 2 2 2 +--R (- a cos(d x + c) - b)\|b - a + (b - a )sin(d x + c) +--R log(--------------------------------------------------------) +--R b cos(d x + c) + a +--R + +--R 5 2 3 2 4 3 2 5 +--R (4b + 11a b )cos(d x + c) + (3a b + 27a b )cos(d x + c) + 2b +--R + +--R 2 3 4 +--R - 5a b + 18a b +--R * +--R +-------+ +--R | 2 2 +--R sin(d x + c)\|b - a +--R / +--R 9 2 7 4 5 6 3 3 +--R (6b - 18a b + 18a b - 6a b )d cos(d x + c) +--R + +--R 8 3 6 5 4 7 2 2 +--R (18a b - 54a b + 54a b - 18a b )d cos(d x + c) +--R + +--R 2 7 4 5 6 3 8 +--R (18a b - 54a b + 54a b - 18a b)d cos(d x + c) +--R + +--R 3 6 5 4 7 2 9 +--R (6a b - 18a b + 18a b - 6a )d +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R , +--R +--R 5 3 3 3 2 4 4 2 2 +--R (- 18a b - 12a b )cos(d x + c) + (- 54a b - 36a b )cos(d x + c) +--R + +--R 3 3 5 4 2 6 +--R (- 54a b - 36a b)cos(d x + c) - 18a b - 12a +--R * +--R +---------+ +--R | 2 2 +--R sin(d x + c)\|- b + a +--R atan(---------------------------) +--R (b + a)cos(d x + c) + b + a +--R + +--R 5 2 3 2 4 3 2 5 +--R (4b + 11a b )cos(d x + c) + (3a b + 27a b )cos(d x + c) + 2b +--R + +--R 2 3 4 +--R - 5a b + 18a b +--R * +--R +---------+ +--R | 2 2 +--R sin(d x + c)\|- b + a +--R / +--R 9 2 7 4 5 6 3 3 +--R (6b - 18a b + 18a b - 6a b )d cos(d x + c) +--R + +--R 8 3 6 5 4 7 2 2 +--R (18a b - 54a b + 54a b - 18a b )d cos(d x + c) +--R + +--R 2 7 4 5 6 3 8 +--R (18a b - 54a b + 54a b - 18a b)d cos(d x + c) +--R + +--R 3 6 5 4 7 2 9 +--R (6a b - 18a b + 18a b - 6a )d +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R ] +--R Type: Union(List Expression Integer,...) +--R +--E 120 + +--S 121 of 504 +--Rm0123a:= a0123.1-r0123 +--R +--R +--R (109) +--R +---------+ +--R 2 3 | 2 2 +--R (3a b + 2a )\|- b + a +--R * +--R +-------+ +--R | 2 2 2 2 +--R (- a cos(d x + c) - b)\|b - a + (b - a )sin(d x + c) +--R log(--------------------------------------------------------) +--R b cos(d x + c) + a +--R + +--R d x + c +--R +-------+ (b - a)tan(-------) +--R 2 3 | 2 2 2 +--R (- 6a b - 4a )\|b - a atan(-------------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +-------+ +--R 6 2 4 4 2 6 | 2 2 | 2 2 +--R (2b - 6a b + 6a b - 2a )d\|- b + a \|b - a +--R Type: Expression Integer +--R +--E 121 + +--S 122 of 504 +--Rd0123a:= D(m0123a,x) +--R +--R +--R (110) +--R 4 2 3 3 2 4 2 +--R (- 3a b + 3a b - 2a b + 2a b)sin(d x + c) +--R + +--R 4 3 2 2 +--R (- 3a b - 2a b )cos(d x + c) +--R + +--R 4 2 3 3 2 4 2 3 4 +--R (- 3a b - 3a b - 2a b - 2a b)cos(d x + c) - 3a b - 2a b +--R * +--R d x + c 2 +--R tan(-------) +--R 2 +--R + +--R 4 2 3 3 2 4 2 +--R (3a b + 3a b + 2a b + 2a b)sin(d x + c) +--R + +--R 4 3 2 2 +--R (3a b + 2a b )cos(d x + c) +--R + +--R 4 2 3 3 2 4 2 3 4 +--R (- 3a b + 3a b - 2a b + 2a b)cos(d x + c) - 3a b - 2a b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 5 3 3 5 5 3 3 5 +--R ((3a b - a b - 2a b)cos(d x + c) + 3a b - a b - 2a b)sin(d x + c) +--R * +--R d x + c 2 +--R tan(-------) +--R 2 +--R + +--R 5 3 3 5 5 3 3 5 +--R ((3a b - a b - 2a b)cos(d x + c) - 3a b + a b + 2a b)sin(d x + c) +--R / +--R 8 2 7 3 6 4 5 5 4 6 3 7 2 8 +--R (2a b - 2a b - 6a b + 6a b + 6a b - 6a b - 2a b + 2a b) +--R * +--R 2 +--R cos(d x + c) +--R + +--R 9 8 2 7 3 6 6 3 7 2 8 9 +--R (2b - 2a b - 4a b + 4a b + 4a b - 4a b - 2a b + 2a ) +--R * +--R cos(d x + c) +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 7 2 8 +--R 2a b - 2a b - 6a b + 6a b + 6a b - 6a b - 2a b + 2a b +--R * +--R d x + c 2 +--R tan(-------) +--R 2 +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 7 2 8 +--R (- 2a b - 2a b + 6a b + 6a b - 6a b - 6a b + 2a b + 2a b) +--R * +--R 2 +--R cos(d x + c) +--R + +--R 9 8 2 7 3 6 6 3 7 2 8 9 +--R (- 2b - 2a b + 4a b + 4a b - 4a b - 4a b + 2a b + 2a ) +--R * +--R cos(d x + c) +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 7 2 8 +--R - 2a b - 2a b + 6a b + 6a b - 6a b - 6a b + 2a b + 2a b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 10 9 2 8 3 7 4 6 5 5 6 4 7 3 +--R - 2b + 2a b + 8a b - 8a b - 12a b + 12a b + 8a b - 8a b +--R + +--R 8 2 9 +--R - 2a b + 2a b +--R * +--R cos(d x + c) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 7 3 8 2 +--R - 2a b + 2a b + 8a b - 8a b - 12a b + 12a b + 8a b - 8a b +--R + +--R 9 10 +--R - 2a b + 2a +--R * +--R d x + c 2 +--R sin(d x + c)tan(-------) +--R 2 +--R + +--R 10 9 2 8 3 7 4 6 5 5 6 4 7 3 +--R 2b + 2a b - 8a b - 8a b + 12a b + 12a b - 8a b - 8a b +--R + +--R 8 2 9 +--R 2a b + 2a b +--R * +--R cos(d x + c) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 7 3 8 2 +--R 2a b + 2a b - 8a b - 8a b + 12a b + 12a b - 8a b - 8a b +--R + +--R 9 10 +--R 2a b + 2a +--R * +--R sin(d x + c) +--R Type: Expression Integer +--R +--E 122 + +--S 123 of 504 +--Rm0123b:= a0123.2-r0123 +--R +--R +--R (111) +--R +---------+ +--R | 2 2 +--R 2 3 sin(d x + c)\|- b + a +--R (- 3a b - 2a )atan(---------------------------) +--R (b + a)cos(d x + c) + b + a +--R + +--R d x + c +--R (b - a)tan(-------) +--R 2 3 2 +--R (- 3a b - 2a )atan(-------------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 6 2 4 4 2 6 | 2 2 +--R (b - 3a b + 3a b - a )d\|- b + a +--R Type: Expression Integer +--R +--E 123 + +--S 124 of 504 +--Rd0123b:= D(m0123b,x) +--R +--R +--R (112) +--R 3 2 2 3 4 2 +--R (3a b - 3a b + 2a b - 2a )sin(d x + c) +--R + +--R 3 2 2 3 4 2 +--R (9a b - 3a b + 6a b - 2a )cos(d x + c) +--R + +--R 3 3 3 2 2 3 4 +--R (12a b + 8a b)cos(d x + c) + 3a b + 3a b + 2a b + 2a +--R * +--R d x + c 2 +--R tan(-------) +--R 2 +--R + +--R 3 2 2 3 4 2 +--R (- 9a b - 3a b - 6a b - 2a )sin(d x + c) +--R + +--R 3 2 2 3 4 2 3 2 2 3 4 +--R (- 3a b - 3a b - 2a b - 2a )cos(d x + c) + 3a b + 3a b + 2a b + 2a +--R / +--R 8 7 2 6 3 5 5 3 6 2 7 8 +--R (2b - 4a b - 4a b + 12a b - 12a b + 4a b + 4a b - 2a ) +--R * +--R 2 +--R sin(d x + c) +--R + +--R 8 2 6 4 4 6 2 8 2 +--R (- 2b + 8a b - 12a b + 8a b - 2a )cos(d x + c) +--R + +--R 8 2 6 4 4 6 2 8 8 2 6 +--R (- 4b + 16a b - 24a b + 16a b - 4a )cos(d x + c) - 2b + 8a b +--R + +--R 4 4 6 2 8 +--R - 12a b + 8a b - 2a +--R * +--R d x + c 2 +--R tan(-------) +--R 2 +--R + +--R 8 2 6 4 4 6 2 8 2 +--R (- 2b + 8a b - 12a b + 8a b - 2a )sin(d x + c) +--R + +--R 8 7 2 6 3 5 5 3 6 2 7 8 2 +--R (2b + 4a b - 4a b - 12a b + 12a b + 4a b - 4a b - 2a )cos(d x + c) +--R + +--R 8 7 2 6 3 5 5 3 6 2 7 8 +--R (4b + 8a b - 8a b - 24a b + 24a b + 8a b - 8a b - 4a )cos(d x + c) +--R + +--R 8 7 2 6 3 5 5 3 6 2 7 8 +--R 2b + 4a b - 4a b - 12a b + 12a b + 4a b - 4a b - 2a +--R Type: Expression Integer +--R +--E 124 + +--S 125 of 504 +--Rt0124:= (a+b*cos(c+d*x))^(1/2) +--R +--R +--R +------------------+ +--R (113) \|b cos(d x + c) + a +--R Type: Expression Integer +--R +--E 125 + +--S 126 of 504 +--Rr0124:= 2*(a+b*cos(c+d*x))^(1/2)*EllipticE(1/2*c+1/2*d*x,2*b/(a+b))/d/((a+b*cos(c+d*x))/(a+b))^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Polynomial Fraction Integer +--R Fraction Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--R +--E 126 + +--S 127 of 504 +--Ra0124:= integrate(t0124,x) +--R +--R +--R x +--R ++ +-------------------+ +--R (114) | \|b cos(%H d + c) + a d%H +--R ++ +--R Type: Union(Expression Integer,...) +--R +--E 127 + +--S 128 of 504 +--Rm0124:= a0124-r0124 +--R +--R +--R x +--R ++ +-------------------+ +--R (115) | \|b cos(%H d + c) + a d%H - r0124 +--R ++ +--R Type: Expression Integer +--R +--E 128 + +--S 129 of 504 +--Rd0124:= D(m0124,x) +--R +--R +--R +------------------+ +--R (116) \|b cos(d x + c) + a +--R Type: Expression Integer +--R +--E 129 + +--S 130 of 504 +--Rt0125:= 1/(a+b*cos(x))^(1/2) +--R +--R +--R 1 +--R (117) --------------- +--R +------------+ +--R \|b cos(x) + a +--R Type: Expression Integer +--R +--E 130 + +--S 131 of 504 +--Rr0125:= 2*((a+b*cos(x))/(a+b))^(1/2)*EllipticF(1/2*x,2*b/(a+b))/(a+b*cos(x))^(1/2) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Polynomial Fraction Integer +--R Fraction Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--R +--E 131 + +--S 132 of 504 +--Ra0125:= integrate(t0125,x) +--R +--R +--R x +--R ++ 1 +--R (118) | ---------------- d%H +--R ++ +-------------+ +--R \|b cos(%H) + a +--R Type: Union(Expression Integer,...) +--R +--E 132 + +--S 133 of 504 +--Rm0125:= a0125-r0125 +--R +--R +--R x +--R ++ 1 +--R (119) | ---------------- d%H - r0125 +--R ++ +-------------+ +--R \|b cos(%H) + a +--R Type: Expression Integer +--R +--E 133 + +--S 134 of 504 +--Rd0125:= D(m0125,x) +--R +--R +--R 1 +--R (120) --------------- +--R +------------+ +--R \|b cos(x) + a +--R Type: Expression Integer +--R +--E 134 + +--S 135 of 504 +--Rt0126:= 1/(a+b*cos(x))^(3/2) +--R +--R +--R 1 +--R (121) ----------------------------- +--R +------------+ +--R (b cos(x) + a)\|b cos(x) + a +--R Type: Expression Integer +--R +--E 135 + +--S 136 of 504 +--Rr0126:= 2*(a+b*cos(x))^(1/2)*EllipticE(1/2*x,2*b/(a+b))/(a^2-b^2)/((a+b*cos(x))/(a+b))^(1/2)-2*b*sin(x)/(a^2-b^2)/(a+b*cos(x))^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Polynomial Fraction Integer +--R Fraction Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--R +--E 136 + +--S 137 of 504 +--Ra0126:= integrate(t0126,x) +--R +--R +--R x +--R ++ 1 +--R (122) | ------------------------------- d%H +--R ++ +-------------+ +--R (b cos(%H) + a)\|b cos(%H) + a +--R Type: Union(Expression Integer,...) +--R +--E 137 + +--S 138 of 504 +--Rm0126:= a0126-r0126 +--R +--R +--R x +--R ++ 1 +--R (123) | ------------------------------- d%H - r0126 +--R ++ +-------------+ +--R (b cos(%H) + a)\|b cos(%H) + a +--R Type: Expression Integer +--R +--E 138 + +--S 139 of 504 +--Rd0126:= D(m0126,x) +--R +--R +--R 1 +--R (124) ----------------------------- +--R +------------+ +--R (b cos(x) + a)\|b cos(x) + a +--R Type: Expression Integer +--R +--E 139 + +--S 140 of 504 +--Rt0127:= 1/(a+b*cos(x))^(5/2) +--R +--R +--R 1 +--R (125) --------------------------------------------- +--R 2 2 2 +------------+ +--R (b cos(x) + 2a b cos(x) + a )\|b cos(x) + a +--R Type: Expression Integer +--R +--E 140 + +--S 141 of 504 +--Rr0127:= 8/3*a*(a+b*cos(x))^(1/2)*EllipticE(1/2*x,2*b/(a+b))/(a^2-b^2)^2/((a+b*cos(x))/(a+b))^(1/2)-2/3*((a+b*cos(x))/(a+b))^(1/2)*EllipticF(1/2*x,2*b/(a+b))/(a^2-b^2)/(a+b*cos(x))^(1/2)-2/3*b*sin(x)/(a^2-b^2)/(a+b*cos(x))^(3/2)-8/3*a*b*sin(x)/(a^2-b^2)^2/(a+b*cos(x))^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Polynomial Fraction Integer +--R Fraction Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--R +--E 141 + +--S 142 of 504 +--Ra0127:= integrate(t0127,x) +--R +--R +--R x +--R ++ 1 +--R (126) | ------------------------------------------------ d%H +--R ++ 2 2 2 +-------------+ +--R (b cos(%H) + 2a b cos(%H) + a )\|b cos(%H) + a +--R Type: Union(Expression Integer,...) +--R +--E 142 + +--S 143 of 504 +--Rm0127:= a0127-r0127 +--R +--R +--R x +--R ++ 1 +--R (127) | ------------------------------------------------ d%H - r0127 +--R ++ 2 2 2 +-------------+ +--R (b cos(%H) + 2a b cos(%H) + a )\|b cos(%H) + a +--R Type: Expression Integer +--R +--E 143 + +--S 144 of 504 +--Rd0127:= D(m0127,x) +--R +--R +--R 1 +--R (128) --------------------------------------------- +--R 2 2 2 +------------+ +--R (b cos(x) + 2a b cos(x) + a )\|b cos(x) + a +--R Type: Expression Integer +--R +--E 144 + +--S 145 of 504 +--Rt0128:= (a+a*cos(c+d*x))^(1/2) +--R +--R +--R +------------------+ +--R (129) \|a cos(d x + c) + a +--R Type: Expression Integer +--R +--E 145 + +--S 146 of 504 +--Rr0128:= 2*a*sin(c+d*x)/d/(a+a*cos(c+d*x))^(1/2) +--R +--R +--R 2a sin(d x + c) +--R (130) ---------------------- +--R +------------------+ +--R d\|a cos(d x + c) + a +--R Type: Expression Integer +--R +--E 146 + +--S 147 of 504 +--Ra0128:= integrate(t0128,x) +--R +--R +--R +------------------+ +--R 2sin(d x + c)\|a cos(d x + c) + a +--R (131) ---------------------------------- +--R d cos(d x + c) + d +--R Type: Union(Expression Integer,...) +--R +--E 147 + +--S 148 of 504 +--Rm0128:= a0128-r0128 +--R +--R +--R (132) 0 +--R Type: Expression Integer +--R +--E 148 + +--S 149 of 504 +--Rd0128:= D(m0128,x) +--R +--R +--R (133) 0 +--R Type: Expression Integer +--R +--E 149 + +--S 150 of 504 +--Rt0129:= (a+a*cos(c+d*x))^(3/2) +--R +--R +--R +------------------+ +--R (134) (a cos(d x + c) + a)\|a cos(d x + c) + a +--R Type: Expression Integer +--R +--E 150 + +--S 151 of 504 +--Rr0129:= 2/3*a^2*sin(c+d*x)*(5+cos(c+d*x))/(a*(1+cos(c+d*x)))^(1/2)/d +--R +--R +--R 2 2 +--R (2a cos(d x + c) + 10a )sin(d x + c) +--R (135) ------------------------------------ +--R +------------------+ +--R 3d\|a cos(d x + c) + a +--R Type: Expression Integer +--R +--E 151 + +--S 152 of 504 +--Ra0129:= integrate(t0129,x) +--R +--R +--R +------------------+ +--R (2a cos(d x + c) + 10a)sin(d x + c)\|a cos(d x + c) + a +--R (136) -------------------------------------------------------- +--R 3d cos(d x + c) + 3d +--R Type: Union(Expression Integer,...) +--R +--E 152 + +--S 153 of 504 +--Rm0129:= a0129-r0129 +--R +--R +--R (137) 0 +--R Type: Expression Integer +--R +--E 153 + +--S 154 of 504 +--Rd0129:= D(m0129,x) +--R +--R +--R (138) 0 +--R Type: Expression Integer +--R +--E 154 + +--S 155 of 504 +--Rt0130:= (a+a*cos(c+d*x))^(5/2) +--R +--R +--R 2 2 2 2 +------------------+ +--R (139) (a cos(d x + c) + 2a cos(d x + c) + a )\|a cos(d x + c) + a +--R Type: Expression Integer +--R +--E 155 + +--S 156 of 504 +--Rr0130:= 2/15*a^3*sin(c+d*x)*(43+14*cos(c+d*x)+3*cos(c+d*x)^2)/(a*(1+cos(c+d*x)))^(1/2)/d +--R +--R +--R 3 2 3 3 +--R (6a cos(d x + c) + 28a cos(d x + c) + 86a )sin(d x + c) +--R (140) -------------------------------------------------------- +--R +------------------+ +--R 15d\|a cos(d x + c) + a +--R Type: Expression Integer +--R +--E 156 + +--S 157 of 504 +--Ra0130:= integrate(t0130,x) +--R +--R +--R (141) +--R 2 2 2 2 +------------------+ +--R (6a cos(d x + c) + 28a cos(d x + c) + 86a )sin(d x + c)\|a cos(d x + c) + a +--R ----------------------------------------------------------------------------- +--R 15d cos(d x + c) + 15d +--R Type: Union(Expression Integer,...) +--R +--E 157 + +--S 158 of 504 +--Rm0130:= a0130-r0130 +--R +--R +--R (142) 0 +--R Type: Expression Integer +--R +--E 158 + +--S 159 of 504 +--Rd0130:= D(m0130,x) +--R +--R +--R (143) 0 +--R Type: Expression Integer +--R +--E 159 + +--S 160 of 504 +--Rt0131:= 1/(a+a*cos(c+d*x))^(1/2) +--R +--R +--R 1 +--R (144) --------------------- +--R +------------------+ +--R \|a cos(d x + c) + a +--R Type: Expression Integer +--R +--E 160 + +--S 161 of 504 +--Rr0131:= 2*atanh(sin(1/2*c+1/2*d*x))*cos(1/2*c+1/2*d*x)/d/(a+a*cos(c+d*x))^(1/2) +--R +--R +--R d x + c d x + c +--R 2cos(-------)atanh(sin(-------)) +--R 2 2 +--R (145) -------------------------------- +--R +------------------+ +--R d\|a cos(d x + c) + a +--R Type: Expression Integer +--R +--E 161 + +--S 162 of 504 +--Ra0131:= integrate(t0131,x) +--R +--R +--R (146) +--R [ +--R +-+ +--R |2 +--R |- +--R \|a +--R * +--R log +--R +-+ +--R |2 +------------------+ 2 +--R 2sin(d x + c) |- \|a cos(d x + c) + a - cos(d x + c) +--R \|a +--R + +--R 2cos(d x + c) + 3 +--R / +--R 2 +--R cos(d x + c) + 2cos(d x + c) + 1 +--R / +--R 2d +--R , +--R +--R +-+ +--R |2 +--R |- +--R \|a +--R * +--R log +--R 2 +--R cos(d x + c) + 2cos(d x + c) + 1 +--R / +--R +-+ +--R |2 +------------------+ 2 +--R 2sin(d x + c) |- \|a cos(d x + c) + a + cos(d x + c) +--R \|a +--R + +--R - 2cos(d x + c) - 3 +--R / +--R 2d +--R ] +--R Type: Union(List Expression Integer,...) +--R +--E 162 + +--S 163 of 504 +--Rm0131a:= a0131.1-r0131 +--R +--R +--R (147) +--R +-+ +--R |2 +------------------+ +--R |- \|a cos(d x + c) + a +--R \|a +--R * +--R log +--R +-+ +--R |2 +------------------+ 2 +--R 2sin(d x + c) |- \|a cos(d x + c) + a - cos(d x + c) +--R \|a +--R + +--R 2cos(d x + c) + 3 +--R / +--R 2 +--R cos(d x + c) + 2cos(d x + c) + 1 +--R + +--R d x + c d x + c +--R - 4cos(-------)atanh(sin(-------)) +--R 2 2 +--R / +--R +------------------+ +--R 2d\|a cos(d x + c) + a +--R Type: Expression Integer +--R +--E 163 + +--S 164 of 504 +--Rd0131a:= D(m0131a,x) +--R +--R +--R (148) +--R d x + c d x + c 2 d x + c 2 +--R (2cos(-------)sin(-------) - 2cos(-------))sin(d x + c) +--R 2 2 2 +--R + +--R d x + c 3 +--R (- 2cos(d x + c) - 2)sin(-------) +--R 2 +--R + +--R d x + c +--R (2cos(d x + c) + 2)sin(-------) +--R 2 +--R * +--R sin(d x + c) +--R * +--R +-+ +--R |2 d x + c +--R |- atanh(sin(-------)) +--R \|a 2 +--R + +--R d x + c 2 +--R (- 2cos(d x + c) - 2)sin(-------) +--R 2 +--R + +--R d x + c 2 d x + c 2 +--R (- 2cos(-------) + 2)cos(d x + c) - 2cos(-------) + 2 +--R 2 2 +--R * +--R +-+ +--R |2 +--R sin(d x + c) |- +--R \|a +--R * +--R +------------------+ +--R \|a cos(d x + c) + a +--R + +--R d x + c 2 d x + c +--R - cos(-------)cos(d x + c) + 2cos(-------)cos(d x + c) +--R 2 2 +--R + +--R d x + c +--R 3cos(-------) +--R 2 +--R * +--R d x + c 2 +--R sin(-------) +--R 2 +--R + +--R d x + c 2 d x + c +--R cos(-------)cos(d x + c) - 2cos(-------)cos(d x + c) +--R 2 2 +--R + +--R d x + c +--R - 3cos(-------) +--R 2 +--R * +--R sin(d x + c) +--R + +--R 3 2 d x + c 3 +--R (cos(d x + c) - cos(d x + c) - 5cos(d x + c) - 3)sin(-------) +--R 2 +--R + +--R 3 2 d x + c +--R (- cos(d x + c) + cos(d x + c) + 5cos(d x + c) + 3)sin(-------) +--R 2 +--R * +--R d x + c +--R atanh(sin(-------)) +--R 2 +--R + +--R d x + c 2 2 +--R ((- 3cos(d x + c) - 3)sin(-------) + 3cos(d x + c) + 3)sin(d x + c) +--R 2 +--R + +--R 3 2 d x + c 2 +--R (- 2cos(d x + c) - 4cos(d x + c) - 2cos(d x + c))sin(-------) +--R 2 +--R + +--R d x + c 2 3 d x + c 2 2 +--R (cos(-------) + 2)cos(d x + c) + (- cos(-------) + 4)cos(d x + c) +--R 2 2 +--R + +--R d x + c 2 d x + c 2 +--R (- 5cos(-------) + 2)cos(d x + c) - 3cos(-------) +--R 2 2 +--R / +--R 3 2 d x + c 2 +--R (cos(d x + c) - cos(d x + c) - 5cos(d x + c) - 3)sin(-------) +--R 2 +--R + +--R 3 2 +--R - cos(d x + c) + cos(d x + c) + 5cos(d x + c) + 3 +--R * +--R +------------------+ +--R \|a cos(d x + c) + a +--R + +--R 2 d x + c 2 +--R (- 2a cos(d x + c) - 4a cos(d x + c) - 2a)sin(-------) +--R 2 +--R + +--R 2 +--R 2a cos(d x + c) + 4a cos(d x + c) + 2a +--R * +--R +-+ +--R |2 +--R sin(d x + c) |- +--R \|a +--R Type: Expression Integer +--R +--E 164 + +--S 165 of 504 +--Rm0131b:= a0131.2-r0131 +--R +--R +--R (149) +--R +-+ +--R |2 +------------------+ +--R |- \|a cos(d x + c) + a +--R \|a +--R * +--R log +--R 2 +--R cos(d x + c) + 2cos(d x + c) + 1 +--R / +--R +-+ +--R |2 +------------------+ 2 +--R 2sin(d x + c) |- \|a cos(d x + c) + a + cos(d x + c) +--R \|a +--R + +--R - 2cos(d x + c) - 3 +--R + +--R d x + c d x + c +--R - 4cos(-------)atanh(sin(-------)) +--R 2 2 +--R / +--R +------------------+ +--R 2d\|a cos(d x + c) + a +--R Type: Expression Integer +--R +--E 165 + +--S 166 of 504 +--Rd0131b:= D(m0131b,x) +--R +--R +--R (150) +--R d x + c d x + c d x + c 2 +--R (- 4cos(-------)cos(d x + c) + 12cos(-------))sin(-------) +--R 2 2 2 +--R + +--R d x + c d x + c +--R 4cos(-------)cos(d x + c) - 12cos(-------) +--R 2 2 +--R * +--R 2 +--R sin(d x + c) +--R + +--R 2 d x + c 3 +--R (4cos(d x + c) - 8cos(d x + c) - 12)sin(-------) +--R 2 +--R + +--R 2 d x + c +--R (- 4cos(d x + c) + 8cos(d x + c) + 12)sin(-------) +--R 2 +--R * +--R sin(d x + c) +--R * +--R +-+ +--R |2 d x + c +--R |- atanh(sin(-------)) +--R \|a 2 +--R + +--R d x + c 2 3 +--R (- 6sin(-------) + 6)sin(d x + c) +--R 2 +--R + +--R 2 d x + c 2 +--R (- 2cos(d x + c) - 8cos(d x + c) - 6)sin(-------) +--R 2 +--R + +--R d x + c 2 2 +--R (4cos(-------) + 2)cos(d x + c) +--R 2 +--R + +--R d x + c 2 d x + c 2 +--R (- 8cos(-------) + 8)cos(d x + c) - 12cos(-------) + 6 +--R 2 2 +--R * +--R sin(d x + c) +--R * +--R +-+ +--R |2 +--R |- +--R \|a +--R * +--R +------------------+ +--R \|a cos(d x + c) + a +--R + +--R d x + c d x + c 2 d x + c 3 +--R (- 8cos(-------)sin(-------) + 8cos(-------))sin(d x + c) +--R 2 2 2 +--R + +--R d x + c 3 +--R (8cos(d x + c) + 8)sin(-------) +--R 2 +--R + +--R d x + c +--R (- 8cos(d x + c) - 8)sin(-------) +--R 2 +--R * +--R 2 +--R sin(d x + c) +--R + +--R d x + c 3 d x + c 2 +--R - cos(-------)cos(d x + c) + 5cos(-------)cos(d x + c) +--R 2 2 +--R + +--R d x + c d x + c +--R - 3cos(-------)cos(d x + c) - 9cos(-------) +--R 2 2 +--R * +--R d x + c 2 +--R sin(-------) +--R 2 +--R + +--R d x + c 3 d x + c 2 +--R cos(-------)cos(d x + c) - 5cos(-------)cos(d x + c) +--R 2 2 +--R + +--R d x + c d x + c +--R 3cos(-------)cos(d x + c) + 9cos(-------) +--R 2 2 +--R * +--R sin(d x + c) +--R + +--R 4 3 2 +--R cos(d x + c) - 4cos(d x + c) - 2cos(d x + c) + 12cos(d x + c) +--R + +--R 9 +--R * +--R d x + c 3 +--R sin(-------) +--R 2 +--R + +--R 4 3 2 +--R - cos(d x + c) + 4cos(d x + c) + 2cos(d x + c) +--R + +--R - 12cos(d x + c) - 9 +--R * +--R d x + c +--R sin(-------) +--R 2 +--R * +--R d x + c +--R atanh(sin(-------)) +--R 2 +--R + +--R 2 d x + c 2 +--R (- 3cos(d x + c) + 14cos(d x + c) + 17)sin(-------) +--R 2 +--R + +--R 2 d x + c 2 d x + c 2 +--R 3cos(d x + c) + (8cos(-------) - 14)cos(d x + c) + 8cos(-------) +--R 2 2 +--R + +--R - 17 +--R * +--R 2 +--R sin(d x + c) +--R + +--R 4 3 2 +--R (- 2cos(d x + c) + 2cos(d x + c) + 10cos(d x + c) + 6cos(d x + c)) +--R * +--R d x + c 2 +--R sin(-------) +--R 2 +--R + +--R d x + c 2 4 d x + c 2 3 +--R (cos(-------) + 2)cos(d x + c) + (- 4cos(-------) - 2)cos(d x + c) +--R 2 2 +--R + +--R d x + c 2 2 d x + c 2 +--R (- 2cos(-------) - 10)cos(d x + c) + (12cos(-------) - 6)cos(d x + c) +--R 2 2 +--R + +--R d x + c 2 +--R 9cos(-------) +--R 2 +--R / +--R d x + c 2 2 +--R ((8cos(d x + c) + 8)sin(-------) - 8cos(d x + c) - 8)sin(d x + c) +--R 2 +--R + +--R 4 3 2 +--R cos(d x + c) - 4cos(d x + c) - 2cos(d x + c) + 12cos(d x + c) +--R + +--R 9 +--R * +--R d x + c 2 +--R sin(-------) +--R 2 +--R + +--R 4 3 2 +--R - cos(d x + c) + 4cos(d x + c) + 2cos(d x + c) - 12cos(d x + c) - 9 +--R * +--R +------------------+ +--R \|a cos(d x + c) + a +--R + +--R 3 2 +--R (4a cos(d x + c) - 4a cos(d x + c) - 20a cos(d x + c) - 12a) +--R * +--R d x + c 2 +--R sin(-------) +--R 2 +--R + +--R 3 2 +--R - 4a cos(d x + c) + 4a cos(d x + c) + 20a cos(d x + c) + 12a +--R * +--R +-+ +--R |2 +--R sin(d x + c) |- +--R \|a +--R Type: Expression Integer +--R +--E 166 + +--S 167 of 504 +--Rt0132:= 1/(a+a*cos(c+d*x))^(3/2) +--R +--R +--R 1 +--R (151) ----------------------------------------- +--R +------------------+ +--R (a cos(d x + c) + a)\|a cos(d x + c) + a +--R Type: Expression Integer +--R +--E 167 + +--S 168 of 504 +--Rr0132:= 1/2*atanh(sin(1/2*c+1/2*d*x))*cos(1/2*c+1/2*d*x)/a/d/(a+a*cos(c+d*x))^(1/2)+1/2*sin(c+d*x)/d/(a+a*cos(c+d*x))^(3/2) +--R +--R +--R (152) +--R d x + c d x + c d x + c +--R (cos(-------)cos(d x + c) + cos(-------))atanh(sin(-------)) + sin(d x + c) +--R 2 2 2 +--R --------------------------------------------------------------------------- +--R +------------------+ +--R (2a d cos(d x + c) + 2a d)\|a cos(d x + c) + a +--R Type: Expression Integer +--R +--E 168 + +--S 169 of 504 +--Ra0132:= integrate(t0132,x) +--R +--R +--R (153) +--R [ +--R 2 +--+ +--R (cos(d x + c) + 2cos(d x + c) + 1)\|2a +--R * +--R log +--R +--+ +------------------+ 2 +--R 2sin(d x + c)\|2a \|a cos(d x + c) + a - a cos(d x + c) +--R + +--R 2a cos(d x + c) + 3a +--R / +--R 2 +--R cos(d x + c) + 2cos(d x + c) + 1 +--R + +--R +------------------+ +--R 4sin(d x + c)\|a cos(d x + c) + a +--R / +--R 2 2 2 2 +--R 8a d cos(d x + c) + 16a d cos(d x + c) + 8a d +--R , +--R +--R 2 +----+ +--R (- cos(d x + c) - 2cos(d x + c) - 1)\|- 2a +--R * +--R +----+ +------------------+ +--R sin(d x + c)\|- 2a \|a cos(d x + c) + a +--R atan(----------------------------------------) +--R 2a cos(d x + c) + 2a +--R + +--R +------------------+ +--R 2sin(d x + c)\|a cos(d x + c) + a +--R / +--R 2 2 2 2 +--R 4a d cos(d x + c) + 8a d cos(d x + c) + 4a d +--R ] +--R Type: Union(List Expression Integer,...) +--R +--E 169 + +--S 170 of 504 +--Rm0132a:= a0132.1-r0132 +--R +--R +--R (154) +--R +--+ +------------------+ +--R \|2a \|a cos(d x + c) + a +--R * +--R log +--R +--+ +------------------+ 2 +--R 2sin(d x + c)\|2a \|a cos(d x + c) + a - a cos(d x + c) +--R + +--R 2a cos(d x + c) + 3a +--R / +--R 2 +--R cos(d x + c) + 2cos(d x + c) + 1 +--R + +--R d x + c d x + c +--R - 4a cos(-------)atanh(sin(-------)) +--R 2 2 +--R / +--R 2 +------------------+ +--R 8a d\|a cos(d x + c) + a +--R Type: Expression Integer +--R +--E 170 + +--S 171 of 504 +--Rd0132a:= D(m0132a,x) +--R +--R +--R (155) +--R d x + c d x + c 2 d x + c 2 +--R (2cos(-------)sin(-------) - 2cos(-------))sin(d x + c) +--R 2 2 2 +--R + +--R d x + c 3 +--R (- 2cos(d x + c) - 2)sin(-------) +--R 2 +--R + +--R d x + c +--R (2cos(d x + c) + 2)sin(-------) +--R 2 +--R * +--R sin(d x + c) +--R * +--R +--+ d x + c +--R \|2a atanh(sin(-------)) +--R 2 +--R + +--R d x + c 2 +--R (- 2cos(d x + c) - 2)sin(-------) +--R 2 +--R + +--R d x + c 2 d x + c 2 +--R (- 2cos(-------) + 2)cos(d x + c) - 2cos(-------) + 2 +--R 2 2 +--R * +--R +--+ +--R sin(d x + c)\|2a +--R * +--R +------------------+ +--R \|a cos(d x + c) + a +--R + +--R d x + c 2 d x + c +--R - a cos(-------)cos(d x + c) + 2a cos(-------)cos(d x + c) +--R 2 2 +--R + +--R d x + c +--R 3a cos(-------) +--R 2 +--R * +--R d x + c 2 +--R sin(-------) +--R 2 +--R + +--R d x + c 2 d x + c +--R a cos(-------)cos(d x + c) - 2a cos(-------)cos(d x + c) +--R 2 2 +--R + +--R d x + c +--R - 3a cos(-------) +--R 2 +--R * +--R sin(d x + c) +--R + +--R 3 2 +--R (a cos(d x + c) - a cos(d x + c) - 5a cos(d x + c) - 3a) +--R * +--R d x + c 3 +--R sin(-------) +--R 2 +--R + +--R 3 2 +--R (- a cos(d x + c) + a cos(d x + c) + 5a cos(d x + c) + 3a) +--R * +--R d x + c +--R sin(-------) +--R 2 +--R * +--R d x + c +--R atanh(sin(-------)) +--R 2 +--R + +--R d x + c 2 +--R ((- 3a cos(d x + c) - 3a)sin(-------) + 3a cos(d x + c) + 3a) +--R 2 +--R * +--R 2 +--R sin(d x + c) +--R + +--R 3 2 d x + c 2 +--R (- 2a cos(d x + c) - 4a cos(d x + c) - 2a cos(d x + c))sin(-------) +--R 2 +--R + +--R d x + c 2 3 +--R (a cos(-------) + 2a)cos(d x + c) +--R 2 +--R + +--R d x + c 2 2 +--R (- a cos(-------) + 4a)cos(d x + c) +--R 2 +--R + +--R d x + c 2 d x + c 2 +--R (- 5a cos(-------) + 2a)cos(d x + c) - 3a cos(-------) +--R 2 2 +--R / +--R 2 3 2 2 2 2 +--R (4a cos(d x + c) - 4a cos(d x + c) - 20a cos(d x + c) - 12a ) +--R * +--R d x + c 2 +--R sin(-------) +--R 2 +--R + +--R 2 3 2 2 2 2 +--R - 4a cos(d x + c) + 4a cos(d x + c) + 20a cos(d x + c) + 12a +--R * +--R +------------------+ +--R \|a cos(d x + c) + a +--R + +--R 2 2 2 2 d x + c 2 +--R (- 8a cos(d x + c) - 16a cos(d x + c) - 8a )sin(-------) +--R 2 +--R + +--R 2 2 2 2 +--R 8a cos(d x + c) + 16a cos(d x + c) + 8a +--R * +--R +--+ +--R sin(d x + c)\|2a +--R Type: Expression Integer +--R +--E 171 + +--S 172 of 504 +--Rm0132b:= a0132.2-r0132 +--R +--R +--R (156) +--R - +--R +----+ +------------------+ +--R \|- 2a \|a cos(d x + c) + a +--R * +--R +----+ +------------------+ +--R sin(d x + c)\|- 2a \|a cos(d x + c) + a +--R atan(----------------------------------------) +--R 2a cos(d x + c) + 2a +--R + +--R d x + c d x + c +--R - 2a cos(-------)atanh(sin(-------)) +--R 2 2 +--R / +--R 2 +------------------+ +--R 4a d\|a cos(d x + c) + a +--R Type: Expression Integer +--R +--E 172 + +--S 173 of 504 +--Rd0132b:= D(m0132b,x) +--R +--R +--R (157) +--R d x + c d x + c 2 d x + c 3 +--R (- cos(-------)sin(-------) + cos(-------))sin(d x + c) +--R 2 2 2 +--R + +--R d x + c 3 +--R (cos(d x + c) + 1)sin(-------) +--R 2 +--R + +--R d x + c +--R (- cos(d x + c) - 1)sin(-------) +--R 2 +--R * +--R 2 +--R sin(d x + c) +--R + +--R d x + c d x + c d x + c 2 +--R (2cos(-------)cos(d x + c) + 2cos(-------))sin(-------) +--R 2 2 2 +--R + +--R d x + c d x + c +--R - 2cos(-------)cos(d x + c) - 2cos(-------) +--R 2 2 +--R * +--R sin(d x + c) +--R + +--R 2 d x + c 3 +--R (- 2cos(d x + c) - 4cos(d x + c) - 2)sin(-------) +--R 2 +--R + +--R 2 d x + c +--R (2cos(d x + c) + 4cos(d x + c) + 2)sin(-------) +--R 2 +--R * +--R d x + c +--R atanh(sin(-------)) +--R 2 +--R + +--R d x + c 2 d x + c 2 +--R (- cos(d x + c) - 1)sin(-------) + (cos(-------) + 1)cos(d x + c) +--R 2 2 +--R + +--R d x + c 2 +--R cos(-------) + 1 +--R 2 +--R * +--R 2 +--R sin(d x + c) +--R + +--R 3 2 d x + c 2 +--R (- 2cos(d x + c) - 4cos(d x + c) - 2cos(d x + c))sin(-------) +--R 2 +--R + +--R 3 d x + c 2 2 +--R 2cos(d x + c) + (- 2cos(-------) + 4)cos(d x + c) +--R 2 +--R + +--R d x + c 2 d x + c 2 +--R (- 4cos(-------) + 2)cos(d x + c) - 2cos(-------) +--R 2 2 +--R / +--R d x + c 2 +--R ((4a cos(d x + c) + 4a)sin(-------) - 4a cos(d x + c) - 4a) +--R 2 +--R * +--R 2 +--R sin(d x + c) +--R + +--R 2 d x + c 2 +--R (- 8a cos(d x + c) - 16a cos(d x + c) - 8a)sin(-------) +--R 2 +--R + +--R 2 +--R 8a cos(d x + c) + 16a cos(d x + c) + 8a +--R * +--R +------------------+ +--R \|a cos(d x + c) + a +--R Type: Expression Integer +--R +--E 173 + +--S 174 of 504 +--Rt0133:= 1/(a+a*cos(c+d*x))^(5/2) +--R +--R +--R 1 +--R (158) ------------------------------------------------------------- +--R 2 2 2 2 +------------------+ +--R (a cos(d x + c) + 2a cos(d x + c) + a )\|a cos(d x + c) + a +--R Type: Expression Integer +--R +--E 174 + +--S 175 of 504 +--Rr0133:= 3/16*atanh(sin(1/2*c+1/2*d*x))*cos(1/2*c+1/2*d*x)/a^2/d/(a+a*cos(c+d*x))^(1/2)+1/4*sin(c+d*x)/d/(a+a*cos(c+d*x))^(5/2)+3/16*sin(c+d*x)/a/d/(a+a*cos(c+d*x))^(3/2) +--R +--R +--R (159) +--R d x + c 2 d x + c +--R 3cos(-------)cos(d x + c) + 6cos(-------)cos(d x + c) +--R 2 2 +--R + +--R d x + c +--R 3cos(-------) +--R 2 +--R * +--R d x + c +--R atanh(sin(-------)) +--R 2 +--R + +--R (3cos(d x + c) + 7)sin(d x + c) +--R / +--R 2 2 2 2 +------------------+ +--R (16a d cos(d x + c) + 32a d cos(d x + c) + 16a d)\|a cos(d x + c) + a +--R Type: Expression Integer +--R +--E 175 + +--S 176 of 504 +--Ra0133:= integrate(t0133,x) +--R +--R +--R (160) +--R [ +--R 3 2 +--+ +--R (3cos(d x + c) + 9cos(d x + c) + 9cos(d x + c) + 3)\|2a +--R * +--R log +--R +--+ +------------------+ 2 +--R 2sin(d x + c)\|2a \|a cos(d x + c) + a - a cos(d x + c) +--R + +--R 2a cos(d x + c) + 3a +--R / +--R 2 +--R cos(d x + c) + 2cos(d x + c) + 1 +--R + +--R +------------------+ +--R (12cos(d x + c) + 28)sin(d x + c)\|a cos(d x + c) + a +--R / +--R 3 3 3 2 3 3 +--R 64a d cos(d x + c) + 192a d cos(d x + c) + 192a d cos(d x + c) + 64a d +--R , +--R +--R 3 2 +----+ +--R (- 3cos(d x + c) - 9cos(d x + c) - 9cos(d x + c) - 3)\|- 2a +--R * +--R +----+ +------------------+ +--R sin(d x + c)\|- 2a \|a cos(d x + c) + a +--R atan(----------------------------------------) +--R 2a cos(d x + c) + 2a +--R + +--R +------------------+ +--R (6cos(d x + c) + 14)sin(d x + c)\|a cos(d x + c) + a +--R / +--R 3 3 3 2 3 3 +--R 32a d cos(d x + c) + 96a d cos(d x + c) + 96a d cos(d x + c) + 32a d +--R ] +--R Type: Union(List Expression Integer,...) +--R +--E 176 + +--S 177 of 504 +--Rm0133a:= a0133.1-r0133 +--R +--R +--R (161) +--R +--+ +------------------+ +--R 3\|2a \|a cos(d x + c) + a +--R * +--R log +--R +--+ +------------------+ 2 +--R 2sin(d x + c)\|2a \|a cos(d x + c) + a - a cos(d x + c) +--R + +--R 2a cos(d x + c) + 3a +--R / +--R 2 +--R cos(d x + c) + 2cos(d x + c) + 1 +--R + +--R d x + c d x + c +--R - 12a cos(-------)atanh(sin(-------)) +--R 2 2 +--R / +--R 3 +------------------+ +--R 64a d\|a cos(d x + c) + a +--R Type: Expression Integer +--R +--E 177 + +--S 178 of 504 +--Rd0133a:= D(m0133a,x) +--R +--R +--R (162) +--R d x + c d x + c 2 d x + c 2 +--R (6cos(-------)sin(-------) - 6cos(-------))sin(d x + c) +--R 2 2 2 +--R + +--R d x + c 3 +--R (- 6cos(d x + c) - 6)sin(-------) +--R 2 +--R + +--R d x + c +--R (6cos(d x + c) + 6)sin(-------) +--R 2 +--R * +--R sin(d x + c) +--R * +--R +--+ d x + c +--R \|2a atanh(sin(-------)) +--R 2 +--R + +--R d x + c 2 +--R (- 6cos(d x + c) - 6)sin(-------) +--R 2 +--R + +--R d x + c 2 d x + c 2 +--R (- 6cos(-------) + 6)cos(d x + c) - 6cos(-------) + 6 +--R 2 2 +--R * +--R +--+ +--R sin(d x + c)\|2a +--R * +--R +------------------+ +--R \|a cos(d x + c) + a +--R + +--R d x + c 2 d x + c +--R - 3a cos(-------)cos(d x + c) + 6a cos(-------)cos(d x + c) +--R 2 2 +--R + +--R d x + c +--R 9a cos(-------) +--R 2 +--R * +--R d x + c 2 +--R sin(-------) +--R 2 +--R + +--R d x + c 2 d x + c +--R 3a cos(-------)cos(d x + c) - 6a cos(-------)cos(d x + c) +--R 2 2 +--R + +--R d x + c +--R - 9a cos(-------) +--R 2 +--R * +--R sin(d x + c) +--R + +--R 3 2 +--R (3a cos(d x + c) - 3a cos(d x + c) - 15a cos(d x + c) - 9a) +--R * +--R d x + c 3 +--R sin(-------) +--R 2 +--R + +--R 3 2 +--R (- 3a cos(d x + c) + 3a cos(d x + c) + 15a cos(d x + c) + 9a) +--R * +--R d x + c +--R sin(-------) +--R 2 +--R * +--R d x + c +--R atanh(sin(-------)) +--R 2 +--R + +--R d x + c 2 +--R ((- 9a cos(d x + c) - 9a)sin(-------) + 9a cos(d x + c) + 9a) +--R 2 +--R * +--R 2 +--R sin(d x + c) +--R + +--R 3 2 d x + c 2 +--R (- 6a cos(d x + c) - 12a cos(d x + c) - 6a cos(d x + c))sin(-------) +--R 2 +--R + +--R d x + c 2 3 +--R (3a cos(-------) + 6a)cos(d x + c) +--R 2 +--R + +--R d x + c 2 2 +--R (- 3a cos(-------) + 12a)cos(d x + c) +--R 2 +--R + +--R d x + c 2 d x + c 2 +--R (- 15a cos(-------) + 6a)cos(d x + c) - 9a cos(-------) +--R 2 2 +--R / +--R 3 3 3 2 3 3 +--R (32a cos(d x + c) - 32a cos(d x + c) - 160a cos(d x + c) - 96a ) +--R * +--R d x + c 2 +--R sin(-------) +--R 2 +--R + +--R 3 3 3 2 3 3 +--R - 32a cos(d x + c) + 32a cos(d x + c) + 160a cos(d x + c) + 96a +--R * +--R +------------------+ +--R \|a cos(d x + c) + a +--R + +--R 3 2 3 3 d x + c 2 +--R (- 64a cos(d x + c) - 128a cos(d x + c) - 64a )sin(-------) +--R 2 +--R + +--R 3 2 3 3 +--R 64a cos(d x + c) + 128a cos(d x + c) + 64a +--R * +--R +--+ +--R sin(d x + c)\|2a +--R Type: Expression Integer +--R +--E 178 + +--S 179 of 504 +--Rm0133b:= a0133.2-r0133 +--R +--R +--R (163) +--R - +--R +----+ +------------------+ +--R 3\|- 2a \|a cos(d x + c) + a +--R * +--R +----+ +------------------+ +--R sin(d x + c)\|- 2a \|a cos(d x + c) + a +--R atan(----------------------------------------) +--R 2a cos(d x + c) + 2a +--R + +--R d x + c d x + c +--R - 6a cos(-------)atanh(sin(-------)) +--R 2 2 +--R / +--R 3 +------------------+ +--R 32a d\|a cos(d x + c) + a +--R Type: Expression Integer +--R +--E 179 + +--S 180 of 504 +--Rd0133b:= D(m0133b,x) +--R +--R +--R (164) +--R d x + c d x + c 2 d x + c 3 +--R (- 3cos(-------)sin(-------) + 3cos(-------))sin(d x + c) +--R 2 2 2 +--R + +--R d x + c 3 +--R (3cos(d x + c) + 3)sin(-------) +--R 2 +--R + +--R d x + c +--R (- 3cos(d x + c) - 3)sin(-------) +--R 2 +--R * +--R 2 +--R sin(d x + c) +--R + +--R d x + c d x + c d x + c 2 +--R (6cos(-------)cos(d x + c) + 6cos(-------))sin(-------) +--R 2 2 2 +--R + +--R d x + c d x + c +--R - 6cos(-------)cos(d x + c) - 6cos(-------) +--R 2 2 +--R * +--R sin(d x + c) +--R + +--R 2 d x + c 3 +--R (- 6cos(d x + c) - 12cos(d x + c) - 6)sin(-------) +--R 2 +--R + +--R 2 d x + c +--R (6cos(d x + c) + 12cos(d x + c) + 6)sin(-------) +--R 2 +--R * +--R d x + c +--R atanh(sin(-------)) +--R 2 +--R + +--R d x + c 2 d x + c 2 +--R (- 3cos(d x + c) - 3)sin(-------) + (3cos(-------) + 3)cos(d x + c) +--R 2 2 +--R + +--R d x + c 2 +--R 3cos(-------) + 3 +--R 2 +--R * +--R 2 +--R sin(d x + c) +--R + +--R 3 2 d x + c 2 +--R (- 6cos(d x + c) - 12cos(d x + c) - 6cos(d x + c))sin(-------) +--R 2 +--R + +--R 3 d x + c 2 2 +--R 6cos(d x + c) + (- 6cos(-------) + 12)cos(d x + c) +--R 2 +--R + +--R d x + c 2 d x + c 2 +--R (- 12cos(-------) + 6)cos(d x + c) - 6cos(-------) +--R 2 2 +--R / +--R 2 2 d x + c 2 2 2 +--R ((32a cos(d x + c) + 32a )sin(-------) - 32a cos(d x + c) - 32a ) +--R 2 +--R * +--R 2 +--R sin(d x + c) +--R + +--R 2 2 2 2 d x + c 2 +--R (- 64a cos(d x + c) - 128a cos(d x + c) - 64a )sin(-------) +--R 2 +--R + +--R 2 2 2 2 +--R 64a cos(d x + c) + 128a cos(d x + c) + 64a +--R * +--R +------------------+ +--R \|a cos(d x + c) + a +--R Type: Expression Integer +--R +--E 180 + +--S 181 of 504 +--Rt0134:= 1/(a-a*cos(c+d*x))^(3/2) +--R +--R +--R 1 +--R (165) - ------------------------------------------- +--R +--------------------+ +--R (a cos(d x + c) - a)\|- a cos(d x + c) + a +--R Type: Expression Integer +--R +--E 181 + +--S 182 of 504 +--Rr0134:= -1/2*atanh(cos(1/2*c+1/2*d*x))*sin(1/2*c+1/2*d*x)/a/d/(a-a*cos(c+d*x))^(1/2)-1/2*sin(c+d*x)/d/(a-a*cos(c+d*x))^(3/2) +--R +--R +--R d x + c d x + c +--R (- cos(d x + c) + 1)sin(-------)atanh(cos(-------)) + sin(d x + c) +--R 2 2 +--R (166) ------------------------------------------------------------------ +--R +--------------------+ +--R (2a d cos(d x + c) - 2a d)\|- a cos(d x + c) + a +--R Type: Expression Integer +--R +--E 182 + +--S 183 of 504 +--Ra0134:= integrate(t0134,x) +--R +--R +--R (167) +--R [ +--R +--+ +--R (cos(d x + c) - 1)\|2a +--R * +--R +--+ +------------------+ +--R 2\|2a \|a cos(d x + c) + a - a cos(d x + c) - 3a +--R log(-------------------------------------------------) +--R cos(d x + c) - 1 +--R + +--R +------------------+ +--R 4\|a cos(d x + c) + a +--R / +--R 2 2 +--R 8a d cos(d x + c) - 8a d +--R , +--R +--R +----+ +------------------+ +--R +----+ \|- 2a \|a cos(d x + c) + a +--R (cos(d x + c) - 1)\|- 2a atan(----------------------------) +--R 2a +--R + +--R +------------------+ +--R 2\|a cos(d x + c) + a +--R / +--R 2 2 +--R 4a d cos(d x + c) - 4a d +--R ] +--R Type: Union(List Expression Integer,...) +--R +--E 183 + +--S 184 of 504 +--Rm0134a:= a0134.1-r0134 +--R +--R +--R (168) +--R +--+ +--------------------+ +--R (cos(d x + c) - 1)\|2a \|- a cos(d x + c) + a +--R * +--R +--+ +------------------+ +--R 2\|2a \|a cos(d x + c) + a - a cos(d x + c) - 3a +--R log(-------------------------------------------------) +--R cos(d x + c) - 1 +--R + +--R +--------------------+ +------------------+ +--R 4\|- a cos(d x + c) + a \|a cos(d x + c) + a +--R + +--R d x + c d x + c +--R (4a cos(d x + c) - 4a)sin(-------)atanh(cos(-------)) - 4a sin(d x + c) +--R 2 2 +--R / +--R 2 2 +--------------------+ +--R (8a d cos(d x + c) - 8a d)\|- a cos(d x + c) + a +--R Type: Expression Integer +--R +--E 184 + +--S 185 of 504 +--Rd0134a:= D(m0134a,x) +--R +--R +--R (169) +--R d x + c 2 d x + c 2 +--R ((- 4cos(-------) + 4)cos(d x + c) - 12cos(-------) + 12) +--R 2 2 +--R * +--R +--------------------+ +--R sin(d x + c)\|- a cos(d x + c) + a +--R + +--R d x + c 2 2 d x + c 2 +--R ((2cos(-------) - 2)cos(d x + c) - 2cos(-------) + 2) +--R 2 2 +--R * +--R d x + c +--R sin(-------)sin(d x + c) +--R 2 +--R + +--R d x + c 3 d x + c 3 +--R (2cos(-------) - 2cos(-------))cos(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c 2 +--R (- 2cos(-------) + 2cos(-------))cos(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c d x + c 3 +--R (- 2cos(-------) + 2cos(-------))cos(d x + c) + 2cos(-------) +--R 2 2 2 +--R + +--R d x + c +--R - 2cos(-------) +--R 2 +--R * +--R +--+ d x + c +--R \|2a atanh(cos(-------)) +--R 2 +--R + +--R d x + c 2 d x + c 2 +--R ((- 6cos(-------) + 6)cos(d x + c) - 6cos(-------) + 6) +--R 2 2 +--R * +--R 2 +--R sin(d x + c) +--R + +--R 3 2 +--R (2cos(d x + c) - 2cos(d x + c) - 2cos(d x + c) + 2) +--R * +--R d x + c 2 +--R sin(-------) +--R 2 +--R + +--R d x + c 2 3 +--R (- 4cos(-------) + 4)cos(d x + c) +--R 2 +--R + +--R d x + c 2 +--R (4cos(-------) - 4)cos(d x + c) +--R 2 +--R * +--R +--+ +--R \|2a +--R * +--R +------------------+ +--R \|a cos(d x + c) + a +--R + +--R d x + c 2 d x + c 2 +--R ((8cos(-------) - 8)cos(d x + c) + 8cos(-------) - 8)sin(d x + c) +--R 2 2 +--R * +--R +--+ +--------------------+ +--R \|2a \|- a cos(d x + c) + a +--R + +--R d x + c 2 3 +--R (- a cos(-------) + a)cos(d x + c) +--R 2 +--R + +--R d x + c 2 2 +--R (- 3a cos(-------) + 3a)cos(d x + c) +--R 2 +--R + +--R d x + c 2 d x + c 2 +--R (a cos(-------) - a)cos(d x + c) + 3a cos(-------) - 3a +--R 2 2 +--R * +--R d x + c +--R sin(-------)sin(d x + c) +--R 2 +--R + +--R d x + c 3 d x + c 4 +--R (- a cos(-------) + a cos(-------))cos(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c 3 +--R (- 2a cos(-------) + 2a cos(-------))cos(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c 2 +--R (4a cos(-------) - 4a cos(-------))cos(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c d x + c 3 +--R (2a cos(-------) - 2a cos(-------))cos(d x + c) - 3a cos(-------) +--R 2 2 2 +--R + +--R d x + c +--R 3a cos(-------) +--R 2 +--R * +--R d x + c +--R atanh(cos(-------)) +--R 2 +--R + +--R d x + c 2 2 +--R (3a cos(-------) - 3a)cos(d x + c) +--R 2 +--R + +--R d x + c 2 d x + c 2 +--R (12a cos(-------) - 12a)cos(d x + c) + 9a cos(-------) - 9a +--R 2 2 +--R * +--R 2 +--R sin(d x + c) +--R + +--R 4 3 2 +--R - a cos(d x + c) - 2a cos(d x + c) + 4a cos(d x + c) +--R + +--R 2a cos(d x + c) - 3a +--R * +--R d x + c 2 +--R sin(-------) +--R 2 +--R + +--R d x + c 2 4 +--R (2a cos(-------) - 2a)cos(d x + c) +--R 2 +--R + +--R d x + c 2 3 +--R (6a cos(-------) - 6a)cos(d x + c) +--R 2 +--R + +--R d x + c 2 2 +--R (- 2a cos(-------) + 2a)cos(d x + c) +--R 2 +--R + +--R d x + c 2 +--R (- 6a cos(-------) + 6a)cos(d x + c) +--R 2 +--R / +--R d x + c 2 3 +--R (8a cos(-------) - 8a)cos(d x + c) +--R 2 +--R + +--R d x + c 2 2 +--R (- 8a cos(-------) + 8a)cos(d x + c) +--R 2 +--R + +--R d x + c 2 d x + c 2 +--R (- 8a cos(-------) + 8a)cos(d x + c) + 8a cos(-------) - 8a +--R 2 2 +--R * +--R +--+ +--------------------+ +------------------+ +--R \|2a \|- a cos(d x + c) + a \|a cos(d x + c) + a +--R + +--R 2 d x + c 2 2 4 +--R (- 4a cos(-------) + 4a )cos(d x + c) +--R 2 +--R + +--R 2 d x + c 2 2 3 +--R (- 8a cos(-------) + 8a )cos(d x + c) +--R 2 +--R + +--R 2 d x + c 2 2 2 +--R (16a cos(-------) - 16a )cos(d x + c) +--R 2 +--R + +--R 2 d x + c 2 2 2 d x + c 2 2 +--R (8a cos(-------) - 8a )cos(d x + c) - 12a cos(-------) + 12a +--R 2 2 +--R * +--R +--------------------+ +--R \|- a cos(d x + c) + a +--R Type: Expression Integer +--R +--E 185 + +--S 186 of 504 +--Rm0134b:= a0134.2-r0134 +--R +--R +--R (170) +--R +----+ +--------------------+ +--R (cos(d x + c) - 1)\|- 2a \|- a cos(d x + c) + a +--R * +--R +----+ +------------------+ +--R \|- 2a \|a cos(d x + c) + a +--R atan(----------------------------) +--R 2a +--R + +--R +--------------------+ +------------------+ +--R 2\|- a cos(d x + c) + a \|a cos(d x + c) + a +--R + +--R d x + c d x + c +--R (2a cos(d x + c) - 2a)sin(-------)atanh(cos(-------)) - 2a sin(d x + c) +--R 2 2 +--R / +--R 2 2 +--------------------+ +--R (4a d cos(d x + c) - 4a d)\|- a cos(d x + c) + a +--R Type: Expression Integer +--R +--E 186 + +--S 187 of 504 +--Rd0134b:= D(m0134b,x) +--R +--R +--R (171) +--R d x + c 2 d x + c 2 +--R ((cos(-------) - 1)cos(d x + c) - cos(-------) + 1) +--R 2 2 +--R * +--R d x + c +--R sin(-------)sin(d x + c) +--R 2 +--R + +--R d x + c 3 d x + c 2 +--R (cos(-------) - cos(-------))cos(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c d x + c 3 +--R (- 2cos(-------) + 2cos(-------))cos(d x + c) + cos(-------) +--R 2 2 2 +--R + +--R d x + c +--R - cos(-------) +--R 2 +--R * +--R d x + c +--R atanh(cos(-------)) +--R 2 +--R + +--R d x + c 2 2 +--R (- 3cos(-------) + 3)sin(d x + c) +--R 2 +--R + +--R 2 d x + c 2 +--R (cos(d x + c) - 2cos(d x + c) + 1)sin(-------) +--R 2 +--R + +--R d x + c 2 2 d x + c 2 +--R (- 2cos(-------) + 2)cos(d x + c) + (2cos(-------) - 2)cos(d x + c) +--R 2 2 +--R * +--R +------------------+ +--R \|a cos(d x + c) + a +--R + +--R d x + c 2 +--------------------+ +--R (4cos(-------) - 4)sin(d x + c)\|- a cos(d x + c) + a +--R 2 +--R / +--R d x + c 2 2 +--R (4a cos(-------) - 4a)cos(d x + c) +--R 2 +--R + +--R d x + c 2 d x + c 2 +--R (- 8a cos(-------) + 8a)cos(d x + c) + 4a cos(-------) - 4a +--R 2 2 +--R * +--R +--------------------+ +------------------+ +--R \|- a cos(d x + c) + a \|a cos(d x + c) + a +--R Type: Expression Integer +--R +--E 187 + +--S 188 of 504 +--Rt0135:= 1/(a-a*cos(c+d*x))^(5/2) +--R +--R +--R 1 +--R (172) --------------------------------------------------------------- +--R 2 2 2 2 +--------------------+ +--R (a cos(d x + c) - 2a cos(d x + c) + a )\|- a cos(d x + c) + a +--R Type: Expression Integer +--R +--E 188 + +--S 189 of 504 +--Rr0135:= -3/16*atanh(cos(1/2*c+1/2*d*x))*sin(1/2*c+1/2*d*x)/a^2/d/(a-a*cos(c+d*x))^(1/2)-1/4*sin(c+d*x)/d/(a-a*cos(c+d*x))^(5/2)-3/16*sin(c+d*x)/a/d/(a-a*cos(c+d*x))^(3/2) +--R +--R +--R (173) +--R 2 d x + c d x + c +--R (- 3cos(d x + c) + 6cos(d x + c) - 3)sin(-------)atanh(cos(-------)) +--R 2 2 +--R + +--R (3cos(d x + c) - 7)sin(d x + c) +--R / +--R 2 2 2 2 +--------------------+ +--R (16a d cos(d x + c) - 32a d cos(d x + c) + 16a d)\|- a cos(d x + c) + a +--R Type: Expression Integer +--R +--E 189 + +--S 190 of 504 +--Ra0135:= integrate(t0135,x) +--R +--R +--R (174) +--R [ +--R 2 +--+ +--R (3cos(d x + c) - 6cos(d x + c) + 3)\|2a +--R * +--R +--+ +------------------+ +--R 2\|2a \|a cos(d x + c) + a - a cos(d x + c) - 3a +--R log(-------------------------------------------------) +--R cos(d x + c) - 1 +--R + +--R +------------------+ +--R (12cos(d x + c) - 28)\|a cos(d x + c) + a +--R / +--R 3 2 3 3 +--R 64a d cos(d x + c) - 128a d cos(d x + c) + 64a d +--R , +--R +--R 2 +----+ +--R (3cos(d x + c) - 6cos(d x + c) + 3)\|- 2a +--R * +--R +----+ +------------------+ +--R \|- 2a \|a cos(d x + c) + a +--R atan(----------------------------) +--R 2a +--R + +--R +------------------+ +--R (6cos(d x + c) - 14)\|a cos(d x + c) + a +--R / +--R 3 2 3 3 +--R 32a d cos(d x + c) - 64a d cos(d x + c) + 32a d +--R ] +--R Type: Union(List Expression Integer,...) +--R +--E 190 + +--S 191 of 504 +--Rm0135a:= a0135.1-r0135 +--R +--R +--R (175) +--R 2 +--+ +--------------------+ +--R (3cos(d x + c) - 6cos(d x + c) + 3)\|2a \|- a cos(d x + c) + a +--R * +--R +--+ +------------------+ +--R 2\|2a \|a cos(d x + c) + a - a cos(d x + c) - 3a +--R log(-------------------------------------------------) +--R cos(d x + c) - 1 +--R + +--R +--------------------+ +------------------+ +--R (12cos(d x + c) - 28)\|- a cos(d x + c) + a \|a cos(d x + c) + a +--R + +--R 2 d x + c +--R (12a cos(d x + c) - 24a cos(d x + c) + 12a)sin(-------) +--R 2 +--R * +--R d x + c +--R atanh(cos(-------)) +--R 2 +--R + +--R (- 12a cos(d x + c) + 28a)sin(d x + c) +--R / +--R 3 2 3 3 +--------------------+ +--R (64a d cos(d x + c) - 128a d cos(d x + c) + 64a d)\|- a cos(d x + c) + a +--R Type: Expression Integer +--R +--E 191 + +--S 192 of 504 +--Rd0135a:= D(m0135a,x) +--R +--R +--R (176) +--R d x + c 2 d x + c 2 +--R ((32cos(-------) - 32)cos(d x + c) + 96cos(-------) - 96) +--R 2 2 +--R * +--R +--------------------+ +--R sin(d x + c)\|- a cos(d x + c) + a +--R + +--R d x + c 2 3 +--R (6cos(-------) - 6)cos(d x + c) +--R 2 +--R + +--R d x + c 2 2 +--R (- 6cos(-------) + 6)cos(d x + c) +--R 2 +--R + +--R d x + c 2 d x + c 2 +--R (- 6cos(-------) + 6)cos(d x + c) + 6cos(-------) - 6 +--R 2 2 +--R * +--R d x + c +--R sin(-------)sin(d x + c) +--R 2 +--R + +--R d x + c 3 d x + c 4 +--R (6cos(-------) - 6cos(-------))cos(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c 3 +--R (- 12cos(-------) + 12cos(-------))cos(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c d x + c 3 +--R (12cos(-------) - 12cos(-------))cos(d x + c) - 6cos(-------) +--R 2 2 2 +--R + +--R d x + c +--R 6cos(-------) +--R 2 +--R * +--R +--+ d x + c +--R \|2a atanh(cos(-------)) +--R 2 +--R + +--R d x + c 2 2 +--R (- 18cos(-------) + 18)cos(d x + c) +--R 2 +--R + +--R d x + c 2 d x + c 2 +--R (40cos(-------) - 40)cos(d x + c) + 58cos(-------) - 58 +--R 2 2 +--R * +--R 2 +--R sin(d x + c) +--R + +--R 4 3 +--R (6cos(d x + c) - 12cos(d x + c) + 12cos(d x + c) - 6) +--R * +--R d x + c 2 +--R sin(-------) +--R 2 +--R + +--R d x + c 2 4 +--R (- 12cos(-------) + 12)cos(d x + c) +--R 2 +--R + +--R d x + c 2 3 +--R (28cos(-------) - 28)cos(d x + c) +--R 2 +--R + +--R d x + c 2 2 +--R (12cos(-------) - 12)cos(d x + c) +--R 2 +--R + +--R d x + c 2 +--R (- 28cos(-------) + 28)cos(d x + c) +--R 2 +--R * +--R +--+ +--R \|2a +--R * +--R +------------------+ +--R \|a cos(d x + c) + a +--R + +--R d x + c 2 d x + c 2 +--R ((- 64cos(-------) + 64)cos(d x + c) - 64cos(-------) + 64) +--R 2 2 +--R * +--R +--+ +--------------------+ +--R sin(d x + c)\|2a \|- a cos(d x + c) + a +--R + +--R d x + c 2 4 +--R (- 3a cos(-------) + 3a)cos(d x + c) +--R 2 +--R + +--R d x + c 2 3 +--R (- 6a cos(-------) + 6a)cos(d x + c) +--R 2 +--R + +--R d x + c 2 2 +--R (12a cos(-------) - 12a)cos(d x + c) +--R 2 +--R + +--R d x + c 2 d x + c 2 +--R (6a cos(-------) - 6a)cos(d x + c) - 9a cos(-------) + 9a +--R 2 2 +--R * +--R d x + c +--R sin(-------)sin(d x + c) +--R 2 +--R + +--R d x + c 3 d x + c 5 +--R (- 3a cos(-------) + 3a cos(-------))cos(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c 4 +--R (- 3a cos(-------) + 3a cos(-------))cos(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c 3 +--R (18a cos(-------) - 18a cos(-------))cos(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c 2 +--R (- 6a cos(-------) + 6a cos(-------))cos(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c +--R (- 15a cos(-------) + 15a cos(-------))cos(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c +--R 9a cos(-------) - 9a cos(-------) +--R 2 2 +--R * +--R d x + c +--R atanh(cos(-------)) +--R 2 +--R + +--R d x + c 2 3 +--R (9a cos(-------) - 9a)cos(d x + c) +--R 2 +--R + +--R d x + c 2 2 +--R (7a cos(-------) - 7a)cos(d x + c) +--R 2 +--R + +--R d x + c 2 d x + c 2 +--R (- 89a cos(-------) + 89a)cos(d x + c) - 87a cos(-------) + 87a +--R 2 2 +--R * +--R 2 +--R sin(d x + c) +--R + +--R 5 4 3 +--R - 3a cos(d x + c) - 3a cos(d x + c) + 18a cos(d x + c) +--R + +--R 2 +--R - 6a cos(d x + c) - 15a cos(d x + c) + 9a +--R * +--R d x + c 2 +--R sin(-------) +--R 2 +--R + +--R d x + c 2 5 +--R (6a cos(-------) - 6a)cos(d x + c) +--R 2 +--R + +--R d x + c 2 4 +--R (4a cos(-------) - 4a)cos(d x + c) +--R 2 +--R + +--R d x + c 2 3 +--R (- 48a cos(-------) + 48a)cos(d x + c) +--R 2 +--R + +--R d x + c 2 2 +--R (- 4a cos(-------) + 4a)cos(d x + c) +--R 2 +--R + +--R d x + c 2 +--R (42a cos(-------) - 42a)cos(d x + c) +--R 2 +--R / +--R 2 d x + c 2 2 4 +--R (64a cos(-------) - 64a )cos(d x + c) +--R 2 +--R + +--R 2 d x + c 2 2 3 +--R (- 128a cos(-------) + 128a )cos(d x + c) +--R 2 +--R + +--R 2 d x + c 2 2 2 d x + c 2 2 +--R (128a cos(-------) - 128a )cos(d x + c) - 64a cos(-------) + 64a +--R 2 2 +--R * +--R +--+ +--------------------+ +------------------+ +--R \|2a \|- a cos(d x + c) + a \|a cos(d x + c) + a +--R + +--R 3 d x + c 2 3 5 +--R (- 32a cos(-------) + 32a )cos(d x + c) +--R 2 +--R + +--R 3 d x + c 2 3 4 +--R (- 32a cos(-------) + 32a )cos(d x + c) +--R 2 +--R + +--R 3 d x + c 2 3 3 +--R (192a cos(-------) - 192a )cos(d x + c) +--R 2 +--R + +--R 3 d x + c 2 3 2 +--R (- 64a cos(-------) + 64a )cos(d x + c) +--R 2 +--R + +--R 3 d x + c 2 3 3 d x + c 2 3 +--R (- 160a cos(-------) + 160a )cos(d x + c) + 96a cos(-------) - 96a +--R 2 2 +--R * +--R +--------------------+ +--R \|- a cos(d x + c) + a +--R Type: Expression Integer +--R +--E 192 + +--S 193 of 504 +--Rm0135b:= a0135.2-r0135 +--R +--R +--R (177) +--R 2 +----+ +--------------------+ +--R (3cos(d x + c) - 6cos(d x + c) + 3)\|- 2a \|- a cos(d x + c) + a +--R * +--R +----+ +------------------+ +--R \|- 2a \|a cos(d x + c) + a +--R atan(----------------------------) +--R 2a +--R + +--R +--------------------+ +------------------+ +--R (6cos(d x + c) - 14)\|- a cos(d x + c) + a \|a cos(d x + c) + a +--R + +--R 2 d x + c d x + c +--R (6a cos(d x + c) - 12a cos(d x + c) + 6a)sin(-------)atanh(cos(-------)) +--R 2 2 +--R + +--R (- 6a cos(d x + c) + 14a)sin(d x + c) +--R / +--R 3 2 3 3 +--------------------+ +--R (32a d cos(d x + c) - 64a d cos(d x + c) + 32a d)\|- a cos(d x + c) + a +--R Type: Expression Integer +--R +--E 193 + +--S 194 of 504 +--Rd0135b:= D(m0135b,x) +--R +--R +--R (178) +--R d x + c 2 2 +--R (3cos(-------) - 3)cos(d x + c) +--R 2 +--R + +--R d x + c 2 d x + c 2 +--R (- 6cos(-------) + 6)cos(d x + c) + 3cos(-------) - 3 +--R 2 2 +--R * +--R d x + c +--R sin(-------)sin(d x + c) +--R 2 +--R + +--R d x + c 3 d x + c 3 +--R (3cos(-------) - 3cos(-------))cos(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c 2 +--R (- 9cos(-------) + 9cos(-------))cos(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c d x + c 3 +--R (9cos(-------) - 9cos(-------))cos(d x + c) - 3cos(-------) +--R 2 2 2 +--R + +--R d x + c +--R 3cos(-------) +--R 2 +--R * +--R d x + c +--R atanh(cos(-------)) +--R 2 +--R + +--R d x + c 2 d x + c 2 +--R ((- 9cos(-------) + 9)cos(d x + c) + 29cos(-------) - 29) +--R 2 2 +--R * +--R 2 +--R sin(d x + c) +--R + +--R 3 2 d x + c 2 +--R (3cos(d x + c) - 9cos(d x + c) + 9cos(d x + c) - 3)sin(-------) +--R 2 +--R + +--R d x + c 2 3 +--R (- 6cos(-------) + 6)cos(d x + c) +--R 2 +--R + +--R d x + c 2 2 +--R (20cos(-------) - 20)cos(d x + c) +--R 2 +--R + +--R d x + c 2 +--R (- 14cos(-------) + 14)cos(d x + c) +--R 2 +--R * +--R +------------------+ +--R \|a cos(d x + c) + a +--R + +--R d x + c 2 +--------------------+ +--R (- 32cos(-------) + 32)sin(d x + c)\|- a cos(d x + c) + a +--R 2 +--R / +--R 2 d x + c 2 2 3 +--R (32a cos(-------) - 32a )cos(d x + c) +--R 2 +--R + +--R 2 d x + c 2 2 2 +--R (- 96a cos(-------) + 96a )cos(d x + c) +--R 2 +--R + +--R 2 d x + c 2 2 2 d x + c 2 2 +--R (96a cos(-------) - 96a )cos(d x + c) - 32a cos(-------) + 32a +--R 2 2 +--R * +--R +--------------------+ +------------------+ +--R \|- a cos(d x + c) + a \|a cos(d x + c) + a +--R Type: Expression Integer +--R +--E 194 + +--S 195 of 504 +--Rt0136:= (b*cos(c+d*x))^(1/2) +--R +--R +--R +--------------+ +--R (179) \|b cos(d x + c) +--R Type: Expression Integer +--R +--E 195 + +--S 196 of 504 +--Rr0136:= 2*(b*cos(c+d*x))^(1/2)*EllipticE(1/2*c+1/2*d*x,2)/d/cos(c+d*x)^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Polynomial Fraction Integer +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--R +--E 196 + +--S 197 of 504 +--Ra0136:= integrate(t0136,x) +--R +--R +--R x +--R ++ +---------------+ +--R (180) | \|b cos(%H d + c) d%H +--R ++ +--R Type: Union(Expression Integer,...) +--R +--E 197 + +--S 198 of 504 +--Rm0136:= a0136-r0136 +--R +--R +--R x +--R ++ +---------------+ +--R (181) | \|b cos(%H d + c) d%H - r0136 +--R ++ +--R Type: Expression Integer +--R +--E 198 + +--S 199 of 504 +--Rd0136:= D(m0136,x) +--R +--R +--R +--------------+ +--R (182) \|b cos(d x + c) +--R Type: Expression Integer +--R +--E 199 + +--S 200 of 504 +--Rt0137:= (b*cos(c+d*x))^(3/2) +--R +--R +--R +--------------+ +--R (183) b cos(d x + c)\|b cos(d x + c) +--R Type: Expression Integer +--R +--E 200 + +--S 201 of 504 +--Rr0137:= 2/3*b^2*(cos(c+d*x)^(1/2)*EllipticF(1/2*c+1/2*d*x,2)+cos(c+d*x)*sin(c+d*x))/d/(b*cos(c+d*x))^(1/2) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Polynomial Fraction Integer +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--R +--E 201 + +--S 202 of 504 +--Ra0137:= integrate(t0137,x) +--R +--R +--R x +--R ++ +---------------+ +--R (184) | b cos(%H d + c)\|b cos(%H d + c) d%H +--R ++ +--R Type: Union(Expression Integer,...) +--R +--E 202 + +--S 203 of 504 +--Rm0137:= a0137-r0137 +--R +--R +--R x +--R ++ +---------------+ +--R (185) | b cos(%H d + c)\|b cos(%H d + c) d%H - r0137 +--R ++ +--R Type: Expression Integer +--R +--E 203 + +--S 204 of 504 +--Rd0137:= D(m0137,x) +--R +--R +--R +--------------+ +--R (186) b cos(d x + c)\|b cos(d x + c) +--R Type: Expression Integer +--R +--E 204 + +--S 205 of 504 +--Rt0138:= (b*cos(c+d*x))^(5/2) +--R +--R +--R 2 2 +--------------+ +--R (187) b cos(d x + c) \|b cos(d x + c) +--R Type: Expression Integer +--R +--E 205 + +--S 206 of 504 +--Rr0138:= 2/5*b^2*(b*cos(c+d*x))^(1/2)*(3*EllipticE(1/2*c+1/2*d*x,2)+cos(c+d*x)^(3/2)*sin(c+d*x))/d/cos(c+d*x)^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Polynomial Fraction Integer +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--R +--E 206 + +--S 207 of 504 +--Ra0138:= integrate(t0138,x) +--R +--R +--R x +--R ++ 2 2 +---------------+ +--R (188) | b cos(%H d + c) \|b cos(%H d + c) d%H +--R ++ +--R Type: Union(Expression Integer,...) +--R +--E 207 + +--S 208 of 504 +--Rm0138:= a0138-r0138 +--R +--R +--R x +--R ++ 2 2 +---------------+ +--R (189) | b cos(%H d + c) \|b cos(%H d + c) d%H - r0138 +--R ++ +--R Type: Expression Integer +--R +--E 208 + +--S 209 of 504 +--Rd0138:= D(m0138,x) +--R +--R +--R 2 2 +--------------+ +--R (190) b cos(d x + c) \|b cos(d x + c) +--R Type: Expression Integer +--R +--E 209 + +--S 210 of 504 +--Rt0139:= 1/(b*cos(c+d*x))^(1/2) +--R +--R +--R 1 +--R (191) ----------------- +--R +--------------+ +--R \|b cos(d x + c) +--R Type: Expression Integer +--R +--E 210 + +--S 211 of 504 +--Rr0139:= 2*cos(c+d*x)^(1/2)*EllipticF(1/2*c+1/2*d*x,2)/d/(b*cos(c+d*x))^(1/2) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Polynomial Fraction Integer +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--R +--E 211 + +--S 212 of 504 +--Ra0139:= integrate(t0139,x) +--R +--R +--R x +--R ++ 1 +--R (192) | ------------------ d%H +--R ++ +---------------+ +--R \|b cos(%H d + c) +--R Type: Union(Expression Integer,...) +--R +--E 212 + +--S 213 of 504 +--Rm0139:= a0139-r0139 +--R +--R +--R x +--R ++ 1 +--R (193) | ------------------ d%H - r0139 +--R ++ +---------------+ +--R \|b cos(%H d + c) +--R Type: Expression Integer +--R +--E 213 + +--S 214 of 504 +--Rd0139:= D(m0139,x) +--R +--R +--R 1 +--R (194) ----------------- +--R +--------------+ +--R \|b cos(d x + c) +--R Type: Expression Integer +--R +--E 214 + +--S 215 of 504 +--Rt0140:= 1/(b*cos(c+d*x))^(3/2) +--R +--R +--R 1 +--R (195) ------------------------------- +--R +--------------+ +--R b cos(d x + c)\|b cos(d x + c) +--R Type: Expression Integer +--R +--E 215 + +--S 216 of 504 +--Rr0140:= -2/b*(cos(c+d*x)*EllipticE(1/2*c+1/2*d*x,2)-sin(c+d*x)*cos(c+d*x)^(1/2))/d/cos(c+d*x)^(1/2)/(b*cos(c+d*x))^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Polynomial Fraction Integer +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--R +--E 216 + +--S 217 of 504 +--Ra0140:= integrate(t0140,x) +--R +--R +--R x +--R ++ 1 +--R (196) | --------------------------------- d%H +--R ++ +---------------+ +--R b cos(%H d + c)\|b cos(%H d + c) +--R Type: Union(Expression Integer,...) +--R +--E 217 + +--S 218 of 504 +--Rm0140:= a0140-r0140 +--R +--R +--R x +--R ++ 1 +--R (197) | --------------------------------- d%H - r0140 +--R ++ +---------------+ +--R b cos(%H d + c)\|b cos(%H d + c) +--R Type: Expression Integer +--R +--E 218 + +--S 219 of 504 +--Rd0140:= D(m0140,x) +--R +--R +--R 1 +--R (198) ------------------------------- +--R +--------------+ +--R b cos(d x + c)\|b cos(d x + c) +--R Type: Expression Integer +--R +--E 219 + +--S 220 of 504 +--Rt0141:= 1/(b*cos(c+d*x))^(5/2) +--R +--R +--R 1 +--R (199) -------------------------------- +--R 2 2 +--------------+ +--R b cos(d x + c) \|b cos(d x + c) +--R Type: Expression Integer +--R +--E 220 + +--S 221 of 504 +--Rr0141:= 2/3/b^2*(cos(c+d*x)^(3/2)*EllipticF(1/2*c+1/2*d*x,2)+sin(c+d*x))/d/cos(c+d*x)/(b*cos(c+d*x))^(1/2) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Polynomial Fraction Integer +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--R +--E 221 + +--S 222 of 504 +--Ra0141:= integrate(t0141,x) +--R +--R +--R x +--R ++ 1 +--R (200) | ---------------------------------- d%H +--R ++ 2 2 +---------------+ +--R b cos(%H d + c) \|b cos(%H d + c) +--R Type: Union(Expression Integer,...) +--R +--E 222 + +--S 223 of 504 +--Rm0141:= a0141-r0141 +--R +--R +--R x +--R ++ 1 +--R (201) | ---------------------------------- d%H - r0141 +--R ++ 2 2 +---------------+ +--R b cos(%H d + c) \|b cos(%H d + c) +--R Type: Expression Integer +--R +--E 223 + +--S 224 of 504 +--Rd0141:= D(m0141,x) +--R +--R +--R 1 +--R (202) -------------------------------- +--R 2 2 +--------------+ +--R b cos(d x + c) \|b cos(d x + c) +--R Type: Expression Integer +--R +--E 224 + +--S 225 of 504 +--Rt0142:= x^2/(a+b*cos(x)) +--R +--R +--R 2 +--R x +--R (203) ------------ +--R b cos(x) + a +--R Type: Expression Integer +--R +--E 225 + +--S 226 of 504 +--Rr0142:= -(%i*x^2*log((-a+(a^2-b^2)^(1/2)-b*exp(%i*x))/(-a+(a^2-b^2)^(1/2)))-%i*x^2*log((a+(a^2-b^2)^(1/2)+b*exp(%i*x))/(a+(a^2-b^2)^(1/2)))+2*x*polylog(2,b*exp(%i*x)/(-a+(a^2-b^2)^(1/2)))-2*x*polylog(2,-b*exp(%i*x)/(a+(a^2-b^2)^(1/2)))+2*%i*polylog(3,b*exp(%i*x)/(-a+(a^2-b^2)^(1/2)))-2*%i*polylog(3,-b*exp(%i*x)/(a+(a^2-b^2)^(1/2))))/(a^2-b^2)^(1/2) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Complex Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--R +--E 226 + +--S 227 of 504 +--Ra0142:= integrate(t0142,x) +--R +--R +--R x 2 +--R ++ %H +--R (204) | ------------- d%H +--R ++ b cos(%H) + a +--R Type: Union(Expression Integer,...) +--R +--E 227 + +--S 228 of 504 +--Rm0142:= a0142-r0142 +--R +--R +--R x 2 +--R ++ %H +--R (205) | ------------- d%H - r0142 +--R ++ b cos(%H) + a +--R Type: Expression Integer +--R +--E 228 + +--S 229 of 504 +--Rd0142:= D(m0142,x) +--R +--R +--R 2 +--R x +--R (206) ------------ +--R b cos(x) + a +--R Type: Expression Integer +--R +--E 229 + +--S 230 of 504 +--Rt0143:= x^3/(a+b*cos(x)) +--R +--R +--R 3 +--R x +--R (207) ------------ +--R b cos(x) + a +--R Type: Expression Integer +--R +--E 230 + +--S 231 of 504 +--Rr0143:= -(%i*x^3*log((-a+(a^2-b^2)^(1/2)-b*exp(%i*x))/(-a+(a^2-b^2)^(1/2)))-%i*x^3*log((a+(a^2-b^2)^(1/2)+b*exp(%i*x))/(a+(a^2-b^2)^(1/2)))+3*x^2*polylog(2,b*exp(%i*x)/(-a+(a^2-b^2)^(1/2)))-3*x^2*polylog(2,-b*exp(%i*x)/(a+(a^2-b^2)^(1/2)))+6*%i*x*polylog(3,b*exp(%i*x)/(-a+(a^2-b^2)^(1/2)))-6*%i*x*polylog(3,-b*exp(%i*x)/(a+(a^2-b^2)^(1/2)))-6*polylog(4,b*exp(%i*x)/(-a+(a^2-b^2)^(1/2)))+6*polylog(4,-b*exp(%i*x)/(a+(a^2-b^2)^(1/2))))/(a^2-b^2)^(1/2) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Complex Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--R +--E 231 + +--S 232 of 504 +--Ra0143:= integrate(t0143,x) +--R +--R +--R x 3 +--R ++ %H +--R (208) | ------------- d%H +--R ++ b cos(%H) + a +--R Type: Union(Expression Integer,...) +--R +--E 232 + +--S 233 of 504 +--Rm0143:= a0143-r0143 +--R +--R +--R x 3 +--R ++ %H +--R (209) | ------------- d%H - r0143 +--R ++ b cos(%H) + a +--R Type: Expression Integer +--R +--E 233 + +--S 234 of 504 +--Rd0143:= D(m0143,x) +--R +--R +--R 3 +--R x +--R (210) ------------ +--R b cos(x) + a +--R Type: Expression Integer +--R +--E 234 + +--S 235 of 504 +--Rt0144:= x/(a-a*cos(x)) +--R +--R +--R x +--R (211) - ------------ +--R a cos(x) - a +--R Type: Expression Integer +--R +--E 235 + +--S 236 of 504 +--Rr0144:= -x*cot(1/2*x)/a+2*log(sin(1/2*x))/a +--R +--R +--R x x +--R 2log(sin(-)) - x cot(-) +--R 2 2 +--R (212) ----------------------- +--R a +--R Type: Expression Integer +--R +--E 236 + +--S 237 of 504 +--Ra0144:= integrate(t0144,x) +--R +--R +--R sin(x) 2 +--R 2sin(x)log(----------) - sin(x)log(----------) - x cos(x) - x +--R cos(x) + 1 cos(x) + 1 +--R (213) ------------------------------------------------------------- +--R a sin(x) +--R Type: Union(Expression Integer,...) +--R +--E 237 + +--S 238 of 504 +--Rm0144:= a0144-r0144 +--R +--R +--R (214) +--R sin(x) x 2 +--R 2sin(x)log(----------) - 2sin(x)log(sin(-)) - sin(x)log(----------) +--R cos(x) + 1 2 cos(x) + 1 +--R + +--R x +--R x cot(-)sin(x) - x cos(x) - x +--R 2 +--R / +--R a sin(x) +--R Type: Expression Integer +--R +--E 238 + +--S 239 of 504 +--Rd0144:= D(m0144,x) +--R +--R +--R (215) +--R x 3 +--R 2sin(-)sin(x) +--R 2 +--R + +--R x 2 x x +--R ((- x cos(x) - x)cot(-) + (2cos(x) + 2)cot(-) + x cos(x) + x)sin(-) +--R 2 2 2 +--R + +--R x x +--R - 2cos(-)cos(x) - 2cos(-) +--R 2 2 +--R * +--R 2 +--R sin(x) +--R + +--R 2 x 3 2 x +--R (2cos(x) - 2)sin(-)sin(x) + (2x cos(x) + 4x cos(x) + 2x cos(x))sin(-) +--R 2 2 +--R / +--R x 2 +--R (2a cos(x) + 2a)sin(-)sin(x) +--R 2 +--R Type: Expression Integer +--R +--E 239 + +--S 240 of 504 +--Rt0145:= x/(a+b*cos(x))^2 +--R +--R +--R x +--R (216) ---------------------------- +--R 2 2 2 +--R b cos(x) + 2a b cos(x) + a +--R Type: Expression Integer +--R +--E 240 + +--S 241 of 504 +--Rr0145:= -%i*a*x*log(1+b*exp(1)^(%i*x)/(a-(a^2-b^2)^(1/2)))/(a^2-b^2)^(3/2)+%i*a*x*log(1+b*exp(1)^(%i*x)/(a+(a^2-b^2)^(1/2)))/(a^2-b^2)^(3/2)-log(a+b*cos(x))/(a^2-b^2)-a*polylog(2,-b*exp(1)^(%i*x)/(a-(a^2-b^2)^(1/2)))/(a^2-b^2)^(3/2)+a*polylog(2,-b*exp(1)^(%i*x)/(a+(a^2-b^2)^(1/2)))/(a^2-b^2)^(3/2)-b*x*sin(x)/(a^2-b^2)/(a+b*cos(x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Complex Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--R +--E 241 + +--S 242 of 504 +--Ra0145:= integrate(t0145,x) +--R +--R +--R x +--R ++ %H +--R (217) | ------------------------------ d%H +--R ++ 2 2 2 +--R b cos(%H) + 2a b cos(%H) + a +--R Type: Union(Expression Integer,...) +--R +--E 242 + +--S 243 of 504 +--Rm0145:= a0145-r0145 +--R +--R +--R x +--R ++ %H +--R (218) | ------------------------------ d%H - r0145 +--R ++ 2 2 2 +--R b cos(%H) + 2a b cos(%H) + a +--R Type: Expression Integer +--R +--E 243 + +--S 244 of 504 +--Rd0145:= D(m0145,x) +--R +--R +--R x +--R (219) ---------------------------- +--R 2 2 2 +--R b cos(x) + 2a b cos(x) + a +--R Type: Expression Integer +--R +--E 244 + +--S 245 of 504 +--Rt0146:= x*(a+a*cos(c+d*x))^(1/2) +--R +--R +--R +------------------+ +--R (220) x\|a cos(d x + c) + a +--R Type: Expression Integer +--R +--E 245 + +--S 246 of 504 +--Rr0146:= 2*2^(1/2)*(a*cos(1/2*c+1/2*d*x)^2)^(1/2)*sec(1/2*c+1/2*d*x)*(2*cos(1/2*c+1/2*d*x)+d*x*sin(1/2*c+1/2*d*x))/d^2 +--R +--R +--R (221) +--R +-+ d x + c d x + c +-+ d x + c d x + c +--R (2d x\|2 sec(-------)sin(-------) + 4\|2 cos(-------)sec(-------)) +--R 2 2 2 2 +--R * +--R +---------------+ +--R | d x + c 2 +--R |a cos(-------) +--R \| 2 +--R / +--R 2 +--R d +--R Type: Expression Integer +--R +--E 246 + +--S 247 of 504 +--Ra0146:= integrate(t0146,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--R +--E 247 + +--S 248 of 504 +--Rm0146:= a0146-r0146 +--R +--R +--R (222) +--R +-+ d x + c d x + c +-+ d x + c d x + c +--R (- 2d x\|2 sec(-------)sin(-------) - 4\|2 cos(-------)sec(-------)) +--R 2 2 2 2 +--R * +--R +---------------+ +--R | d x + c 2 +--R |a cos(-------) +--R \| 2 +--R + +--R 2 +--R a0146 d +--R / +--R 2 +--R d +--R Type: Expression Integer +--R +--E 248 + +--S 249 of 504 +--Rd0146:= D(m0146,x) +--R +--R +--R (223) +--R +-+ d x + c 2 d x + c d x + c +--R - a d x\|2 cos(-------) sec(-------)sin(-------) +--R 2 2 2 +--R + +--R +-+ d x + c 3 d x + c +--R - 2a\|2 cos(-------) sec(-------) +--R 2 2 +--R * +--R d x + c +--R tan(-------) +--R 2 +--R + +--R +-+ d x + c d x + c d x + c 2 +--R a d x\|2 cos(-------)sec(-------)sin(-------) +--R 2 2 2 +--R + +--R +-+ d x + c 2 d x + c d x + c +--R 2a\|2 cos(-------) sec(-------)sin(-------) +--R 2 2 2 +--R + +--R +-+ d x + c 3 d x + c +--R - a d x\|2 cos(-------) sec(-------) +--R 2 2 +--R / +--R +---------------+ +--R | d x + c 2 +--R d |a cos(-------) +--R \| 2 +--R Type: Expression Integer +--R +--E 249 + +--S 250 of 504 +--Rt0147:= x^2*(a+a*cos(c+d*x))^(1/2) +--R +--R +--R 2 +------------------+ +--R (224) x \|a cos(d x + c) + a +--R Type: Expression Integer +--R +--E 250 + +--S 251 of 504 +--Rr0147:= 2*2^(1/2)*(a*cos(1/2*c+1/2*d*x)^2)^(1/2)*sec(1/2*c+1/2*d*x)*(4*d*x*cos(1/2*c+1/2*d*x)-(8-d^2*x^2)*sin(1/2*c+1/2*d*x))/d^3 +--R +--R +--R (225) +--R 2 2 +-+ d x + c d x + c +--R (2d x - 16)\|2 sec(-------)sin(-------) +--R 2 2 +--R + +--R +-+ d x + c d x + c +--R 8d x\|2 cos(-------)sec(-------) +--R 2 2 +--R * +--R +---------------+ +--R | d x + c 2 +--R |a cos(-------) +--R \| 2 +--R / +--R 3 +--R d +--R Type: Expression Integer +--R +--E 251 + +--S 252 of 504 +--Ra0147:= integrate(t0147,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--R +--E 252 + +--S 253 of 504 +--Rm0147:= a0147-r0147 +--R +--R +--R (226) +--R 2 2 +-+ d x + c d x + c +--R (- 2d x + 16)\|2 sec(-------)sin(-------) +--R 2 2 +--R + +--R +-+ d x + c d x + c +--R - 8d x\|2 cos(-------)sec(-------) +--R 2 2 +--R * +--R +---------------+ +--R | d x + c 2 +--R |a cos(-------) +--R \| 2 +--R + +--R 3 +--R a0147 d +--R / +--R 3 +--R d +--R Type: Expression Integer +--R +--E 253 + +--S 254 of 504 +--Rd0147:= D(m0147,x) +--R +--R +--R (227) +--R 2 2 +-+ d x + c 2 d x + c d x + c +--R (- a d x + 8a)\|2 cos(-------) sec(-------)sin(-------) +--R 2 2 2 +--R + +--R +-+ d x + c 3 d x + c +--R - 4a d x\|2 cos(-------) sec(-------) +--R 2 2 +--R * +--R d x + c +--R tan(-------) +--R 2 +--R + +--R 2 2 +-+ d x + c d x + c d x + c 2 +--R (a d x - 8a)\|2 cos(-------)sec(-------)sin(-------) +--R 2 2 2 +--R + +--R +-+ d x + c 2 d x + c d x + c +--R 4a d x\|2 cos(-------) sec(-------)sin(-------) +--R 2 2 2 +--R + +--R 2 2 +-+ d x + c 3 d x + c +--R - a d x \|2 cos(-------) sec(-------) +--R 2 2 +--R / +--R +---------------+ +--R 2 | d x + c 2 +--R d |a cos(-------) +--R \| 2 +--R Type: Expression Integer +--R +--E 254 + +--S 255 of 504 +--Rt0148:= (a+a*cos(c+d*x))^(1/2)/x +--R +--R +--R +------------------+ +--R \|a cos(d x + c) + a +--R (228) --------------------- +--R x +--R Type: Expression Integer +--R +--E 255 + +--S 256 of 504 +--Rr0148:= 2^(1/2)*(a*cos(1/2*c+1/2*d*x)^2)^(1/2)*sec(1/2*c+1/2*d*x)*(cos(1/2*c)*Ci(1/2*d*x)-sin(1/2*c)*Si(1/2*d*x)) +--R +--R +--R (229) +--R +-+ d x d x + c c +-+ d x c d x + c +--R (- \|2 Si(---)sec(-------)sin(-) + \|2 Ci(---)cos(-)sec(-------)) +--R 2 2 2 2 2 2 +--R * +--R +---------------+ +--R | d x + c 2 +--R |a cos(-------) +--R \| 2 +--R Type: Expression Integer +--R +--E 256 + +--S 257 of 504 +--Ra0148:= integrate(t0148,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--R +--E 257 + +--S 258 of 504 +--Rm0148:= a0148-r0148 +--R +--R +--R (230) +--R +-+ d x d x + c c +-+ d x c d x + c +--R (\|2 Si(---)sec(-------)sin(-) - \|2 Ci(---)cos(-)sec(-------)) +--R 2 2 2 2 2 2 +--R * +--R +---------------+ +--R | d x + c 2 +--R |a cos(-------) +--R \| 2 +--R + +--R a0148 +--R Type: Expression Integer +--R +--E 258 + +--S 259 of 504 +--Rd0148:= D(m0148,x) +--R +--R +--R (231) +--R +-+ d x d x + c 2 d x + c c +--R a d x\|2 Si(---)cos(-------) sec(-------)sin(-) +--R 2 2 2 2 +--R + +--R +-+ d x c d x + c 2 d x + c +--R - a d x\|2 Ci(---)cos(-)cos(-------) sec(-------) +--R 2 2 2 2 +--R * +--R d x + c +--R tan(-------) +--R 2 +--R + +--R +-+ d x d x + c d x + c c +--R - a d x\|2 Si(---)cos(-------)sec(-------)sin(-) +--R 2 2 2 2 +--R + +--R +-+ d x c d x + c d x + c +--R a d x\|2 Ci(---)cos(-)cos(-------)sec(-------) +--R 2 2 2 2 +--R * +--R d x + c +--R sin(-------) +--R 2 +--R + +--R +-+ d x + c 2 d x + c c d x +--R 2a\|2 cos(-------) sec(-------)sin(-)sin(---) +--R 2 2 2 2 +--R + +--R +-+ c d x d x + c 2 d x + c +--R - 2a\|2 cos(-)cos(---)cos(-------) sec(-------) +--R 2 2 2 2 +--R / +--R +---------------+ +--R | d x + c 2 +--R 2x |a cos(-------) +--R \| 2 +--R Type: Expression Integer +--R +--E 259 + +--S 260 of 504 +--Rt0149:= (a+a*cos(c+d*x))^(1/2)/x^2 +--R +--R +--R +------------------+ +--R \|a cos(d x + c) + a +--R (232) --------------------- +--R 2 +--R x +--R Type: Expression Integer +--R +--E 260 + +--S 261 of 504 +--Rr0149:= -1/2*(a*cos(1/2*c+1/2*d*x)^2)^(1/2)*sec(1/2*c+1/2*d*x)*(2*cos(1/2*c+1/2*d*x)/x+d*Ci(1/2*d*x)*sin(1/2*c)+d*cos(1/2*c)*Si(1/2*d*x))*2^(1/2) +--R +--R +--R (233) +--R +-+ d x d x + c c +--R - d x\|2 Ci(---)sec(-------)sin(-) +--R 2 2 2 +--R + +--R +-+ d x + c +-+ d x c d x + c +--R (- 2\|2 cos(-------) - d x\|2 Si(---)cos(-))sec(-------) +--R 2 2 2 2 +--R * +--R +---------------+ +--R | d x + c 2 +--R |a cos(-------) +--R \| 2 +--R / +--R 2x +--R Type: Expression Integer +--R +--E 261 + +--S 262 of 504 +--Ra0149:= integrate(t0149,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--R +--E 262 + +--S 263 of 504 +--Rm0149:= a0149-r0149 +--R +--R +--R (234) +--R +-+ d x d x + c c +--R d x\|2 Ci(---)sec(-------)sin(-) +--R 2 2 2 +--R + +--R +-+ d x + c +-+ d x c d x + c +--R (2\|2 cos(-------) + d x\|2 Si(---)cos(-))sec(-------) +--R 2 2 2 2 +--R * +--R +---------------+ +--R | d x + c 2 +--R |a cos(-------) +--R \| 2 +--R + +--R 2a0149 x +--R / +--R 2x +--R Type: Expression Integer +--R +--E 263 + +--S 264 of 504 +--Rd0149:= D(m0149,x) +--R +--R +--R (235) +--R 2 2 +-+ d x d x + c 2 d x + c c +--R a d x \|2 Ci(---)cos(-------) sec(-------)sin(-) +--R 2 2 2 2 +--R + +--R +-+ d x + c 3 2 2 +-+ d x c d x + c 2 +--R (2a d x\|2 cos(-------) + a d x \|2 Si(---)cos(-)cos(-------) ) +--R 2 2 2 2 +--R * +--R d x + c +--R sec(-------) +--R 2 +--R * +--R d x + c +--R tan(-------) +--R 2 +--R + +--R 2 2 +-+ d x d x + c d x + c c +--R - a d x \|2 Ci(---)cos(-------)sec(-------)sin(-) +--R 2 2 2 2 +--R + +--R +-+ d x + c 2 2 2 +-+ d x c d x + c +--R (- 4a d x\|2 cos(-------) - a d x \|2 Si(---)cos(-)cos(-------)) +--R 2 2 2 2 +--R * +--R d x + c +--R sec(-------) +--R 2 +--R * +--R d x + c +--R sin(-------) +--R 2 +--R + +--R +-+ c d x + c 2 d x + c d x +--R 2a d x\|2 cos(-)cos(-------) sec(-------)sin(---) +--R 2 2 2 2 +--R + +--R +-+ d x d x + c 2 d x + c c +--R 2a d x\|2 cos(---)cos(-------) sec(-------)sin(-) +--R 2 2 2 2 +--R + +--R +-+ d x + c 3 d x + c +--R - 4a\|2 cos(-------) sec(-------) +--R 2 2 +--R / +--R +---------------+ +--R 2 | d x + c 2 +--R 4x |a cos(-------) +--R \| 2 +--R Type: Expression Integer +--R +--E 264 + +--S 265 of 504 +--Rt0150:= (a+a*cos(c+d*x))^(1/2)/x^3 +--R +--R +--R +------------------+ +--R \|a cos(d x + c) + a +--R (236) --------------------- +--R 3 +--R x +--R Type: Expression Integer +--R +--E 265 + +--S 266 of 504 +--Rr0150:= -1/8*2^(1/2)*(a*cos(1/2*c+1/2*d*x)^2)^(1/2)*sec(1/2*c+1/2*d*x)*(4*cos(1/2*c+1/2*d*x)/x^2+d^2*cos(1/2*c)*Ci(1/2*d*x)-2*d*sin(1/2*c+1/2*d*x)/x-d^2*sin(1/2*c)*Si(1/2*d*x)) +--R +--R +--R (237) +--R +-+ d x + c d x + c 2 2 +-+ d x d x + c c +--R 2d x\|2 sec(-------)sin(-------) + d x \|2 Si(---)sec(-------)sin(-) +--R 2 2 2 2 2 +--R + +--R +-+ d x + c 2 2 +-+ d x c d x + c +--R (- 4\|2 cos(-------) - d x \|2 Ci(---)cos(-))sec(-------) +--R 2 2 2 2 +--R * +--R +---------------+ +--R | d x + c 2 +--R |a cos(-------) +--R \| 2 +--R / +--R 2 +--R 8x +--R Type: Expression Integer +--R +--E 266 + +--S 267 of 504 +--Ra0150:= integrate(t0150,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--R +--E 267 + +--S 268 of 504 +--Rm0150:= a0150-r0150 +--R +--R +--R (238) +--R +-+ d x + c d x + c +--R - 2d x\|2 sec(-------)sin(-------) +--R 2 2 +--R + +--R 2 2 +-+ d x d x + c c +--R - d x \|2 Si(---)sec(-------)sin(-) +--R 2 2 2 +--R + +--R +-+ d x + c 2 2 +-+ d x c d x + c +--R (4\|2 cos(-------) + d x \|2 Ci(---)cos(-))sec(-------) +--R 2 2 2 2 +--R * +--R +---------------+ +--R | d x + c 2 +--R |a cos(-------) +--R \| 2 +--R + +--R 2 +--R 8a0150 x +--R / +--R 2 +--R 8x +--R Type: Expression Integer +--R +--E 268 + +--S 269 of 504 +--Rd0150:= D(m0150,x) +--R +--R +--R (239) +--R 2 2 +-+ d x + c 2 d x + c d x + c +--R - 2a d x \|2 cos(-------) sec(-------)sin(-------) +--R 2 2 2 +--R + +--R 3 3 +-+ d x d x + c 2 d x + c c +--R - a d x \|2 Si(---)cos(-------) sec(-------)sin(-) +--R 2 2 2 2 +--R + +--R +-+ d x + c 3 3 3 +-+ d x c d x + c 2 +--R (4a d x\|2 cos(-------) + a d x \|2 Ci(---)cos(-)cos(-------) ) +--R 2 2 2 2 +--R * +--R d x + c +--R sec(-------) +--R 2 +--R * +--R d x + c +--R tan(-------) +--R 2 +--R + +--R 2 2 +-+ d x + c d x + c d x + c 2 +--R 2a d x \|2 cos(-------)sec(-------)sin(-------) +--R 2 2 2 +--R + +--R 3 3 +-+ d x d x + c d x + c c +--R a d x \|2 Si(---)cos(-------)sec(-------)sin(-) +--R 2 2 2 2 +--R + +--R +-+ d x + c 2 3 3 +-+ d x c d x + c +--R (- 4a d x\|2 cos(-------) - a d x \|2 Ci(---)cos(-)cos(-------)) +--R 2 2 2 2 +--R * +--R d x + c +--R sec(-------) +--R 2 +--R * +--R d x + c +--R sin(-------) +--R 2 +--R + +--R 2 2 +-+ d x + c 2 d x + c c d x +--R - 2a d x \|2 cos(-------) sec(-------)sin(-)sin(---) +--R 2 2 2 2 +--R + +--R 2 2 +-+ d x + c 3 +--R (- 2a d x - 16a)\|2 cos(-------) +--R 2 +--R + +--R 2 2 +-+ c d x d x + c 2 +--R 2a d x \|2 cos(-)cos(---)cos(-------) +--R 2 2 2 +--R * +--R d x + c +--R sec(-------) +--R 2 +--R / +--R +---------------+ +--R 3 | d x + c 2 +--R 16x |a cos(-------) +--R \| 2 +--R Type: Expression Integer +--R +--E 269 + +--S 270 of 504 +--Rt0151:= x*(a-a*cos(c+d*x))^(1/2) +--R +--R +--R +--------------------+ +--R (240) x\|- a cos(d x + c) + a +--R Type: Expression Integer +--R +--E 270 + +--S 271 of 504 +--Rr0151:= -2*2^(1/2)*csc(1/2*c+1/2*d*x)*(d*x*cos(1/2*c+1/2*d*x)-2*sin(1/2*c+1/2*d*x))*(a*sin(1/2*c+1/2*d*x)^2)^(1/2)/d^2 +--R +--R +--R (241) +--R +-+ d x + c d x + c +-+ d x + c d x + c +--R (4\|2 csc(-------)sin(-------) - 2d x\|2 cos(-------)csc(-------)) +--R 2 2 2 2 +--R * +--R +---------------+ +--R | d x + c 2 +--R |a sin(-------) +--R \| 2 +--R / +--R 2 +--R d +--R Type: Expression Integer +--R +--E 271 + +--S 272 of 504 +--Ra0151:= integrate(t0151,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--R +--E 272 + +--S 273 of 504 +--Rm0151:= a0151-r0151 +--R +--R +--R (242) +--R +-+ d x + c d x + c +-+ d x + c d x + c +--R (- 4\|2 csc(-------)sin(-------) + 2d x\|2 cos(-------)csc(-------)) +--R 2 2 2 2 +--R * +--R +---------------+ +--R | d x + c 2 +--R |a sin(-------) +--R \| 2 +--R + +--R 2 +--R a0151 d +--R / +--R 2 +--R d +--R Type: Expression Integer +--R +--E 273 + +--S 274 of 504 +--Rd0151:= D(m0151,x) +--R +--R +--R (243) +--R +-+ d x + c +-+ d x + c d x + c 3 +--R (2a\|2 cot(-------) - a d x\|2 )csc(-------)sin(-------) +--R 2 2 2 +--R + +--R +-+ d x + c d x + c +-+ d x + c d x + c +--R (- a d x\|2 cos(-------)cot(-------) - 2a\|2 cos(-------))csc(-------) +--R 2 2 2 2 +--R * +--R d x + c 2 +--R sin(-------) +--R 2 +--R + +--R +-+ d x + c 2 d x + c d x + c +--R a d x\|2 cos(-------) csc(-------)sin(-------) +--R 2 2 2 +--R / +--R +---------------+ +--R | d x + c 2 +--R d |a sin(-------) +--R \| 2 +--R Type: Expression Integer +--R +--E 274 + +--S 275 of 504 +--Rt0152:= x^2*(a-a*cos(c+d*x))^(1/2) +--R +--R +--R 2 +--------------------+ +--R (244) x \|- a cos(d x + c) + a +--R Type: Expression Integer +--R +--E 275 + +--S 276 of 504 +--Rr0152:= 2*2^(1/2)*csc(1/2*c+1/2*d*x)*(8*cos(1/2*c+1/2*d*x)-d*x*(d*x*cos(1/2*c+1/2*d*x)-4*sin(1/2*c+1/2*d*x)))*(a*sin(1/2*c+1/2*d*x)^2)^(1/2)/d^3 +--R +--R +--R (245) +--R +-+ d x + c d x + c +--R 8d x\|2 csc(-------)sin(-------) +--R 2 2 +--R + +--R 2 2 +-+ d x + c d x + c +--R (- 2d x + 16)\|2 cos(-------)csc(-------) +--R 2 2 +--R * +--R +---------------+ +--R | d x + c 2 +--R |a sin(-------) +--R \| 2 +--R / +--R 3 +--R d +--R Type: Expression Integer +--R +--E 276 + +--S 277 of 504 +--Ra0152:= integrate(t0152,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--R +--E 277 + +--S 278 of 504 +--Rm0152:= a0152-r0152 +--R +--R +--R (246) +--R +-+ d x + c d x + c +--R - 8d x\|2 csc(-------)sin(-------) +--R 2 2 +--R + +--R 2 2 +-+ d x + c d x + c +--R (2d x - 16)\|2 cos(-------)csc(-------) +--R 2 2 +--R * +--R +---------------+ +--R | d x + c 2 +--R |a sin(-------) +--R \| 2 +--R + +--R 3 +--R a0152 d +--R / +--R 3 +--R d +--R Type: Expression Integer +--R +--E 278 + +--S 279 of 504 +--Rd0152:= D(m0152,x) +--R +--R +--R (247) +--R +-+ d x + c 2 2 +-+ d x + c d x + c 3 +--R (4a d x\|2 cot(-------) - a d x \|2 )csc(-------)sin(-------) +--R 2 2 2 +--R + +--R 2 2 +-+ d x + c d x + c +-+ d x + c +--R ((- a d x + 8a)\|2 cos(-------)cot(-------) - 4a d x\|2 cos(-------)) +--R 2 2 2 +--R * +--R d x + c d x + c 2 +--R csc(-------)sin(-------) +--R 2 2 +--R + +--R 2 2 +-+ d x + c 2 d x + c d x + c +--R (a d x - 8a)\|2 cos(-------) csc(-------)sin(-------) +--R 2 2 2 +--R / +--R +---------------+ +--R 2 | d x + c 2 +--R d |a sin(-------) +--R \| 2 +--R Type: Expression Integer +--R +--E 279 + +--S 280 of 504 +--Rt0153:= (a-a*cos(c+d*x))^(1/2)/x +--R +--R +--R +--------------------+ +--R \|- a cos(d x + c) + a +--R (248) ----------------------- +--R x +--R Type: Expression Integer +--R +--E 280 + +--S 281 of 504 +--Rr0153:= 2^(1/2)*csc(1/2*c+1/2*d*x)*(a*sin(1/2*c+1/2*d*x)^2)^(1/2)*(Ci(1/2*d*x)*sin(1/2*c)+cos(1/2*c)*Si(1/2*d*x)) +--R +--R +--R (249) +--R +-+ d x d x + c c +-+ d x c d x + c +--R (\|2 Ci(---)csc(-------)sin(-) + \|2 Si(---)cos(-)csc(-------)) +--R 2 2 2 2 2 2 +--R * +--R +---------------+ +--R | d x + c 2 +--R |a sin(-------) +--R \| 2 +--R Type: Expression Integer +--R +--E 281 + +--S 282 of 504 +--Ra0153:= integrate(t0153,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--R +--E 282 + +--S 283 of 504 +--Rm0153:= a0153-r0153 +--R +--R +--R (250) +--R +-+ d x d x + c c +-+ d x c d x + c +--R (- \|2 Ci(---)csc(-------)sin(-) - \|2 Si(---)cos(-)csc(-------)) +--R 2 2 2 2 2 2 +--R * +--R +---------------+ +--R | d x + c 2 +--R |a sin(-------) +--R \| 2 +--R + +--R a0153 +--R Type: Expression Integer +--R +--E 283 + +--S 284 of 504 +--Rd0153:= D(m0153,x) +--R +--R +--R (251) +--R +-+ c d x + c d x +--R - 2a\|2 cos(-)csc(-------)sin(---) +--R 2 2 2 +--R + +--R +-+ d x d x + c +-+ d x d x + c c +--R (a d x\|2 Ci(---)cot(-------) - 2a\|2 cos(---))csc(-------)sin(-) +--R 2 2 2 2 2 +--R + +--R +-+ d x c d x + c d x + c +--R a d x\|2 Si(---)cos(-)cot(-------)csc(-------) +--R 2 2 2 2 +--R * +--R d x + c 2 +--R sin(-------) +--R 2 +--R + +--R +-+ d x d x + c d x + c c +--R - a d x\|2 Ci(---)cos(-------)csc(-------)sin(-) +--R 2 2 2 2 +--R + +--R +-+ d x c d x + c d x + c +--R - a d x\|2 Si(---)cos(-)cos(-------)csc(-------) +--R 2 2 2 2 +--R * +--R d x + c +--R sin(-------) +--R 2 +--R / +--R +---------------+ +--R | d x + c 2 +--R 2x |a sin(-------) +--R \| 2 +--R Type: Expression Integer +--R +--E 284 + +--S 285 of 504 +--Rt0154:= (a-a*cos(c+d*x))^(1/2)/x^2 +--R +--R +--R +--------------------+ +--R \|- a cos(d x + c) + a +--R (252) ----------------------- +--R 2 +--R x +--R Type: Expression Integer +--R +--E 285 + +--S 286 of 504 +--Rr0154:= 1/2*csc(1/2*c+1/2*d*x)*(a*sin(1/2*c+1/2*d*x)^2)^(1/2)*(d*cos(1/2*c)*Ci(1/2*d*x)-2*sin(1/2*c+1/2*d*x)/x-d*sin(1/2*c)*Si(1/2*d*x))*2^(1/2) +--R +--R +--R (253) +--R +-+ d x + c d x + c +-+ d x d x + c c +--R - 2\|2 csc(-------)sin(-------) - d x\|2 Si(---)csc(-------)sin(-) +--R 2 2 2 2 2 +--R + +--R +-+ d x c d x + c +--R d x\|2 Ci(---)cos(-)csc(-------) +--R 2 2 2 +--R * +--R +---------------+ +--R | d x + c 2 +--R |a sin(-------) +--R \| 2 +--R / +--R 2x +--R Type: Expression Integer +--R +--E 286 + +--S 287 of 504 +--Ra0154:= integrate(t0154,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--R +--E 287 + +--S 288 of 504 +--Rm0154:= a0154-r0154 +--R +--R +--R (254) +--R +-+ d x + c d x + c +-+ d x d x + c c +--R 2\|2 csc(-------)sin(-------) + d x\|2 Si(---)csc(-------)sin(-) +--R 2 2 2 2 2 +--R + +--R +-+ d x c d x + c +--R - d x\|2 Ci(---)cos(-)csc(-------) +--R 2 2 2 +--R * +--R +---------------+ +--R | d x + c 2 +--R |a sin(-------) +--R \| 2 +--R + +--R 2a0154 x +--R / +--R 2x +--R Type: Expression Integer +--R +--E 288 + +--S 289 of 504 +--Rd0154:= D(m0154,x) +--R +--R +--R (255) +--R +-+ d x + c +-+ d x + c d x + c 3 +--R (- 2a d x\|2 cot(-------) - 4a\|2 )csc(-------)sin(-------) +--R 2 2 2 +--R + +--R +-+ d x + c c d x +--R 2a d x\|2 csc(-------)sin(-)sin(---) +--R 2 2 2 +--R + +--R 2 2 +-+ d x d x + c d x + c c +--R - a d x \|2 Si(---)cot(-------)csc(-------)sin(-) +--R 2 2 2 2 +--R + +--R 2 2 +-+ d x c d x + c +-+ d x + c +--R a d x \|2 Ci(---)cos(-)cot(-------) + 4a d x\|2 cos(-------) +--R 2 2 2 2 +--R + +--R +-+ c d x +--R - 2a d x\|2 cos(-)cos(---) +--R 2 2 +--R * +--R d x + c +--R csc(-------) +--R 2 +--R * +--R d x + c 2 +--R sin(-------) +--R 2 +--R + +--R 2 2 +-+ d x d x + c d x + c c +--R a d x \|2 Si(---)cos(-------)csc(-------)sin(-) +--R 2 2 2 2 +--R + +--R 2 2 +-+ d x c d x + c d x + c +--R - a d x \|2 Ci(---)cos(-)cos(-------)csc(-------) +--R 2 2 2 2 +--R * +--R d x + c +--R sin(-------) +--R 2 +--R / +--R +---------------+ +--R 2 | d x + c 2 +--R 4x |a sin(-------) +--R \| 2 +--R Type: Expression Integer +--R +--E 289 + +--S 290 of 504 +--Rt0155:= (a-a*cos(c+d*x))^(1/2)/x^3 +--R +--R +--R +--------------------+ +--R \|- a cos(d x + c) + a +--R (256) ----------------------- +--R 3 +--R x +--R Type: Expression Integer +--R +--E 290 + +--S 291 of 504 +--Rr0155:= -1/8*2^(1/2)*csc(1/2*c+1/2*d*x)*(a*sin(1/2*c+1/2*d*x)^2)^(1/2)*(2*d*cos(1/2*c+1/2*d*x)/x+d^2*Ci(1/2*d*x)*sin(1/2*c)+4*sin(1/2*c+1/2*d*x)/x^2+d^2*cos(1/2*c)*Si(1/2*d*x)) +--R +--R +--R (257) +--R +-+ d x + c d x + c 2 2 +-+ d x d x + c c +--R - 4\|2 csc(-------)sin(-------) - d x \|2 Ci(---)csc(-------)sin(-) +--R 2 2 2 2 2 +--R + +--R +-+ d x + c 2 2 +-+ d x c d x + c +--R (- 2d x\|2 cos(-------) - d x \|2 Si(---)cos(-))csc(-------) +--R 2 2 2 2 +--R * +--R +---------------+ +--R | d x + c 2 +--R |a sin(-------) +--R \| 2 +--R / +--R 2 +--R 8x +--R Type: Expression Integer +--R +--E 291 + +--S 292 of 504 +--Ra0155:= integrate(t0155,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--R +--E 292 + +--S 293 of 504 +--Rm0155:= a0155-r0155 +--R +--R +--R (258) +--R +-+ d x + c d x + c 2 2 +-+ d x d x + c c +--R 4\|2 csc(-------)sin(-------) + d x \|2 Ci(---)csc(-------)sin(-) +--R 2 2 2 2 2 +--R + +--R +-+ d x + c 2 2 +-+ d x c d x + c +--R (2d x\|2 cos(-------) + d x \|2 Si(---)cos(-))csc(-------) +--R 2 2 2 2 +--R * +--R +---------------+ +--R | d x + c 2 +--R |a sin(-------) +--R \| 2 +--R + +--R 2 +--R 8a0155 x +--R / +--R 2 +--R 8x +--R Type: Expression Integer +--R +--E 293 + +--S 294 of 504 +--Rd0155:= D(m0155,x) +--R +--R +--R (259) +--R +-+ d x + c 2 2 +-+ d x + c +--R (- 4a d x\|2 cot(-------) + (- 2a d x - 16a)\|2 )csc(-------) +--R 2 2 +--R * +--R d x + c 3 +--R sin(-------) +--R 2 +--R + +--R 2 2 +-+ c d x + c d x +--R 2a d x \|2 cos(-)csc(-------)sin(---) +--R 2 2 2 +--R + +--R 3 3 +-+ d x d x + c 2 2 +-+ d x d x + c +--R (- a d x \|2 Ci(---)cot(-------) + 2a d x \|2 cos(---))csc(-------) +--R 2 2 2 2 +--R * +--R c +--R sin(-) +--R 2 +--R + +--R 2 2 +-+ d x + c 3 3 +-+ d x c d x + c +--R (- 2a d x \|2 cos(-------) - a d x \|2 Si(---)cos(-))cot(-------) +--R 2 2 2 2 +--R + +--R +-+ d x + c +--R 4a d x\|2 cos(-------) +--R 2 +--R * +--R d x + c +--R csc(-------) +--R 2 +--R * +--R d x + c 2 +--R sin(-------) +--R 2 +--R + +--R 3 3 +-+ d x d x + c d x + c c +--R a d x \|2 Ci(---)cos(-------)csc(-------)sin(-) +--R 2 2 2 2 +--R + +--R 2 2 +-+ d x + c 2 3 3 +-+ d x c d x + c +--R (2a d x \|2 cos(-------) + a d x \|2 Si(---)cos(-)cos(-------)) +--R 2 2 2 2 +--R * +--R d x + c +--R csc(-------) +--R 2 +--R * +--R d x + c +--R sin(-------) +--R 2 +--R / +--R +---------------+ +--R 3 | d x + c 2 +--R 16x |a sin(-------) +--R \| 2 +--R Type: Expression Integer +--R +--E 294 + +--S 295 of 504 +--Rt0156:= (1+cos(x)^2)^(1/2) +--R +--R +--R +-----------+ +--R | 2 +--R (260) \|cos(x) + 1 +--R Type: Expression Integer +--R +--E 295 + +--S 296 of 504 +--Rr0156:= 2^(1/2)*EllipticE(x,1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Variable x +--R Fraction Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--R +--E 296 + +--S 297 of 504 +--Ra0156:= integrate(t0156,x) +--R +--R +--R x +------------+ +--R ++ | 2 +--R (261) | \|cos(%H) + 1 d%H +--R ++ +--R Type: Union(Expression Integer,...) +--R +--E 297 + +--S 298 of 504 +--Rm0156:= a0156-r0156 +--R +--R +--R x +------------+ +--R ++ | 2 +--R (262) | \|cos(%H) + 1 d%H - r0156 +--R ++ +--R Type: Expression Integer +--R +--E 298 + +--S 299 of 504 +--Rd0156:= D(m0156,x) +--R +--R +--R +-----------+ +--R | 2 +--R (263) \|cos(x) + 1 +--R Type: Expression Integer +--R +--E 299 + +--S 300 of 504 +--Rt0157:= (-1-cos(x)^2)^(1/2) +--R +--R +--R +-------------+ +--R | 2 +--R (264) \|- cos(x) - 1 +--R Type: Expression Integer +--R +--E 300 + +--S 301 of 504 +--Rr0157:= 2^(1/2)*(-3-cos(2*x))^(1/2)*EllipticE(x,1/2)/(3+cos(2*x))^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Variable x +--R Fraction Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--R +--E 301 + +--S 302 of 504 +--Ra0157:= integrate(t0157,x) +--R +--R +--R (265) +--R +---+ 2 +---+ +--R x\|- 1 x\|- 1 +--R (2(%e ) - 2%e ) +--R * +--R +----------------------------------+ +--R +---+ 2 | +---+ 4 +---+ 2 +--R x %H\|- 1 | %H\|- 1 %H\|- 1 +--R ++ (4(%e ) + 4)\|(%e ) + 6(%e ) + 1 +--R | --------------------------------------------------------- d%H +--R ++ +---+ 6 +---+ 4 +---+ 2 +--R %H\|- 1 %H\|- 1 %H\|- 1 +--R (%e ) + 6(%e ) + (%e ) +--R + +--R +--------------------------------+ +--R +---+ | +---+ 4 +---+ 2 +--R x\|- 1 | x\|- 1 x\|- 1 +--R (%e + 1)\|(%e ) + 6(%e ) + 1 +--R / +--R +---+ 2 +---+ +--R x\|- 1 x\|- 1 +--R 2(%e ) - 2%e +--R Type: Union(Expression Integer,...) +--R +--E 302 + +--S 303 of 504 +--Rm0157:= a0157-r0157 +--R +--R +--R (266) +--R +---+ 2 +---+ +--R x\|- 1 x\|- 1 +--R (2(%e ) - 2%e ) +--R * +--R +----------------------------------+ +--R +---+ 2 | +---+ 4 +---+ 2 +--R x %H\|- 1 | %H\|- 1 %H\|- 1 +--R ++ (4(%e ) + 4)\|(%e ) + 6(%e ) + 1 +--R | --------------------------------------------------------- d%H +--R ++ +---+ 6 +---+ 4 +---+ 2 +--R %H\|- 1 %H\|- 1 %H\|- 1 +--R (%e ) + 6(%e ) + (%e ) +--R + +--R +--------------------------------+ +--R +---+ | +---+ 4 +---+ 2 +---+ 2 +--R x\|- 1 | x\|- 1 x\|- 1 x\|- 1 +--R (%e + 1)\|(%e ) + 6(%e ) + 1 - 2r0157 (%e ) +--R + +--R +---+ +--R x\|- 1 +--R 2r0157 %e +--R / +--R +---+ 2 +---+ +--R x\|- 1 x\|- 1 +--R 2(%e ) - 2%e +--R Type: Expression Integer +--R +--E 303 + +--S 304 of 504 +--Rd0157:= D(m0157,x) +--R +--R +--R (267) +--R +---+ 7 +---+ 6 +---+ 5 +--R +---+ x\|- 1 +---+ x\|- 1 +---+ x\|- 1 +--R \|- 1 (%e ) - 2\|- 1 (%e ) - \|- 1 (%e ) +--R + +--R +---+ 4 +---+ 3 +--R +---+ x\|- 1 +---+ x\|- 1 +--R (- 12\|- 1 + 8)(%e ) + (- \|- 1 - 16)(%e ) +--R + +--R +---+ 2 +---+ +--R +---+ x\|- 1 +---+ x\|- 1 +--R (- 2\|- 1 + 16)(%e ) + (\|- 1 - 16)%e + 8 +--R / +--R +---+ 4 +---+ 3 +---+ 2 +--R x\|- 1 x\|- 1 x\|- 1 +--R (2(%e ) - 4(%e ) + 2(%e ) ) +--R * +--R +--------------------------------+ +--R | +---+ 4 +---+ 2 +--R | x\|- 1 x\|- 1 +--R \|(%e ) + 6(%e ) + 1 +--R Type: Expression Integer +--R +--E 304 + +--S 305 of 504 +--Rt0158:= 1/(1+cos(x)^2)^(1/2) +--R +--R +--R 1 +--R (268) -------------- +--R +-----------+ +--R | 2 +--R \|cos(x) + 1 +--R Type: Expression Integer +--R +--E 305 + +--S 306 of 504 +--Rr0158:= 1/2*EllipticF(x,1/2)*2^(1/2) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Variable x +--R Fraction Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--R +--E 306 + +--S 307 of 504 +--Ra0158:= integrate(t0158,x) +--R +--R +--R x +--R ++ 1 +--R (269) | --------------- d%H +--R ++ +------------+ +--R | 2 +--R \|cos(%H) + 1 +--R Type: Union(Expression Integer,...) +--R +--E 307 + +--S 308 of 504 +--Rm0158:= a0158-r0158 +--R +--R +--R x +--R ++ 1 +--R (270) | --------------- d%H - r0158 +--R ++ +------------+ +--R | 2 +--R \|cos(%H) + 1 +--R Type: Expression Integer +--R +--E 308 + +--S 309 of 504 +--Rd0158:= D(m0158,x) +--R +--R +--R 1 +--R (271) -------------- +--R +-----------+ +--R | 2 +--R \|cos(x) + 1 +--R Type: Expression Integer +--R +--E 309 + +--S 310 of 504 +--Rt0159:= 1/(-1-cos(x)^2)^(1/2) +--R +--R +--R 1 +--R (272) ---------------- +--R +-------------+ +--R | 2 +--R \|- cos(x) - 1 +--R Type: Expression Integer +--R +--E 310 + +--S 311 of 504 +--Rr0159:= 1/2*(3+cos(2*x))^(1/2)*EllipticF(x,1/2)*2^(1/2)/(-3-cos(2*x))^(1/2) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Variable x +--R Fraction Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--R +--E 311 + +--S 312 of 504 +--Ra0159:= integrate(t0159,x) +--R +--R +--R +----------------------------------+ +--R | +---+ 4 +---+ 2 +--R x | %H\|- 1 %H\|- 1 +--R ++ 2\|(%e ) + 6(%e ) + 1 +--R (273) | ---------------------------------------------- d%H +--R ++ +---+ 6 +---+ 4 +---+ 2 +--R %H\|- 1 %H\|- 1 %H\|- 1 +--R (%e ) + 6(%e ) + (%e ) +--R Type: Union(Expression Integer,...) +--R +--E 312 + +--S 313 of 504 +--Rm0159:= a0159-r0159 +--R +--R +--R +----------------------------------+ +--R | +---+ 4 +---+ 2 +--R x | %H\|- 1 %H\|- 1 +--R ++ 2\|(%e ) + 6(%e ) + 1 +--R (274) | ---------------------------------------------- d%H - r0159 +--R ++ +---+ 6 +---+ 4 +---+ 2 +--R %H\|- 1 %H\|- 1 %H\|- 1 +--R (%e ) + 6(%e ) + (%e ) +--R Type: Expression Integer +--R +--E 313 + +--S 314 of 504 +--Rd0159:= D(m0159,x) +--R +--R +--R +--------------------------------+ +--R | +---+ 4 +---+ 2 +--R | x\|- 1 x\|- 1 +--R 2\|(%e ) + 6(%e ) + 1 +--R (275) ------------------------------------------- +--R +---+ 6 +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 x\|- 1 +--R (%e ) + 6(%e ) + (%e ) +--R Type: Expression Integer +--R +--E 314 + +--S 315 of 504 +--Rt0160:= x/(a+b*cos(x)^2) +--R +--R +--R x +--R (276) ------------- +--R 2 +--R b cos(x) + a +--R Type: Expression Integer +--R +--E 315 + +--S 316 of 504 +--Rr0160:= -1/4*(2*%i*x*log((-2*a-b+2*a^(1/2)*(a+b)^(1/2)-b*exp(2*%i*x))/(-2*a-b+2*a^(1/2)*(a+b)^(1/2)))-2*%i*x*log((2*a+b+2*a^(1/2)*(a+b)^(1/2)+b*exp(2*%i*x))/(2*a+b+2*a^(1/2)*(a+b)^(1/2)))+polylog(2,b*exp(2*%i*x)/(-2*a-b+2*a^(1/2)*(a+b)^(1/2)))-polylog(2,-b*exp(2*%i*x)/(2*a+b+2*a^(1/2)*(a+b)^(1/2))))/a^(1/2)/(a+b)^(1/2) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Complex Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--R +--E 316 + +--S 317 of 504 +--Ra0160:= integrate(t0160,x) +--R +--R +--R x +--R ++ %H +--R (277) | -------------- d%H +--R ++ 2 +--R b cos(%H) + a +--R Type: Union(Expression Integer,...) +--R +--E 317 + +--S 318 of 504 +--Rm0160:= a0160-r0160 +--R +--R +--R x +--R ++ %H +--R (278) | -------------- d%H - r0160 +--R ++ 2 +--R b cos(%H) + a +--R Type: Expression Integer +--R +--E 318 + +--S 319 of 504 +--Rd0160:= D(m0160,x) +--R +--R +--R x +--R (279) ------------- +--R 2 +--R b cos(x) + a +--R Type: Expression Integer +--R +--E 319 + +--S 320 of 504 +--Rt0161:= x^2/(a+b*cos(x)^2) +--R +--R +--R 2 +--R x +--R (280) ------------- +--R 2 +--R b cos(x) + a +--R Type: Expression Integer +--R +--E 320 + +--S 321 of 504 +--Rr0161:= -1/4*(2*%i*x^2*log((-2*a-b+2*a^(1/2)*(a+b)^(1/2)-b*exp(2*%i*x))/(-2*a-b+2*a^(1/2)*(a+b)^(1/2)))-2*%i*x^2*log((2*a+b+2*a^(1/2)*(a+b)^(1/2)+b*exp(2*%i*x))/(2*a+b+2*a^(1/2)*(a+b)^(1/2)))+2*x*polylog(2,b*exp(2*%i*x)/(-2*a-b+2*a^(1/2)*(a+b)^(1/2)))-2*x*polylog(2,-b*exp(2*%i*x)/(2*a+b+2*a^(1/2)*(a+b)^(1/2)))+%i*polylog(3,b*exp(2*%i*x)/(-2*a-b+2*a^(1/2)*(a+b)^(1/2)))-%i*polylog(3,-b*exp(2*%i*x)/(2*a+b+2*a^(1/2)*(a+b)^(1/2))))/a^(1/2)/(a+b)^(1/2) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Complex Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--R +--E 321 + +--S 322 of 504 +--Ra0161:= integrate(t0161,x) +--R +--R +--R x 2 +--R ++ %H +--R (281) | -------------- d%H +--R ++ 2 +--R b cos(%H) + a +--R Type: Union(Expression Integer,...) +--R +--E 322 + +--S 323 of 504 +--Rm0161:= a0161-r0161 +--R +--R +--R x 2 +--R ++ %H +--R (282) | -------------- d%H - r0161 +--R ++ 2 +--R b cos(%H) + a +--R Type: Expression Integer +--R +--E 323 + +--S 324 of 504 +--Rd0161:= D(m0161,x) +--R +--R +--R 2 +--R x +--R (283) ------------- +--R 2 +--R b cos(x) + a +--R Type: Expression Integer +--R +--E 324 + +--S 325 of 504 +--Rt0162:= x^3/(a+b*cos(x)^2) +--R +--R +--R 3 +--R x +--R (284) ------------- +--R 2 +--R b cos(x) + a +--R Type: Expression Integer +--R +--E 325 + +--S 326 of 504 +--Rr0162:= 1/8*(-4*%i*x^3*log((-2*a-b+2*a^(1/2)*(a+b)^(1/2)-b*exp(2*%i*x))/(-2*a-b+2*a^(1/2)*(a+b)^(1/2)))+4*%i*x^3*log((2*a+b+2*a^(1/2)*(a+b)^(1/2)+b*exp(2*%i*x))/(2*a+b+2*a^(1/2)*(a+b)^(1/2)))-6*x^2*polylog(2,b*exp(2*%i*x)/(-2*a-b+2*a^(1/2)*(a+b)^(1/2)))+6*x^2*polylog(2,-b*exp(2*%i*x)/(2*a+b+2*a^(1/2)*(a+b)^(1/2)))-6*%i*x*polylog(3,b*exp(2*%i*x)/(-2*a-b+2*a^(1/2)*(a+b)^(1/2)))+6*%i*x*polylog(3,-b*exp(2*%i*x)/(2*a+b+2*a^(1/2)*(a+b)^(1/2)))+3*polylog(4,b*exp(2*%i*x)/(-2*a-b+2*a^(1/2)*(a+b)^(1/2)))-3*polylog(4,-b*exp(2*%i*x)/(2*a+b+2*a^(1/2)*(a+b)^(1/2))))/a^(1/2)/(a+b)^(1/2) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Complex Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--R +--E 326 + +--S 327 of 504 +--Ra0162:= integrate(t0162,x) +--R +--R +--R x 3 +--R ++ %H +--R (285) | -------------- d%H +--R ++ 2 +--R b cos(%H) + a +--R Type: Union(Expression Integer,...) +--R +--E 327 + +--S 328 of 504 +--Rm0162:= a0162-r0162 +--R +--R +--R x 3 +--R ++ %H +--R (286) | -------------- d%H - r0162 +--R ++ 2 +--R b cos(%H) + a +--R Type: Expression Integer +--R +--E 328 + +--S 329 of 504 +--Rd0162:= D(m0162,x) +--R +--R +--R 3 +--R x +--R (287) ------------- +--R 2 +--R b cos(x) + a +--R Type: Expression Integer +--R +--E 329 + +--S 330 of 504 +--Rt0163:= 1/(a+b*cos(x)^3) +--R +--R +--R 1 +--R (288) ------------- +--R 3 +--R b cos(x) + a +--R Type: Expression Integer +--R +--E 330 + +--S 331 of 504 +--Rr0163:= 2/3*atan((a^(1/3)-b^(1/3))*tan(1/2*x)/(a^(2/3)-b^(2/3))^(1/2))/a^(2/3)/(a^(2/3)-b^(2/3))^(1/2)+2/3*atan((a^(1/3)-(-1)^(2/3)*b^(1/3))*tan(1/2*x)/(a^(2/3)+(-1)^(1/3)*b^(2/3))^(1/2))/a^(2/3)/(a^(2/3)+(-1)^(1/3)*b^(2/3))^(1/2)+2/3*atan((a^(1/3)+(-1)^(1/3)*b^(1/3))*tan(1/2*x)/(a^(2/3)-(-1)^(2/3)*b^(2/3))^(1/2))/a^(2/3)/(a^(2/3)-(-1)^(2/3)*b^(2/3))^(1/2) +--R +--R +--R (289) +--R +---------------+ +-------------------+ +--R | 3+-+2 3+-+2 |3+---+3+-+2 3+-+2 +--R 2\|- \|b + \|a \|\|- 1 \|b + \|a +--R * +--R 3+---+ x 3+-+ x 3+-+ +--R \|- 1 tan(-)\|b + tan(-)\|a +--R 2 2 +--R atan(-----------------------------) +--R +----------------------+ +--R | 3+---+2 3+-+2 3+-+2 +--R \|- \|- 1 \|b + \|a +--R + +--R - +--R +----------------------+ +-------------------+ +--R | 3+---+2 3+-+2 3+-+2 |3+---+3+-+2 3+-+2 +--R 2\|- \|- 1 \|b + \|a \|\|- 1 \|b + \|a +--R * +--R x 3+-+ x 3+-+ +--R tan(-)\|b - tan(-)\|a +--R 2 2 +--R atan(-----------------------) +--R +---------------+ +--R | 3+-+2 3+-+2 +--R \|- \|b + \|a +--R + +--R - +--R +----------------------+ +---------------+ +--R | 3+---+2 3+-+2 3+-+2 | 3+-+2 3+-+2 +--R 2\|- \|- 1 \|b + \|a \|- \|b + \|a +--R * +--R 3+---+2 x 3+-+ x 3+-+ +--R \|- 1 tan(-)\|b - tan(-)\|a +--R 2 2 +--R atan(------------------------------) +--R +-------------------+ +--R |3+---+3+-+2 3+-+2 +--R \|\|- 1 \|b + \|a +--R / +--R +----------------------+ +---------------+ +-------------------+ +--R 3+-+2 | 3+---+2 3+-+2 3+-+2 | 3+-+2 3+-+2 |3+---+3+-+2 3+-+2 +--R 3\|a \|- \|- 1 \|b + \|a \|- \|b + \|a \|\|- 1 \|b + \|a +--R Type: Expression Integer +--R +--E 331 + +--S 332 of 504 +--Ra0163:= integrate(t0163,x) +--R +--R +--R (290) +--R ROOT +--R 2 2 +--R (6b - 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--R (- 81a b + 162a b - 81a )%%EJ0 +--R + +--R 2 2 4 2 2 +--R (18a b - 18a )%%EJ0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 2 2 +--R (- 6b + 6a )%%EJ0 + 2 +--R / +--R 2 2 +--R 3b - 3a +--R * +--R log +--R 4 2 6 4 2 6 +--R ((243a b - 243a )cos(x) + 243a b - 243a )%%EJ0 +--R + +--R 2 2 4 2 2 4 +--R (27a b - 27a )cos(x) + 27a b - 27a +--R * +--R ROOT +--R 2 4 4 2 6 2 +--R (- 81a b + 162a b - 81a )%%EJ0 +--R + +--R 2 2 4 2 2 +--R (18a b - 18a )%%EJ0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 4 2 6 4 2 6 2 +--R ((243a b - 243a )cos(x) + 243a b - 243a )%%EJ0 +--R + +--R 2 2 4 2 2 4 +--R ((- 27a b - 54a )cos(x) - 27a b - 54a )%%EJ0 +--R + +--R 2 2 +--R (6a b - 3a )cos(x) + 6a b - 3a +--R * +--R ROOT +--R 2 2 +--R (6b - 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--R (- 81a b + 162a b - 81a )%%EJ0 +--R + +--R 2 2 4 2 2 +--R (18a b - 18a )%%EJ0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 2 2 +--R (- 6b + 6a )%%EJ0 + 2 +--R / +--R 2 2 +--R 3b - 3a +--R + +--R 4b sin(x) +--R / +--R cos(x) + 1 +--R + +--R - +--R ROOT +--R 2 2 +--R (- 6b + 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--R (- 81a b + 162a b - 81a )%%EJ0 +--R + +--R 2 2 4 2 2 +--R (18a b - 18a )%%EJ0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 2 2 +--R (- 6b + 6a )%%EJ0 + 2 +--R / +--R 2 2 +--R 3b - 3a +--R * +--R log +--R 4 2 6 4 2 6 +--R ((243a b - 243a )cos(x) + 243a b - 243a )%%EJ0 +--R + +--R 2 2 4 2 2 4 +--R (27a b - 27a )cos(x) + 27a b - 27a +--R * +--R ROOT +--R 2 4 4 2 6 2 +--R (- 81a b + 162a b - 81a )%%EJ0 +--R + +--R 2 2 4 2 2 +--R (18a b - 18a )%%EJ0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 4 2 6 4 2 6 2 +--R ((- 243a b + 243a )cos(x) - 243a b + 243a )%%EJ0 +--R + +--R 2 2 4 2 2 4 +--R ((27a b + 54a )cos(x) + 27a b + 54a )%%EJ0 +--R + +--R 2 2 +--R (- 6a b + 3a )cos(x) - 6a b + 3a +--R * +--R ROOT +--R 2 2 +--R (- 6b + 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--R (- 81a b + 162a b - 81a )%%EJ0 +--R + +--R 2 2 4 2 2 +--R (18a b - 18a )%%EJ0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 2 2 +--R (- 6b + 6a )%%EJ0 + 2 +--R / +--R 2 2 +--R 3b - 3a +--R + +--R 4b sin(x) +--R / +--R cos(x) + 1 +--R + +--R ROOT +--R 2 2 +--R (- 6b + 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--R (- 81a b + 162a b - 81a )%%EJ0 +--R + +--R 2 2 4 2 2 +--R (18a b - 18a )%%EJ0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 2 2 +--R (- 6b + 6a )%%EJ0 + 2 +--R / +--R 2 2 +--R 3b - 3a +--R * +--R log +--R 4 2 6 4 2 6 +--R ((- 243a b + 243a )cos(x) - 243a b + 243a )%%EJ0 +--R + +--R 2 2 4 2 2 4 +--R (- 27a b + 27a )cos(x) - 27a b + 27a +--R * +--R ROOT +--R 2 4 4 2 6 2 +--R (- 81a b + 162a b - 81a )%%EJ0 +--R + +--R 2 2 4 2 2 +--R (18a b - 18a )%%EJ0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 4 2 6 4 2 6 2 +--R ((243a b - 243a )cos(x) + 243a b - 243a )%%EJ0 +--R + +--R 2 2 4 2 2 4 +--R ((- 27a b - 54a )cos(x) - 27a b - 54a )%%EJ0 +--R + +--R 2 2 +--R (6a b - 3a )cos(x) + 6a b - 3a +--R * +--R ROOT +--R 2 2 +--R (- 6b + 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--R (- 81a b + 162a b - 81a )%%EJ0 +--R + +--R 2 2 4 2 2 +--R (18a b - 18a )%%EJ0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 2 2 +--R (- 6b + 6a )%%EJ0 + 2 +--R / +--R 2 2 +--R 3b - 3a +--R + +--R 4b sin(x) +--R / +--R cos(x) + 1 +--R + +--R - +--R ROOT +--R 2 2 +--R (6b - 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--R (- 81a b + 162a b - 81a )%%EJ0 +--R + +--R 2 2 4 2 2 +--R (18a b - 18a )%%EJ0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 2 2 +--R (- 6b + 6a )%%EJ0 + 2 +--R / +--R 2 2 +--R 3b - 3a +--R * +--R log +--R 4 2 6 4 2 6 +--R ((- 243a b + 243a )cos(x) - 243a b + 243a )%%EJ0 +--R + +--R 2 2 4 2 2 4 +--R (- 27a b + 27a )cos(x) - 27a b + 27a +--R * +--R ROOT +--R 2 4 4 2 6 2 +--R (- 81a b + 162a b - 81a )%%EJ0 +--R + +--R 2 2 4 2 2 +--R (18a b - 18a )%%EJ0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 4 2 6 4 2 6 2 +--R ((- 243a b + 243a )cos(x) - 243a b + 243a )%%EJ0 +--R + +--R 2 2 4 2 2 4 +--R ((27a b + 54a )cos(x) + 27a b + 54a )%%EJ0 +--R + +--R 2 2 +--R (- 6a b + 3a )cos(x) - 6a b + 3a +--R * +--R ROOT +--R 2 2 +--R (6b - 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--R (- 81a b + 162a b - 81a )%%EJ0 +--R + +--R 2 2 4 2 2 +--R (18a b - 18a )%%EJ0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 2 2 +--R (- 6b + 6a )%%EJ0 + 2 +--R / +--R 2 2 +--R 3b - 3a +--R + +--R 4b sin(x) +--R / +--R cos(x) + 1 +--R + +--R - +--R +------+ +--R \|4%%EJ0 +--R * +--R log +--R 4 2 6 4 2 6 2 +--R ((243a b - 243a )cos(x) + 243a b - 243a )%%EJ0 +--R + +--R 2 2 4 2 2 4 +--R ((- 27a b - 54a )cos(x) - 27a b - 54a )%%EJ0 +--R + +--R 2 2 +--R (- 3a b - 3a )cos(x) - 3a b - 3a +--R * +--R +------+ +--R \|4%%EJ0 +--R + +--R 2b sin(x) +--R / +--R cos(x) + 1 +--R + +--R +------+ +--R \|4%%EJ0 +--R * +--R log +--R 4 2 6 4 2 6 2 +--R ((- 243a b + 243a )cos(x) - 243a b + 243a )%%EJ0 +--R + +--R 2 2 4 2 2 4 +--R ((27a b + 54a )cos(x) + 27a b + 54a )%%EJ0 +--R + +--R 2 2 +--R (3a b + 3a )cos(x) + 3a b + 3a +--R * +--R +------+ +--R \|4%%EJ0 +--R + +--R 2b sin(x) +--R / +--R cos(x) + 1 +--R / +--R 2 +--R Type: Union(Expression Integer,...) +--R +--E 332 + +--S 333 of 504 +--m0163:= a0163-r0163 +--E 333 + +--S 334 of 504 +--d0163:= D(m0163,x) +--E 334 + +--S 335 of 504 +--Rt0164:= 1/(a+b*cos(x)^4) +--R +--R +--R 1 +--R (291) ------------- +--R 4 +--R b cos(x) + a +--R Type: Expression Integer +--R +--E 335 + +--S 336 of 504 +--Rr0164:= 1/2*atan(a^(1/4)*tan(x)/(a^(1/2)-(-b)^(1/2))^(1/2))/a^(3/4)/(a^(1/2)-(-b)^(1/2))^(1/2)+1/2*atan(a^(1/4)*tan(x)/(a^(1/2)+(-b)^(1/2))^(1/2))/a^(3/4)/(a^(1/2)+(-b)^(1/2))^(1/2) +--R +--R +--R (292) +--R +-------------+ 4+-+ +--R | +-+ +---+ tan(x)\|a +--R \|\|a + \|- b atan(----------------) +--R +-------------+ +--R | +-+ +---+ +--R \|\|a - \|- b +--R + +--R +-------------+ 4+-+ +--R | +-+ +---+ tan(x)\|a +--R \|\|a - \|- b atan(----------------) +--R +-------------+ +--R | +-+ +---+ +--R \|\|a + \|- b +--R / +--R +-------------+ +-------------+ +--R 4+-+3 | +-+ +---+ | +-+ +---+ +--R 2\|a \|\|a - \|- b \|\|a + \|- b +--R Type: Expression Integer +--R +--E 336 + +--S 337 of 504 +--Ra0164:= integrate(t0164,x) +--R +--R +--R (293) +--R +-------------------------------------------+ +--R | +------------------------+ +--R | 2 | b +--R |(8a b + 8a ) |- ---------------------- - 1 +--R | | 3 2 4 5 +--R | \| 64a b + 128a b + 64a +--R |------------------------------------------- +--R | 2 +--R \| 4a b + 4a +--R * +--R +-------------------------------------------+ +--R | +------------------------+ +--R | 2 | b +--R |(8a b + 8a ) |- ---------------------- - 1 +--R | | 3 2 4 5 +--R | \| 64a b + 128a b + 64a +--R 4a sin(x) |------------------------------------------- - 2cos(x) +--R | 2 +--R \| 4a b + 4a +--R log(-----------------------------------------------------------------) +--R cos(x) + 1 +--R + +--R +---------------------------------------------+ +--R | +------------------------+ +--R | 2 | b +--R |(- 8a b - 8a ) |- ---------------------- - 1 +--R | | 3 2 4 5 +--R | \| 64a b + 128a b + 64a +--R |--------------------------------------------- +--R | 2 +--R \| 4a b + 4a +--R * +--R +---------------------------------------------+ +--R | +------------------------+ +--R | 2 | b +--R |(- 8a b - 8a ) |- ---------------------- - 1 +--R | | 3 2 4 5 +--R | \| 64a b + 128a b + 64a +--R 4a sin(x) |--------------------------------------------- - 2cos(x) +--R | 2 +--R \| 4a b + 4a +--R log(-------------------------------------------------------------------) +--R cos(x) + 1 +--R + +--R - +--R +---------------------------------------------+ +--R | +------------------------+ +--R | 2 | b +--R |(- 8a b - 8a ) |- ---------------------- - 1 +--R | | 3 2 4 5 +--R | \| 64a b + 128a b + 64a +--R |--------------------------------------------- +--R | 2 +--R \| 4a b + 4a +--R * +--R log +--R +---------------------------------------------+ +--R | +------------------------+ +--R | 2 | b +--R |(- 8a b - 8a ) |- ---------------------- - 1 +--R | | 3 2 4 5 +--R | \| 64a b + 128a b + 64a +--R - 4a sin(x) |--------------------------------------------- +--R | 2 +--R \| 4a b + 4a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R - +--R +-------------------------------------------+ +--R | +------------------------+ +--R | 2 | b +--R |(8a b + 8a ) |- ---------------------- - 1 +--R | | 3 2 4 5 +--R | \| 64a b + 128a b + 64a +--R |------------------------------------------- +--R | 2 +--R \| 4a b + 4a +--R * +--R log +--R +-------------------------------------------+ +--R | +------------------------+ +--R | 2 | b +--R |(8a b + 8a ) |- ---------------------- - 1 +--R | | 3 2 4 5 +--R | \| 64a b + 128a b + 64a +--R - 4a sin(x) |------------------------------------------- +--R | 2 +--R \| 4a b + 4a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R / +--R 2 +--R Type: Union(Expression Integer,...) +--R +--E 337 + +--S 338 of 504 +--Rm0164:= a0164-r0164 +--R +--R +--R (294) +--R +-------------------------------------------+ +--R | +------------------------+ +--R | 2 | b +--R |(8a b + 8a ) |- ---------------------- - 1 +--R | | 3 2 4 5 +-------------+ +--R 4+-+3 | \| 64a b + 128a b + 64a | +-+ +---+ +--R \|a |------------------------------------------- \|\|a - \|- b +--R | 2 +--R \| 4a b + 4a +--R * +--R +-------------+ +--R | +-+ +---+ +--R \|\|a + \|- b +--R * +--R +-------------------------------------------+ +--R | +------------------------+ +--R | 2 | b +--R |(8a b + 8a ) |- ---------------------- - 1 +--R | | 3 2 4 5 +--R | \| 64a b + 128a b + 64a +--R 4a sin(x) |------------------------------------------- - 2cos(x) +--R | 2 +--R \| 4a b + 4a +--R log(-----------------------------------------------------------------) +--R cos(x) + 1 +--R + +--R +---------------------------------------------+ +--R | +------------------------+ +--R | 2 | b +--R |(- 8a b - 8a ) |- ---------------------- - 1 +--R | | 3 2 4 5 +-------------+ +--R 4+-+3 | \| 64a b + 128a b + 64a | +-+ +---+ +--R \|a |--------------------------------------------- \|\|a - \|- b +--R | 2 +--R \| 4a b + 4a +--R * +--R +-------------+ +--R | +-+ +---+ +--R \|\|a + \|- b +--R * +--R +---------------------------------------------+ +--R | +------------------------+ +--R | 2 | b +--R |(- 8a b - 8a ) |- ---------------------- - 1 +--R | | 3 2 4 5 +--R | \| 64a b + 128a b + 64a +--R 4a sin(x) |--------------------------------------------- - 2cos(x) +--R | 2 +--R \| 4a b + 4a +--R log(-------------------------------------------------------------------) +--R cos(x) + 1 +--R + +--R - +--R +---------------------------------------------+ +--R | +------------------------+ +--R | 2 | b +--R |(- 8a b - 8a ) |- ---------------------- - 1 +--R | | 3 2 4 5 +--R 4+-+3 | \| 64a b + 128a b + 64a +--R \|a |--------------------------------------------- +--R | 2 +--R \| 4a b + 4a +--R * +--R +-------------+ +-------------+ +--R | +-+ +---+ | +-+ +---+ +--R \|\|a - \|- b \|\|a + \|- b +--R * +--R log +--R +---------------------------------------------+ +--R | +------------------------+ +--R | 2 | b +--R |(- 8a b - 8a ) |- ---------------------- - 1 +--R | | 3 2 4 5 +--R | \| 64a b + 128a b + 64a +--R - 4a sin(x) |--------------------------------------------- +--R | 2 +--R \| 4a b + 4a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R - +--R +-------------------------------------------+ +--R | +------------------------+ +--R | 2 | b +--R |(8a b + 8a ) |- ---------------------- - 1 +--R | | 3 2 4 5 +-------------+ +--R 4+-+3 | \| 64a b + 128a b + 64a | +-+ +---+ +--R \|a |------------------------------------------- \|\|a - \|- b +--R | 2 +--R \| 4a b + 4a +--R * +--R +-------------+ +--R | +-+ +---+ +--R \|\|a + \|- b +--R * +--R log +--R +-------------------------------------------+ +--R | +------------------------+ +--R | 2 | b +--R |(8a b + 8a ) |- ---------------------- - 1 +--R | | 3 2 4 5 +--R | \| 64a b + 128a b + 64a +--R - 4a sin(x) |------------------------------------------- +--R | 2 +--R \| 4a b + 4a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R +-------------+ 4+-+ +--R | +-+ +---+ tan(x)\|a +--R - \|\|a + \|- b atan(----------------) +--R +-------------+ +--R | +-+ +---+ +--R \|\|a - \|- b +--R + +--R +-------------+ 4+-+ +--R | +-+ +---+ tan(x)\|a +--R - \|\|a - \|- b atan(----------------) +--R +-------------+ +--R | +-+ +---+ +--R \|\|a + \|- b +--R / +--R +-------------+ +-------------+ +--R 4+-+3 | +-+ +---+ | +-+ +---+ +--R 2\|a \|\|a - \|- b \|\|a + \|- b +--R Type: Expression Integer +--R +--E 338 + +--S 339 of 504 +--Rd0164:= D(m0164,x) +--R +--R +--R (295) +--R 4 4 +--R - b cos(x) tan(x) +--R + +--R 4 2 2 4 2 +--R (- a sin(x) - 2a cos(x) sin(x) + (- b - a)cos(x) )tan(x) +--R + +--R 4 2 2 4 +--R (b + a)sin(x) + (2b + 2a)cos(x) sin(x) + (b + a)cos(x) +--R * +--R 4+-+2 +--R \|a +--R + +--R 4 2 2 4 2 4 +--R (a sin(x) + 2a cos(x) sin(x) + (- b + a)cos(x) )tan(x) - a sin(x) +--R + +--R 2 2 4 +--R - 2a cos(x) sin(x) + (- b - a)cos(x) +--R * +--R +-+ +--R \|a +--R / +--R 2 4 2 2 2 2 4 4 +--R (a sin(x) + 2a cos(x) sin(x) + (a b + a )cos(x) )tan(x) +--R + +--R 2 4 2 2 2 +--R (a b + a )sin(x) + (2a b + 2a )cos(x) sin(x) +--R + +--R 2 2 4 +--R (b + 2a b + a )cos(x) +--R * +--R 4+-+2 +--R \|a +--R + +--R 2 4 2 2 2 2 4 2 +-+ +--R (2a sin(x) + 4a cos(x) sin(x) + (2a b + 2a )cos(x) )tan(x) \|a +--R Type: Expression Integer +--R +--E 339 + +--S 340 of 504 +--Rt0165:= 1/(a+b*cos(x)^6) +--R +--R +--R 1 +--R (296) ------------- +--R 6 +--R b cos(x) + a +--R Type: Expression Integer +--R +--E 340 + +--S 341 of 504 +--Rr0165:= 1/3*atan(a^(1/6)*tan(x)/(a^(1/3)+b^(1/3))^(1/2))/a^(5/6)/(a^(1/3)+b^(1/3))^(1/2)+1/3*atan(a^(1/6)*tan(x)/(a^(1/3)-(-1)^(1/3)*b^(1/3))^(1/2))/a^(5/6)/(a^(1/3)-(-1)^(1/3)*b^(1/3))^(1/2)+1/3*atan(a^(1/6)*tan(x)/(a^(1/3)+(-1)^(2/3)*b^(1/3))^(1/2))/a^(5/6)/(a^(1/3)+(-1)^(2/3)*b^(1/3))^(1/2) +--R +--R +--R (297) +--R +-----------+ +------------------+ 6+-+ +--R |3+-+ 3+-+ |3+---+2 3+-+ 3+-+ tan(x)\|a +--R \|\|b + \|a \|\|- 1 \|b + \|a atan(----------------------) +--R +-------------------+ +--R | 3+---+3+-+ 3+-+ +--R \|- \|- 1 \|b + \|a +--R + +--R +-------------------+ +------------------+ 6+-+ +--R | 3+---+3+-+ 3+-+ |3+---+2 3+-+ 3+-+ tan(x)\|a +--R \|- \|- 1 \|b + \|a \|\|- 1 \|b + \|a atan(--------------) +--R +-----------+ +--R |3+-+ 3+-+ +--R \|\|b + \|a +--R + +--R +-------------------+ +-----------+ 6+-+ +--R | 3+---+3+-+ 3+-+ |3+-+ 3+-+ tan(x)\|a +--R \|- \|- 1 \|b + \|a \|\|b + \|a atan(---------------------) +--R +------------------+ +--R |3+---+2 3+-+ 3+-+ +--R \|\|- 1 \|b + \|a +--R / +--R +-------------------+ +-----------+ +------------------+ +--R 6+-+5 | 3+---+3+-+ 3+-+ |3+-+ 3+-+ |3+---+2 3+-+ 3+-+ +--R 3\|a \|- \|- 1 \|b + \|a \|\|b + \|a \|\|- 1 \|b + \|a +--R Type: Expression Integer +--R +--E 341 + +--S 342 of 504 +--Ra0165:= integrate(t0165,x) +--R +--R +--R (298) +--R ROOT +--R 2 +--R (12a b + 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--R (- 1296a b - 2592a b - 1296a )%%EL0 +--R + +--R 2 3 +--R (- 72a b - 72a )%%EL0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 2 +--R (- 12a b - 12a )%%EL0 - 1 +--R / +--R 2 +--R 6a b + 6a +--R * +--R log +--R 6a sin(x) +--R * +--R ROOT +--R 2 +--R (12a b + 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--R (- 1296a b - 2592a b - 1296a )%%EL0 +--R + +--R 2 3 +--R (- 72a b - 72a )%%EL0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 2 +--R (- 12a b - 12a )%%EL0 - 1 +--R / +--R 2 +--R 6a b + 6a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R ROOT +--R 2 +--R (- 12a b - 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--R (- 1296a b - 2592a b - 1296a )%%EL0 +--R + +--R 2 3 +--R (- 72a b - 72a )%%EL0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 2 +--R (- 12a b - 12a )%%EL0 - 1 +--R / +--R 2 +--R 6a b + 6a +--R * +--R log +--R 6a sin(x) +--R * +--R ROOT +--R 2 +--R (- 12a b - 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--R (- 1296a b - 2592a b - 1296a )%%EL0 +--R + +--R 2 3 +--R (- 72a b - 72a )%%EL0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 2 +--R (- 12a b - 12a )%%EL0 - 1 +--R / +--R 2 +--R 6a b + 6a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R - +--R ROOT +--R 2 +--R (- 12a b - 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--R (- 1296a b - 2592a b - 1296a )%%EL0 +--R + +--R 2 3 +--R (- 72a b - 72a )%%EL0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 2 +--R (- 12a b - 12a )%%EL0 - 1 +--R / +--R 2 +--R 6a b + 6a +--R * +--R log +--R - +--R 6a sin(x) +--R * +--R ROOT +--R 2 +--R (- 12a b - 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--R (- 1296a b - 2592a b - 1296a )%%EL0 +--R + +--R 2 3 +--R (- 72a b - 72a )%%EL0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 2 +--R (- 12a b - 12a )%%EL0 - 1 +--R / +--R 2 +--R 6a b + 6a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R - +--R ROOT +--R 2 +--R (12a b + 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--R (- 1296a b - 2592a b - 1296a )%%EL0 +--R + +--R 2 3 +--R (- 72a b - 72a )%%EL0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 2 +--R (- 12a b - 12a )%%EL0 - 1 +--R / +--R 2 +--R 6a b + 6a +--R * +--R log +--R - +--R 6a sin(x) +--R * +--R ROOT +--R 2 +--R (12a b + 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--R (- 1296a b - 2592a b - 1296a )%%EL0 +--R + +--R 2 3 +--R (- 72a b - 72a )%%EL0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 2 +--R (- 12a b - 12a )%%EL0 - 1 +--R / +--R 2 +--R 6a b + 6a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R +------+ +--R +------+ 6a sin(x)\|4%%EL0 - 2cos(x) +--R \|4%%EL0 log(----------------------------) +--R cos(x) + 1 +--R + +--R +------+ +--R +------+ - 6a sin(x)\|4%%EL0 - 2cos(x) +--R - \|4%%EL0 log(------------------------------) +--R cos(x) + 1 +--R / +--R 2 +--R Type: Union(Expression Integer,...) +--R +--E 342 + +--S 343 of 504 +--Rm0165:= a0165-r0165 +--R +--R +--R (299) +--R +-------------------+ +-----------+ +------------------+ +--R 6+-+5 | 3+---+3+-+ 3+-+ |3+-+ 3+-+ |3+---+2 3+-+ 3+-+ +--R 3\|a \|- \|- 1 \|b + \|a \|\|b + \|a \|\|- 1 \|b + \|a +--R * +--R ROOT +--R 2 +--R (12a b + 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--R (- 1296a b - 2592a b - 1296a )%%EL0 +--R + +--R 2 3 +--R (- 72a b - 72a )%%EL0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 2 +--R (- 12a b - 12a )%%EL0 - 1 +--R / +--R 2 +--R 6a b + 6a +--R * +--R log +--R 6a sin(x) +--R * +--R ROOT +--R 2 +--R (12a b + 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--R (- 1296a b - 2592a b - 1296a )%%EL0 +--R + +--R 2 3 +--R (- 72a b - 72a )%%EL0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 2 +--R (- 12a b - 12a )%%EL0 - 1 +--R / +--R 2 +--R 6a b + 6a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R +-------------------+ +-----------+ +------------------+ +--R 6+-+5 | 3+---+3+-+ 3+-+ |3+-+ 3+-+ |3+---+2 3+-+ 3+-+ +--R 3\|a \|- \|- 1 \|b + \|a \|\|b + \|a \|\|- 1 \|b + \|a +--R * +--R ROOT +--R 2 +--R (- 12a b - 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--R (- 1296a b - 2592a b - 1296a )%%EL0 +--R + +--R 2 3 +--R (- 72a b - 72a )%%EL0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 2 +--R (- 12a b - 12a )%%EL0 - 1 +--R / +--R 2 +--R 6a b + 6a +--R * +--R log +--R 6a sin(x) +--R * +--R ROOT +--R 2 +--R (- 12a b - 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--R (- 1296a b - 2592a b - 1296a )%%EL0 +--R + +--R 2 3 +--R (- 72a b - 72a )%%EL0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 2 +--R (- 12a b - 12a )%%EL0 - 1 +--R / +--R 2 +--R 6a b + 6a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R - +--R +-------------------+ +-----------+ +------------------+ +--R 6+-+5 | 3+---+3+-+ 3+-+ |3+-+ 3+-+ |3+---+2 3+-+ 3+-+ +--R 3\|a \|- \|- 1 \|b + \|a \|\|b + \|a \|\|- 1 \|b + \|a +--R * +--R ROOT +--R 2 +--R (- 12a b - 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--R (- 1296a b - 2592a b - 1296a )%%EL0 +--R + +--R 2 3 +--R (- 72a b - 72a )%%EL0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 2 +--R (- 12a b - 12a )%%EL0 - 1 +--R / +--R 2 +--R 6a b + 6a +--R * +--R log +--R - +--R 6a sin(x) +--R * +--R ROOT +--R 2 +--R (- 12a b - 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--R (- 1296a b - 2592a b - 1296a )%%EL0 +--R + +--R 2 3 +--R (- 72a b - 72a )%%EL0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 2 +--R (- 12a b - 12a )%%EL0 - 1 +--R / +--R 2 +--R 6a b + 6a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R - +--R +-------------------+ +-----------+ +------------------+ +--R 6+-+5 | 3+---+3+-+ 3+-+ |3+-+ 3+-+ |3+---+2 3+-+ 3+-+ +--R 3\|a \|- \|- 1 \|b + \|a \|\|b + \|a \|\|- 1 \|b + \|a +--R * +--R ROOT +--R 2 +--R (12a b + 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--R (- 1296a b - 2592a b - 1296a )%%EL0 +--R + +--R 2 3 +--R (- 72a b - 72a )%%EL0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 2 +--R (- 12a b - 12a )%%EL0 - 1 +--R / +--R 2 +--R 6a b + 6a +--R * +--R log +--R - +--R 6a sin(x) +--R * +--R ROOT +--R 2 +--R (12a b + 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--R (- 1296a b - 2592a b - 1296a )%%EL0 +--R + +--R 2 3 +--R (- 72a b - 72a )%%EL0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 2 +--R (- 12a b - 12a )%%EL0 - 1 +--R / +--R 2 +--R 6a b + 6a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R +-------------------+ +-----------+ +------------------+ +--R 6+-+5 | 3+---+3+-+ 3+-+ |3+-+ 3+-+ |3+---+2 3+-+ 3+-+ +--R 3\|a \|- \|- 1 \|b + \|a \|\|b + \|a \|\|- 1 \|b + \|a +--R * +--R +------+ +--R +------+ 6a sin(x)\|4%%EL0 - 2cos(x) +--R \|4%%EL0 log(----------------------------) +--R cos(x) + 1 +--R + +--R - +--R +-------------------+ +-----------+ +------------------+ +--R 6+-+5 | 3+---+3+-+ 3+-+ |3+-+ 3+-+ |3+---+2 3+-+ 3+-+ +--R 3\|a \|- \|- 1 \|b + \|a \|\|b + \|a \|\|- 1 \|b + \|a +--R * +--R +------+ +--R +------+ - 6a sin(x)\|4%%EL0 - 2cos(x) +--R \|4%%EL0 log(------------------------------) +--R cos(x) + 1 +--R + +--R +-----------+ +------------------+ 6+-+ +--R |3+-+ 3+-+ |3+---+2 3+-+ 3+-+ tan(x)\|a +--R - 2\|\|b + \|a \|\|- 1 \|b + \|a atan(----------------------) +--R +-------------------+ +--R | 3+---+3+-+ 3+-+ +--R \|- \|- 1 \|b + \|a +--R + +--R +-------------------+ +------------------+ 6+-+ +--R | 3+---+3+-+ 3+-+ |3+---+2 3+-+ 3+-+ tan(x)\|a +--R - 2\|- \|- 1 \|b + \|a \|\|- 1 \|b + \|a atan(--------------) +--R +-----------+ +--R |3+-+ 3+-+ +--R \|\|b + \|a +--R + +--R +-------------------+ +-----------+ 6+-+ +--R | 3+---+3+-+ 3+-+ |3+-+ 3+-+ tan(x)\|a +--R - 2\|- \|- 1 \|b + \|a \|\|b + \|a atan(---------------------) +--R +------------------+ +--R |3+---+2 3+-+ 3+-+ +--R \|\|- 1 \|b + \|a +--R / +--R +-------------------+ +-----------+ +------------------+ +--R 6+-+5 | 3+---+3+-+ 3+-+ |3+-+ 3+-+ |3+---+2 3+-+ 3+-+ +--R 6\|a \|- \|- 1 \|b + \|a \|\|b + \|a \|\|- 1 \|b + \|a +--R Type: Expression Integer +--R +--E 343 + +--S 344 of 504 +--Rd0165:= D(m0165,x) +--R +--R +--R (300) +--R 3+---+2 3+---+ 6 6 +--R (- 3b \|- 1 + 3b\|- 1 - 3b)cos(x) tan(x) +--R + +--R 3+---+2 3+---+ 6 +--R (- 3a \|- 1 + 3a\|- 1 - 3a)sin(x) +--R + +--R 3+---+2 3+---+ 2 4 +--R (- 9a \|- 1 + 9a\|- 1 - 9a)cos(x) sin(x) +--R + +--R 3+---+2 3+---+ 4 2 +--R (- 9a \|- 1 + 9a\|- 1 - 9a)cos(x) sin(x) +--R + +--R 3+---+2 3+---+ 6 +--R ((- 3b - 3a)\|- 1 + (3b + 3a)\|- 1 - 3b - 3a)cos(x) +--R * +--R 4 +--R tan(x) +--R + +--R 3+---+2 3+---+ 6 +--R ((6b + 15a)\|- 1 + (- 6b - 15a)\|- 1 + 6b + 15a)sin(x) +--R + +--R 3+---+2 3+---+ 2 +--R ((18b + 45a)\|- 1 + (- 18b - 45a)\|- 1 + 18b + 45a)cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 3+---+2 3+---+ 4 +--R ((18b + 45a)\|- 1 + (- 18b - 45a)\|- 1 + 18b + 45a)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 3+---+2 3+---+ 6 +--R ((6b + 15a)\|- 1 + (- 6b - 15a)\|- 1 + 6b + 15a)cos(x) +--R * +--R 3+-+6+-+4 +--R \|a \|a +--R + +--R 3+---+2 3+---+ 6 +--R (6a \|- 1 - 6a\|- 1 + 6a)sin(x) +--R + +--R 3+---+2 3+---+ 2 4 +--R (18a \|- 1 - 18a\|- 1 + 18a)cos(x) sin(x) +--R + +--R 3+---+2 3+---+ 4 2 +--R (18a \|- 1 - 18a\|- 1 + 18a)cos(x) sin(x) +--R + +--R 3+---+2 3+---+ 6 +--R ((- 12b + 6a)\|- 1 + (12b - 6a)\|- 1 - 12b + 6a)cos(x) +--R * +--R 4 +--R tan(x) +--R + +--R 3+---+2 3+---+ 6 +--R (- 12a \|- 1 + 12a\|- 1 - 12a)sin(x) +--R + +--R 3+---+2 3+---+ 2 4 +--R (- 36a \|- 1 + 36a\|- 1 - 36a)cos(x) sin(x) +--R + +--R 3+---+2 3+---+ 4 2 +--R (- 36a \|- 1 + 36a\|- 1 - 36a)cos(x) sin(x) +--R + +--R 3+---+2 3+---+ 6 +--R ((- 12b - 12a)\|- 1 + (12b + 12a)\|- 1 - 12b - 12a)cos(x) +--R * +--R 2 +--R tan(x) +--R * +--R 3+-+2 6+-+2 +--R \|a \|a +--R + +--R 2 3+---+2 2 3+---+ 2 +--R ((2a b + 20a )\|- 1 + (- 2a b - 20a )\|- 1 + 2a b + 20a ) +--R * +--R 6 +--R sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R ((6a b + 60a )\|- 1 + (- 6a b - 60a )\|- 1 + 6a b + 60a ) +--R * +--R 2 4 +--R cos(x) sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R ((6a b + 60a )\|- 1 + (- 6a b - 60a )\|- 1 + 6a b + 60a ) +--R * +--R 4 2 +--R cos(x) sin(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 +--R (- b - 8a b + 20a )\|- 1 + (b + 8a b - 20a )\|- 1 - b +--R + +--R 2 +--R - 8a b + 20a +--R * +--R 6 +--R cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 2 3+---+2 2 3+---+ 2 6 +--R ((- a b - 10a )\|- 1 + (a b + 10a )\|- 1 - a b - 10a )sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 +--R ((- 3a b - 30a )\|- 1 + (3a b + 30a )\|- 1 - 3a b - 30a )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 4 +--R ((- 3a b - 30a )\|- 1 + (3a b + 30a )\|- 1 - 3a b - 30a )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 +--R (- b - 11a b - 10a )\|- 1 + (b + 11a b + 10a )\|- 1 - b +--R + +--R 2 +--R - 11a b - 10a +--R * +--R 6 +--R cos(x) +--R * +--R 3+-+2 +--R \|b +--R + +--R 3+---+2 3+---+ 6 6 +--R (- 3b \|- 1 + 3b\|- 1 - 3b)cos(x) tan(x) +--R + +--R 3+---+2 3+---+ 6 +--R (- 3a \|- 1 + 3a\|- 1 - 3a)sin(x) +--R + +--R 3+---+2 3+---+ 2 4 +--R (- 9a \|- 1 + 9a\|- 1 - 9a)cos(x) sin(x) +--R + +--R 3+---+2 3+---+ 4 2 +--R (- 9a \|- 1 + 9a\|- 1 - 9a)cos(x) sin(x) +--R + +--R 3+---+2 3+---+ 6 +--R ((- 3b - 3a)\|- 1 + (3b + 3a)\|- 1 - 3b - 3a)cos(x) +--R * +--R 4 +--R tan(x) +--R + +--R 3+---+2 3+---+ 6 +--R ((15b + 6a)\|- 1 + (- 15b - 6a)\|- 1 + 15b + 6a)sin(x) +--R + +--R 3+---+2 3+---+ 2 +--R ((45b + 18a)\|- 1 + (- 45b - 18a)\|- 1 + 45b + 18a)cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 3+---+2 3+---+ 4 +--R ((45b + 18a)\|- 1 + (- 45b - 18a)\|- 1 + 45b + 18a)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 3+---+2 3+---+ 6 +--R ((15b + 6a)\|- 1 + (- 15b - 6a)\|- 1 + 15b + 6a)cos(x) +--R * +--R 3+-+2 6+-+4 +--R \|a \|a +--R + +--R 2 3+---+2 2 3+---+ 2 6 +--R ((a b + 4a )\|- 1 + (- a b - 4a )\|- 1 + a b + 4a )sin(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (3a b + 12a )\|- 1 + (- 3a b - 12a )\|- 1 + 3a b +--R + +--R 2 +--R 12a +--R * +--R 2 4 +--R cos(x) sin(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (3a b + 12a )\|- 1 + (- 3a b - 12a )\|- 1 + 3a b +--R + +--R 2 +--R 12a +--R * +--R 4 2 +--R cos(x) sin(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ +--R (- 2b - 7a b + 4a )\|- 1 + (2b + 7a b - 4a )\|- 1 +--R + +--R 2 2 +--R - 2b - 7a b + 4a +--R * +--R 6 +--R cos(x) +--R * +--R 4 +--R tan(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R ((- 2a b - 8a )\|- 1 + (2a b + 8a )\|- 1 - 2a b - 8a ) +--R * +--R 6 +--R sin(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (- 6a b - 24a )\|- 1 + (6a b + 24a )\|- 1 - 6a b +--R + +--R 2 +--R - 24a +--R * +--R 2 4 +--R cos(x) sin(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (- 6a b - 24a )\|- 1 + (6a b + 24a )\|- 1 - 6a b +--R + +--R 2 +--R - 24a +--R * +--R 4 2 +--R cos(x) sin(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ +--R (- 2b - 10a b - 8a )\|- 1 + (2b + 10a b + 8a )\|- 1 +--R + +--R 2 2 +--R - 2b - 10a b - 8a +--R * +--R 6 +--R cos(x) +--R * +--R 2 +--R tan(x) +--R * +--R 6+-+2 +--R \|a +--R + +--R 2 3+---+2 2 3+---+ +--R (10a b + 10a )\|- 1 + (- 10a b - 10a )\|- 1 + 10a b +--R + +--R 2 +--R 10a +--R * +--R 6 +--R sin(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (30a b + 30a )\|- 1 + (- 30a b - 30a )\|- 1 + 30a b +--R + +--R 2 +--R 30a +--R * +--R 2 4 +--R cos(x) sin(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (30a b + 30a )\|- 1 + (- 30a b - 30a )\|- 1 + 30a b +--R + +--R 2 +--R 30a +--R * +--R 4 2 +--R cos(x) sin(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ +--R (- 5b + 5a b + 10a )\|- 1 + (5b - 5a b - 10a )\|- 1 +--R + +--R 2 2 +--R - 5b + 5a b + 10a +--R * +--R 6 +--R cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 2 3+---+2 2 3+---+ 2 6 +--R ((- 5a b - 5a )\|- 1 + (5a b + 5a )\|- 1 - 5a b - 5a )sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R ((- 15a b - 15a )\|- 1 + (15a b + 15a )\|- 1 - 15a b - 15a ) +--R * +--R 2 4 +--R cos(x) sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R ((- 15a b - 15a )\|- 1 + (15a b + 15a )\|- 1 - 15a b - 15a ) +--R * +--R 4 2 +--R cos(x) sin(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ +--R (- 5b - 10a b - 5a )\|- 1 + (5b + 10a b + 5a )\|- 1 +--R + +--R 2 2 +--R - 5b - 10a b - 5a +--R * +--R 6 +--R cos(x) +--R * +--R 3+-+ +--R \|a +--R * +--R 3+-+ +--R \|b +--R + +--R 2 6 6 +--R (- 3b - 3a b)cos(x) tan(x) +--R + +--R 2 6 2 2 4 +--R (- 3a b - 3a )sin(x) + (- 9a b - 9a )cos(x) sin(x) +--R + +--R 2 4 2 2 2 6 +--R (- 9a b - 9a )cos(x) sin(x) + (- 3b - 6a b - 3a )cos(x) +--R * +--R 4 +--R tan(x) +--R + +--R 3+---+2 3+---+ 2 2 6 +--R (18a b \|- 1 - 18a b\|- 1 + 3b + 24a b + 3a )sin(x) +--R + +--R 3+---+2 3+---+ 2 2 2 4 +--R (54a b \|- 1 - 54a b\|- 1 + 9b + 72a b + 9a )cos(x) sin(x) +--R + +--R 3+---+2 3+---+ 2 2 4 2 +--R (54a b \|- 1 - 54a b\|- 1 + 9b + 72a b + 9a )cos(x) sin(x) +--R + +--R 3+---+2 3+---+ 2 2 6 +--R (18a b \|- 1 - 18a b\|- 1 + 3b + 24a b + 3a )cos(x) +--R * +--R 6+-+4 +--R \|a +--R + +--R 3+---+2 3+---+ 2 6 +--R (3a b \|- 1 - 3a b\|- 1 + 6a b + 3a )sin(x) +--R + +--R 3+---+2 3+---+ 2 2 4 +--R (9a b \|- 1 - 9a b\|- 1 + 18a b + 9a )cos(x) sin(x) +--R + +--R 3+---+2 3+---+ 2 4 2 +--R (9a b \|- 1 - 9a b\|- 1 + 18a b + 9a )cos(x) sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 6 +--R ((- 6b + 3a b)\|- 1 + (6b - 3a b)\|- 1 - 12b + 3a )cos(x) +--R * +--R 4 +--R tan(x) +--R + +--R 3+---+2 3+---+ 2 6 +--R (- 6a b \|- 1 + 6a b\|- 1 - 12a b - 6a )sin(x) +--R + +--R 3+---+2 3+---+ 2 2 4 +--R (- 18a b \|- 1 + 18a b\|- 1 - 36a b - 18a )cos(x) sin(x) +--R + +--R 3+---+2 3+---+ 2 4 2 +--R (- 18a b \|- 1 + 18a b\|- 1 - 36a b - 18a )cos(x) sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (- 6b - 6a b)\|- 1 + (6b + 6a b)\|- 1 - 12b - 18a b +--R + +--R 2 +--R - 6a +--R * +--R 6 +--R cos(x) +--R * +--R 2 +--R tan(x) +--R * +--R 3+-+6+-+2 +--R \|a \|a +--R + +--R 3+---+2 3+---+ 2 6 +--R (18a b \|- 1 - 18a b\|- 1 + 24a b + 6a )sin(x) +--R + +--R 3+---+2 3+---+ 2 2 4 +--R (54a b \|- 1 - 54a b\|- 1 + 72a b + 18a )cos(x) sin(x) +--R + +--R 3+---+2 3+---+ 2 4 2 +--R (54a b \|- 1 - 54a b\|- 1 + 72a b + 18a )cos(x) sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (- 9b + 18a b)\|- 1 + (9b - 18a b)\|- 1 - 12b + 21a b +--R + +--R 2 +--R 6a +--R * +--R 6 +--R cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 3+---+2 3+---+ 2 6 +--R (- 9a b \|- 1 + 9a b\|- 1 - 12a b - 3a )sin(x) +--R + +--R 3+---+2 3+---+ 2 2 4 +--R (- 27a b \|- 1 + 27a b\|- 1 - 36a b - 9a )cos(x) sin(x) +--R + +--R 3+---+2 3+---+ 2 4 2 +--R (- 27a b \|- 1 + 27a b\|- 1 - 36a b - 9a )cos(x) sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 +--R ((- 9b - 9a b)\|- 1 + (9b + 9a b)\|- 1 - 12b - 15a b - 3a ) +--R * +--R 6 +--R cos(x) +--R * +--R 3+-+2 +--R \|a +--R / +--R 2 3+---+2 2 3+---+ 2 6 +--R (3a \|- 1 - 3a \|- 1 + 3a )sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 4 +--R (9a \|- 1 - 9a \|- 1 + 9a )cos(x) sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 4 2 +--R (9a \|- 1 - 9a \|- 1 + 9a )cos(x) sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R ((3a b + 3a )\|- 1 + (- 3a b - 3a )\|- 1 + 3a b + 3a ) +--R * +--R 6 +--R cos(x) +--R * +--R 6 +--R tan(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R ((6a b + 15a )\|- 1 + (- 6a b - 15a )\|- 1 + 6a b + 15a ) +--R * +--R 6 +--R sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R ((18a b + 45a )\|- 1 + (- 18a b - 45a )\|- 1 + 18a b + 45a ) +--R * +--R 2 4 +--R cos(x) sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R ((18a b + 45a )\|- 1 + (- 18a b - 45a )\|- 1 + 18a b + 45a ) +--R * +--R 4 2 +--R cos(x) sin(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ +--R (6b + 21a b + 15a )\|- 1 + (- 6b - 21a b - 15a )\|- 1 +--R + +--R 2 2 +--R 6b + 21a b + 15a +--R * +--R 6 +--R cos(x) +--R * +--R 3+-+6+-+4 +--R \|a \|a +--R + +--R 2 3+---+2 2 3+---+ 2 6 +--R (18a \|- 1 - 18a \|- 1 + 18a )sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 4 +--R (54a \|- 1 - 54a \|- 1 + 54a )cos(x) sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 4 2 +--R (54a \|- 1 - 54a \|- 1 + 54a )cos(x) sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R ((18a b + 18a )\|- 1 + (- 18a b - 18a )\|- 1 + 18a b + 18a ) +--R * +--R 6 +--R cos(x) +--R * +--R 4 3+-+2 6+-+2 +--R tan(x) \|a \|a +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 3 +--R ((3a b + 30a )\|- 1 + (- 3a b - 30a )\|- 1 + 3a b + 30a ) +--R * +--R 6 +--R sin(x) +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 3 +--R ((9a b + 90a )\|- 1 + (- 9a b - 90a )\|- 1 + 9a b + 90a ) +--R * +--R 2 4 +--R cos(x) sin(x) +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 3 +--R ((9a b + 90a )\|- 1 + (- 9a b - 90a )\|- 1 + 9a b + 90a ) +--R * +--R 4 2 +--R cos(x) sin(x) +--R + +--R 2 2 3 3+---+2 +--R (3a b + 33a b + 30a )\|- 1 +--R + +--R 2 2 3 3+---+ 2 2 3 +--R (- 3a b - 33a b - 30a )\|- 1 + 3a b + 33a b + 30a +--R * +--R 6 +--R cos(x) +--R * +--R 2 +--R tan(x) +--R * +--R 3+-+2 +--R \|b +--R + +--R 2 3+---+2 2 3+---+ 2 6 +--R (3a \|- 1 - 3a \|- 1 + 3a )sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 4 +--R (9a \|- 1 - 9a \|- 1 + 9a )cos(x) sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 4 2 +--R (9a \|- 1 - 9a \|- 1 + 9a )cos(x) sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R ((3a b + 3a )\|- 1 + (- 3a b - 3a )\|- 1 + 3a b + 3a ) +--R * +--R 6 +--R cos(x) +--R * +--R 6 +--R tan(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R ((15a b + 6a )\|- 1 + (- 15a b - 6a )\|- 1 + 15a b + 6a ) +--R * +--R 6 +--R sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R ((45a b + 18a )\|- 1 + (- 45a b - 18a )\|- 1 + 45a b + 18a ) +--R * +--R 2 4 +--R cos(x) sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R ((45a b + 18a )\|- 1 + (- 45a b - 18a )\|- 1 + 45a b + 18a ) +--R * +--R 4 2 +--R cos(x) sin(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ +--R (15b + 21a b + 6a )\|- 1 + (- 15b - 21a b - 6a )\|- 1 +--R + +--R 2 2 +--R 15b + 21a b + 6a +--R * +--R 6 +--R cos(x) +--R * +--R 3+-+2 6+-+4 +--R \|a \|a +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 3 +--R ((3a b + 12a )\|- 1 + (- 3a b - 12a )\|- 1 + 3a b + 12a ) +--R * +--R 6 +--R sin(x) +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 3 +--R ((9a b + 36a )\|- 1 + (- 9a b - 36a )\|- 1 + 9a b + 36a ) +--R * +--R 2 4 +--R cos(x) sin(x) +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 3 +--R ((9a b + 36a )\|- 1 + (- 9a b - 36a )\|- 1 + 9a b + 36a ) +--R * +--R 4 2 +--R cos(x) sin(x) +--R + +--R 2 2 3 3+---+2 +--R (3a b + 15a b + 12a )\|- 1 +--R + +--R 2 2 3 3+---+ 2 2 3 +--R (- 3a b - 15a b - 12a )\|- 1 + 3a b + 15a b + 12a +--R * +--R 6 +--R cos(x) +--R * +--R 4 6+-+2 +--R tan(x) \|a +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 3 +--R ((15a b + 15a )\|- 1 + (- 15a b - 15a )\|- 1 + 15a b + 15a ) +--R * +--R 6 +--R sin(x) +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 3 +--R ((45a b + 45a )\|- 1 + (- 45a b - 45a )\|- 1 + 45a b + 45a ) +--R * +--R 2 4 +--R cos(x) sin(x) +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 3 +--R ((45a b + 45a )\|- 1 + (- 45a b - 45a )\|- 1 + 45a b + 45a ) +--R * +--R 4 2 +--R cos(x) sin(x) +--R + +--R 2 2 3 3+---+2 +--R (15a b + 30a b + 15a )\|- 1 +--R + +--R 2 2 3 3+---+ 2 2 3 +--R (- 15a b - 30a b - 15a )\|- 1 + 15a b + 30a b + 15a +--R * +--R 6 +--R cos(x) +--R * +--R 2 3+-+ +--R tan(x) \|a +--R * +--R 3+-+ +--R \|b +--R + +--R 2 3 6 2 3 2 4 +--R (3a b + 3a )sin(x) + (9a b + 9a )cos(x) sin(x) +--R + +--R 2 3 4 2 2 2 3 6 +--R (9a b + 9a )cos(x) sin(x) + (3a b + 6a b + 3a )cos(x) +--R * +--R 6 +--R tan(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 3 6 +--R (18a b \|- 1 - 18a b\|- 1 + 3a b + 24a b + 3a )sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 3 2 4 +--R (54a b \|- 1 - 54a b\|- 1 + 9a b + 72a b + 9a )cos(x) sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 3 4 2 +--R (54a b \|- 1 - 54a b\|- 1 + 9a b + 72a b + 9a )cos(x) sin(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 3 2 +--R (18a b + 18a b)\|- 1 + (- 18a b - 18a b)\|- 1 + 3b + 27a b +--R + +--R 2 3 +--R 27a b + 3a +--R * +--R 6 +--R cos(x) +--R * +--R 6+-+4 +--R \|a +--R + +--R 2 3+---+2 2 3+---+ 2 3 6 +--R (9a b \|- 1 - 9a b\|- 1 + 18a b + 9a )sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 3 2 4 +--R (27a b \|- 1 - 27a b\|- 1 + 54a b + 27a )cos(x) sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 3 4 2 +--R (27a b \|- 1 - 27a b\|- 1 + 54a b + 27a )cos(x) sin(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 +--R (9a b + 9a b)\|- 1 + (- 9a b - 9a b)\|- 1 + 18a b + 27a b +--R + +--R 3 +--R 9a +--R * +--R 6 +--R cos(x) +--R * +--R 4 3+-+6+-+2 +--R tan(x) \|a \|a +--R + +--R 2 3+---+2 2 3+---+ 2 3 6 +--R (27a b \|- 1 - 27a b\|- 1 + 36a b + 9a )sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 3 2 4 +--R (81a b \|- 1 - 81a b\|- 1 + 108a b + 27a )cos(x) sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 3 4 2 +--R (81a b \|- 1 - 81a b\|- 1 + 108a b + 27a )cos(x) sin(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 +--R (27a b + 27a b)\|- 1 + (- 27a b - 27a b)\|- 1 + 36a b +--R + +--R 2 3 +--R 45a b + 9a +--R * +--R 6 +--R cos(x) +--R * +--R 2 3+-+2 +--R tan(x) \|a +--R Type: Expression Integer +--R +--E 344 + +--S 345 of 504 +--Rt0166:= 1/(a+b*cos(x)^8) +--R +--R +--R 1 +--R (301) ------------- +--R 8 +--R b cos(x) + a +--R Type: Expression Integer +--R +--E 345 + +--S 346 of 504 +--Rr0166:= 1/4*atan(a^(1/8)*tan(x)/(a^(1/4)+(-b)^(1/4))^(1/2))/a^(7/8)/(a^(1/4)+(-b)^(1/4))^(1/2)+1/4*atan(a^(1/4)*tan(x)/(a^(1/2)-a^(1/4)*(-b)^(1/4))^(1/2))/a^(3/4)/(a^(1/2)-a^(1/4)*(-b)^(1/4))^(1/2)+1/4*atan(a^(1/4)*tan(x)/(a^(1/2)-%i*a^(1/4)*(-b)^(1/4))^(1/2))/a^(3/4)/(a^(1/2)-%i*a^(1/4)*(-b)^(1/4))^(1/2)+1/4*atan(a^(1/4)*tan(x)/(a^(1/2)+%i*a^(1/4)*(-b)^(1/4))^(1/2))/a^(3/4)/(a^(1/2)+%i*a^(1/4)*(-b)^(1/4))^(1/2) +--R +--R +--R (302) +--R +---------------------+ +-------------+ +-------------------+ +--R 8+-+7 | 4+---+4+-+ +-+ |4+-+ 4+---+ | 4+---+4+-+ +-+ +--R \|a \|- %i\|- b \|a + \|a \|\|a + \|- b \|%i\|- b \|a + \|a +--R * +--R 4+-+ +--R tan(x)\|a +--R atan(----------------------) +--R +-------------------+ +--R | 4+---+4+-+ +-+ +--R \|- \|- b \|a + \|a +--R + +--R +-------------------+ +-------------+ +-------------------+ +--R 8+-+7 | 4+---+4+-+ +-+ |4+-+ 4+---+ | 4+---+4+-+ +-+ +--R \|a \|- \|- b \|a + \|a \|\|a + \|- b \|%i\|- b \|a + \|a +--R * +--R 4+-+ +--R tan(x)\|a +--R atan(------------------------) +--R +---------------------+ +--R | 4+---+4+-+ +-+ +--R \|- %i\|- b \|a + \|a +--R + +--R +-------------------+ +---------------------+ +--R 4+-+3 | 4+---+4+-+ +-+ | 4+---+4+-+ +-+ +--R \|a \|- \|- b \|a + \|a \|- %i\|- b \|a + \|a +--R * +--R +-------------------+ 8+-+ +--R | 4+---+4+-+ +-+ tan(x)\|a +--R \|%i\|- b \|a + \|a atan(----------------) +--R +-------------+ +--R |4+-+ 4+---+ +--R \|\|a + \|- b +--R + +--R +-------------------+ +---------------------+ +-------------+ +--R 8+-+7 | 4+---+4+-+ +-+ | 4+---+4+-+ +-+ |4+-+ 4+---+ +--R \|a \|- \|- b \|a + \|a \|- %i\|- b \|a + \|a \|\|a + \|- b +--R * +--R 4+-+ +--R tan(x)\|a +--R atan(----------------------) +--R +-------------------+ +--R | 4+---+4+-+ +-+ +--R \|%i\|- b \|a + \|a +--R / +--R +-------------------+ +---------------------+ +-------------+ +--R 4+-+3 8+-+7 | 4+---+4+-+ +-+ | 4+---+4+-+ +-+ |4+-+ 4+---+ +--R 4\|a \|a \|- \|- b \|a + \|a \|- %i\|- b \|a + \|a \|\|a + \|- b +--R * +--R +-------------------+ +--R | 4+---+4+-+ +-+ +--R \|%i\|- b \|a + \|a +--R Type: Expression Complex Integer +--R +--E 346 + +--S 347 of 504 +--Ra0166:= integrate(t0166,x) +--R +--R +--R (303) +--R ROOT +--R 2 +--R (16a b + 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--R (- 1536a b - 3072a b - 1536a )%%EM1 +--R + +--R 3 2 4 5 2 3 +--R ((- 1024a b - 2048a b - 1024a )%%EM0 - 64a b - 64a ) +--R * +--R %%EM1 +--R + +--R 3 2 4 5 2 +--R (- 1536a b - 3072a b - 1536a )%%EM0 +--R + +--R 2 3 +--R (- 64a b - 64a )%%EM0 - 3b - a +--R / +--R 3 2 4 5 +--R 512a b + 1024a b + 512a +--R + +--R 2 2 +--R (- 16a b - 16a )%%EM1 + (- 16a b - 16a )%%EM0 - 1 +--R / +--R 2 +--R 8a b + 8a +--R * +--R log +--R 8a sin(x) +--R * +--R ROOT +--R 2 +--R (16a b + 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--R (- 1536a b - 3072a b - 1536a )%%EM1 +--R + +--R 3 2 4 5 +--R (- 1024a b - 2048a b - 1024a )%%EM0 +--R + +--R 2 3 +--R - 64a b - 64a +--R * +--R %%EM1 +--R + +--R 3 2 4 5 2 +--R (- 1536a b - 3072a b - 1536a )%%EM0 +--R + +--R 2 3 +--R (- 64a b - 64a )%%EM0 - 3b - a +--R / +--R 3 2 4 5 +--R 512a b + 1024a b + 512a +--R + +--R 2 2 +--R (- 16a b - 16a )%%EM1 + (- 16a b - 16a )%%EM0 - 1 +--R / +--R 2 +--R 8a b + 8a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R ROOT +--R 2 +--R (- 16a b - 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--R (- 1536a b - 3072a b - 1536a )%%EM1 +--R + +--R 3 2 4 5 2 3 +--R ((- 1024a b - 2048a b - 1024a )%%EM0 - 64a b - 64a ) +--R * +--R %%EM1 +--R + +--R 3 2 4 5 2 +--R (- 1536a b - 3072a b - 1536a )%%EM0 +--R + +--R 2 3 +--R (- 64a b - 64a )%%EM0 - 3b - a +--R / +--R 3 2 4 5 +--R 512a b + 1024a b + 512a +--R + +--R 2 2 +--R (- 16a b - 16a )%%EM1 + (- 16a b - 16a )%%EM0 - 1 +--R / +--R 2 +--R 8a b + 8a +--R * +--R log +--R 8a sin(x) +--R * +--R ROOT +--R 2 +--R (- 16a b - 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--R (- 1536a b - 3072a b - 1536a )%%EM1 +--R + +--R 3 2 4 5 +--R (- 1024a b - 2048a b - 1024a )%%EM0 +--R + +--R 2 3 +--R - 64a b - 64a +--R * +--R %%EM1 +--R + +--R 3 2 4 5 2 +--R (- 1536a b - 3072a b - 1536a )%%EM0 +--R + +--R 2 3 +--R (- 64a b - 64a )%%EM0 - 3b - a +--R / +--R 3 2 4 5 +--R 512a b + 1024a b + 512a +--R + +--R 2 2 +--R (- 16a b - 16a )%%EM1 + (- 16a b - 16a )%%EM0 - 1 +--R / +--R 2 +--R 8a b + 8a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R - +--R ROOT +--R 2 +--R (- 16a b - 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--R (- 1536a b - 3072a b - 1536a )%%EM1 +--R + +--R 3 2 4 5 2 +--R (- 1024a b - 2048a b - 1024a )%%EM0 - 64a b +--R + +--R 3 +--R - 64a +--R * +--R %%EM1 +--R + +--R 3 2 4 5 2 +--R (- 1536a b - 3072a b - 1536a )%%EM0 +--R + +--R 2 3 +--R (- 64a b - 64a )%%EM0 - 3b - a +--R / +--R 3 2 4 5 +--R 512a b + 1024a b + 512a +--R + +--R 2 2 +--R (- 16a b - 16a )%%EM1 + (- 16a b - 16a )%%EM0 - 1 +--R / +--R 2 +--R 8a b + 8a +--R * +--R log +--R - +--R 8a sin(x) +--R * +--R ROOT +--R 2 +--R (- 16a b - 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--R (- 1536a b - 3072a b - 1536a )%%EM1 +--R + +--R 3 2 4 5 +--R (- 1024a b - 2048a b - 1024a )%%EM0 +--R + +--R 2 3 +--R - 64a b - 64a +--R * +--R %%EM1 +--R + +--R 3 2 4 5 2 +--R (- 1536a b - 3072a b - 1536a )%%EM0 +--R + +--R 2 3 +--R (- 64a b - 64a )%%EM0 - 3b - a +--R / +--R 3 2 4 5 +--R 512a b + 1024a b + 512a +--R + +--R 2 2 +--R (- 16a b - 16a )%%EM1 + (- 16a b - 16a )%%EM0 - 1 +--R / +--R 2 +--R 8a b + 8a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R - +--R ROOT +--R 2 +--R (16a b + 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--R (- 1536a b - 3072a b - 1536a )%%EM1 +--R + +--R 3 2 4 5 2 +--R (- 1024a b - 2048a b - 1024a )%%EM0 - 64a b +--R + +--R 3 +--R - 64a +--R * +--R %%EM1 +--R + +--R 3 2 4 5 2 +--R (- 1536a b - 3072a b - 1536a )%%EM0 +--R + +--R 2 3 +--R (- 64a b - 64a )%%EM0 - 3b - a +--R / +--R 3 2 4 5 +--R 512a b + 1024a b + 512a +--R + +--R 2 2 +--R (- 16a b - 16a )%%EM1 + (- 16a b - 16a )%%EM0 - 1 +--R / +--R 2 +--R 8a b + 8a +--R * +--R log +--R - +--R 8a sin(x) +--R * +--R ROOT +--R 2 +--R (16a b + 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--R (- 1536a b - 3072a b - 1536a )%%EM1 +--R + +--R 3 2 4 5 +--R (- 1024a b - 2048a b - 1024a )%%EM0 +--R + +--R 2 3 +--R - 64a b - 64a +--R * +--R %%EM1 +--R + +--R 3 2 4 5 2 +--R (- 1536a b - 3072a b - 1536a )%%EM0 +--R + +--R 2 3 +--R (- 64a b - 64a )%%EM0 - 3b - a +--R / +--R 3 2 4 5 +--R 512a b + 1024a b + 512a +--R + +--R 2 2 +--R (- 16a b - 16a )%%EM1 + (- 16a b - 16a )%%EM0 - 1 +--R / +--R 2 +--R 8a b + 8a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R +------+ +--R +------+ 8a sin(x)\|4%%EM1 - 2cos(x) +--R \|4%%EM1 log(----------------------------) +--R cos(x) + 1 +--R + +--R +------+ +--R +------+ - 8a sin(x)\|4%%EM1 - 2cos(x) +--R - \|4%%EM1 log(------------------------------) +--R cos(x) + 1 +--R + +--R +------+ +--R +------+ 8a sin(x)\|4%%EM0 - 2cos(x) +--R \|4%%EM0 log(----------------------------) +--R cos(x) + 1 +--R + +--R +------+ +--R +------+ - 8a sin(x)\|4%%EM0 - 2cos(x) +--R - \|4%%EM0 log(------------------------------) +--R cos(x) + 1 +--R / +--R 2 +--R Type: Union(Expression Integer,...) +--R +--E 347 + +--S 348 of 504 +--m0166:= a0166-r0166 +--E 348 + +--S 349 of 504 +--d0166:= D(m0166,x) +--E 349 + +--S 350 of 504 +--Rt0167:= 1/(a-b*cos(x)^3) +--R +--R +--R 1 +--R (304) - ------------- +--R 3 +--R b cos(x) - a +--R Type: Expression Integer +--R +--E 350 + +--S 351 of 504 +--Rr0167:= 2/3*atan((a^(1/3)+b^(1/3))*tan(1/2*x)/(a^(2/3)-b^(2/3))^(1/2))/a^(2/3)/(a^(2/3)-b^(2/3))^(1/2)+2/3*atan((a^(1/3)+(-1)^(2/3)*b^(1/3))*tan(1/2*x)/(a^(2/3)+(-1)^(1/3)*b^(2/3))^(1/2))/a^(2/3)/(a^(2/3)+(-1)^(1/3)*b^(2/3))^(1/2)+2/3*atan((a^(1/3)-(-1)^(1/3)*b^(1/3))*tan(1/2*x)/(a^(2/3)-(-1)^(2/3)*b^(2/3))^(1/2))/a^(2/3)/(a^(2/3)-(-1)^(2/3)*b^(2/3))^(1/2) +--R +--R +--R (305) +--R - +--R +---------------+ +-------------------+ +--R | 3+-+2 3+-+2 |3+---+3+-+2 3+-+2 +--R 2\|- \|b + \|a \|\|- 1 \|b + \|a +--R * +--R 3+---+ x 3+-+ x 3+-+ +--R \|- 1 tan(-)\|b - tan(-)\|a +--R 2 2 +--R atan(-----------------------------) +--R +----------------------+ +--R | 3+---+2 3+-+2 3+-+2 +--R \|- \|- 1 \|b + \|a +--R + +--R +----------------------+ +-------------------+ +--R | 3+---+2 3+-+2 3+-+2 |3+---+3+-+2 3+-+2 +--R 2\|- \|- 1 \|b + \|a \|\|- 1 \|b + \|a +--R * +--R x 3+-+ x 3+-+ +--R tan(-)\|b + tan(-)\|a +--R 2 2 +--R atan(-----------------------) +--R +---------------+ +--R | 3+-+2 3+-+2 +--R \|- \|b + \|a +--R + +--R +----------------------+ +---------------+ +--R | 3+---+2 3+-+2 3+-+2 | 3+-+2 3+-+2 +--R 2\|- \|- 1 \|b + \|a \|- \|b + \|a +--R * +--R 3+---+2 x 3+-+ x 3+-+ +--R \|- 1 tan(-)\|b + tan(-)\|a +--R 2 2 +--R atan(------------------------------) +--R +-------------------+ +--R |3+---+3+-+2 3+-+2 +--R \|\|- 1 \|b + \|a +--R / +--R +----------------------+ +---------------+ +-------------------+ +--R 3+-+2 | 3+---+2 3+-+2 3+-+2 | 3+-+2 3+-+2 |3+---+3+-+2 3+-+2 +--R 3\|a \|- \|- 1 \|b + \|a \|- \|b + \|a \|\|- 1 \|b + \|a +--R Type: Expression Integer +--R +--E 351 + +--S 352 of 504 +--Ra0167:= integrate(t0167,x) +--R +--R +--R (306) +--R - +--R ROOT +--R 2 2 +--R (6b - 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--R (- 81a b + 162a b - 81a )%%EN0 +--R + +--R 2 2 4 2 2 +--R (18a b - 18a )%%EN0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 2 2 +--R (- 6b + 6a )%%EN0 + 2 +--R / +--R 2 2 +--R 3b - 3a +--R * +--R log +--R 4 2 6 4 2 6 +--R ((243a b - 243a )cos(x) + 243a b - 243a )%%EN0 +--R + +--R 2 2 4 2 2 4 +--R (27a b - 27a )cos(x) + 27a b - 27a +--R * +--R ROOT +--R 2 4 4 2 6 2 +--R (- 81a b + 162a b - 81a )%%EN0 +--R + +--R 2 2 4 2 2 +--R (18a b - 18a )%%EN0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 4 2 6 4 2 6 2 +--R ((243a b - 243a )cos(x) + 243a b - 243a )%%EN0 +--R + +--R 2 2 4 2 2 4 +--R ((- 27a b - 54a )cos(x) - 27a b - 54a )%%EN0 +--R + +--R 2 2 +--R (- 6a b - 3a )cos(x) - 6a b - 3a +--R * +--R ROOT +--R 2 2 +--R (6b - 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--R (- 81a b + 162a b - 81a )%%EN0 +--R + +--R 2 2 4 2 2 +--R (18a b - 18a )%%EN0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 2 2 +--R (- 6b + 6a )%%EN0 + 2 +--R / +--R 2 2 +--R 3b - 3a +--R + +--R 4b sin(x) +--R / +--R cos(x) + 1 +--R + +--R ROOT +--R 2 2 +--R (- 6b + 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--R (- 81a b + 162a b - 81a )%%EN0 +--R + +--R 2 2 4 2 2 +--R (18a b - 18a )%%EN0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 2 2 +--R (- 6b + 6a )%%EN0 + 2 +--R / +--R 2 2 +--R 3b - 3a +--R * +--R log +--R 4 2 6 4 2 6 +--R ((243a b - 243a )cos(x) + 243a b - 243a )%%EN0 +--R + +--R 2 2 4 2 2 4 +--R (27a b - 27a )cos(x) + 27a b - 27a +--R * +--R ROOT +--R 2 4 4 2 6 2 +--R (- 81a b + 162a b - 81a )%%EN0 +--R + +--R 2 2 4 2 2 +--R (18a b - 18a )%%EN0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 4 2 6 4 2 6 2 +--R ((- 243a b + 243a )cos(x) - 243a b + 243a )%%EN0 +--R + +--R 2 2 4 2 2 4 +--R ((27a b + 54a )cos(x) + 27a b + 54a )%%EN0 +--R + +--R 2 2 +--R (6a b + 3a )cos(x) + 6a b + 3a +--R * +--R ROOT +--R 2 2 +--R (- 6b + 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--R (- 81a b + 162a b - 81a )%%EN0 +--R + +--R 2 2 4 2 2 +--R (18a b - 18a )%%EN0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 2 2 +--R (- 6b + 6a )%%EN0 + 2 +--R / +--R 2 2 +--R 3b - 3a +--R + +--R 4b sin(x) +--R / +--R cos(x) + 1 +--R + +--R - +--R ROOT +--R 2 2 +--R (- 6b + 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--R (- 81a b + 162a b - 81a )%%EN0 +--R + +--R 2 2 4 2 2 +--R (18a b - 18a )%%EN0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 2 2 +--R (- 6b + 6a )%%EN0 + 2 +--R / +--R 2 2 +--R 3b - 3a +--R * +--R log +--R 4 2 6 4 2 6 +--R ((- 243a b + 243a )cos(x) - 243a b + 243a )%%EN0 +--R + +--R 2 2 4 2 2 4 +--R (- 27a b + 27a )cos(x) - 27a b + 27a +--R * +--R ROOT +--R 2 4 4 2 6 2 +--R (- 81a b + 162a b - 81a )%%EN0 +--R + +--R 2 2 4 2 2 +--R (18a b - 18a )%%EN0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 4 2 6 4 2 6 2 +--R ((243a b - 243a )cos(x) + 243a b - 243a )%%EN0 +--R + +--R 2 2 4 2 2 4 +--R ((- 27a b - 54a )cos(x) - 27a b - 54a )%%EN0 +--R + +--R 2 2 +--R (- 6a b - 3a )cos(x) - 6a b - 3a +--R * +--R ROOT +--R 2 2 +--R (- 6b + 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--R (- 81a b + 162a b - 81a )%%EN0 +--R + +--R 2 2 4 2 2 +--R (18a b - 18a )%%EN0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 2 2 +--R (- 6b + 6a )%%EN0 + 2 +--R / +--R 2 2 +--R 3b - 3a +--R + +--R 4b sin(x) +--R / +--R cos(x) + 1 +--R + +--R ROOT +--R 2 2 +--R (6b - 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--R (- 81a b + 162a b - 81a )%%EN0 +--R + +--R 2 2 4 2 2 +--R (18a b - 18a )%%EN0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 2 2 +--R (- 6b + 6a )%%EN0 + 2 +--R / +--R 2 2 +--R 3b - 3a +--R * +--R log +--R 4 2 6 4 2 6 +--R ((- 243a b + 243a )cos(x) - 243a b + 243a )%%EN0 +--R + +--R 2 2 4 2 2 4 +--R (- 27a b + 27a )cos(x) - 27a b + 27a +--R * +--R ROOT +--R 2 4 4 2 6 2 +--R (- 81a b + 162a b - 81a )%%EN0 +--R + +--R 2 2 4 2 2 +--R (18a b - 18a )%%EN0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 4 2 6 4 2 6 2 +--R ((- 243a b + 243a )cos(x) - 243a b + 243a )%%EN0 +--R + +--R 2 2 4 2 2 4 +--R ((27a b + 54a )cos(x) + 27a b + 54a )%%EN0 +--R + +--R 2 2 +--R (6a b + 3a )cos(x) + 6a b + 3a +--R * +--R ROOT +--R 2 2 +--R (6b - 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--R (- 81a b + 162a b - 81a )%%EN0 +--R + +--R 2 2 4 2 2 +--R (18a b - 18a )%%EN0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 2 2 +--R (- 6b + 6a )%%EN0 + 2 +--R / +--R 2 2 +--R 3b - 3a +--R + +--R 4b sin(x) +--R / +--R cos(x) + 1 +--R + +--R +------+ +--R \|4%%EN0 +--R * +--R log +--R 4 2 6 4 2 6 2 +--R ((243a b - 243a )cos(x) + 243a b - 243a )%%EN0 +--R + +--R 2 2 4 2 2 4 +--R ((- 27a b - 54a )cos(x) - 27a b - 54a )%%EN0 +--R + +--R 2 2 +--R (3a b - 3a )cos(x) + 3a b - 3a +--R * +--R +------+ +--R \|4%%EN0 +--R + +--R 2b sin(x) +--R / +--R cos(x) + 1 +--R + +--R - +--R +------+ +--R \|4%%EN0 +--R * +--R log +--R 4 2 6 4 2 6 2 +--R ((- 243a b + 243a )cos(x) - 243a b + 243a )%%EN0 +--R + +--R 2 2 4 2 2 4 +--R ((27a b + 54a )cos(x) + 27a b + 54a )%%EN0 +--R + +--R 2 2 +--R (- 3a b + 3a )cos(x) - 3a b + 3a +--R * +--R +------+ +--R \|4%%EN0 +--R + +--R 2b sin(x) +--R / +--R cos(x) + 1 +--R / +--R 2 +--R Type: Union(Expression Integer,...) +--R +--E 352 + +--S 353 of 504 +--m0167:= a0167-r0167 +--E 353 + +--S 354 of 504 +--d0167:= D(m0167,x) +--E 354 + +--S 355 of 504 +--Rt0168:= 1/(a-b*cos(x)^6) +--R +--R +--R 1 +--R (307) - ------------- +--R 6 +--R b cos(x) - a +--R Type: Expression Integer +--R +--E 355 + +--S 356 of 504 +--Rr0168:= 1/3*atan(a^(1/6)*tan(x)/(a^(1/3)-b^(1/3))^(1/2))/a^(5/6)/(a^(1/3)-b^(1/3))^(1/2)+1/3*atan(a^(1/6)*tan(x)/(a^(1/3)+(-1)^(1/3)*b^(1/3))^(1/2))/a^(5/6)/(a^(1/3)+(-1)^(1/3)*b^(1/3))^(1/2)+1/3*atan(a^(1/6)*tan(x)/(a^(1/3)-(-1)^(2/3)*b^(1/3))^(1/2))/a^(5/6)/(a^(1/3)-(-1)^(2/3)*b^(1/3))^(1/2) +--R +--R +--R (308) +--R +-------------+ +-----------------+ 6+-+ +--R | 3+-+ 3+-+ |3+---+3+-+ 3+-+ tan(x)\|a +--R \|- \|b + \|a \|\|- 1 \|b + \|a atan(-----------------------) +--R +--------------------+ +--R | 3+---+2 3+-+ 3+-+ +--R \|- \|- 1 \|b + \|a +--R + +--R +--------------------+ +-----------------+ 6+-+ +--R | 3+---+2 3+-+ 3+-+ |3+---+3+-+ 3+-+ tan(x)\|a +--R \|- \|- 1 \|b + \|a \|\|- 1 \|b + \|a atan(----------------) +--R +-------------+ +--R | 3+-+ 3+-+ +--R \|- \|b + \|a +--R + +--R +--------------------+ +-------------+ 6+-+ +--R | 3+---+2 3+-+ 3+-+ | 3+-+ 3+-+ tan(x)\|a +--R \|- \|- 1 \|b + \|a \|- \|b + \|a atan(--------------------) +--R +-----------------+ +--R |3+---+3+-+ 3+-+ +--R \|\|- 1 \|b + \|a +--R / +--R +--------------------+ +-------------+ +-----------------+ +--R 6+-+5 | 3+---+2 3+-+ 3+-+ | 3+-+ 3+-+ |3+---+3+-+ 3+-+ +--R 3\|a \|- \|- 1 \|b + \|a \|- \|b + \|a \|\|- 1 \|b + \|a +--R Type: Expression Integer +--R +--E 356 + +--S 357 of 504 +--Ra0168:= integrate(t0168,x) +--R +--R +--R (309) +--R ROOT +--R 2 +--R (12a b - 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--R (- 1296a b + 2592a b - 1296a )%%EO0 +--R + +--R 2 3 +--R (72a b - 72a )%%EO0 + 4b - a +--R / +--R 3 2 4 5 +--R 432a b - 864a b + 432a +--R + +--R 2 +--R (- 12a b + 12a )%%EO0 + 1 +--R / +--R 2 +--R 6a b - 6a +--R * +--R log +--R 6a sin(x) +--R * +--R ROOT +--R 2 +--R (12a b - 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--R (- 1296a b + 2592a b - 1296a )%%EO0 +--R + +--R 2 3 +--R (72a b - 72a )%%EO0 + 4b - a +--R / +--R 3 2 4 5 +--R 432a b - 864a b + 432a +--R + +--R 2 +--R (- 12a b + 12a )%%EO0 + 1 +--R / +--R 2 +--R 6a b - 6a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R ROOT +--R 2 +--R (- 12a b + 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--R (- 1296a b + 2592a b - 1296a )%%EO0 +--R + +--R 2 3 +--R (72a b - 72a )%%EO0 + 4b - a +--R / +--R 3 2 4 5 +--R 432a b - 864a b + 432a +--R + +--R 2 +--R (- 12a b + 12a )%%EO0 + 1 +--R / +--R 2 +--R 6a b - 6a +--R * +--R log +--R 6a sin(x) +--R * +--R ROOT +--R 2 +--R (- 12a b + 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--R (- 1296a b + 2592a b - 1296a )%%EO0 +--R + +--R 2 3 +--R (72a b - 72a )%%EO0 + 4b - a +--R / +--R 3 2 4 5 +--R 432a b - 864a b + 432a +--R + +--R 2 +--R (- 12a b + 12a )%%EO0 + 1 +--R / +--R 2 +--R 6a b - 6a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R - +--R ROOT +--R 2 +--R (- 12a b + 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--R (- 1296a b + 2592a b - 1296a )%%EO0 +--R + +--R 2 3 +--R (72a b - 72a )%%EO0 + 4b - a +--R / +--R 3 2 4 5 +--R 432a b - 864a b + 432a +--R + +--R 2 +--R (- 12a b + 12a )%%EO0 + 1 +--R / +--R 2 +--R 6a b - 6a +--R * +--R log +--R - +--R 6a sin(x) +--R * +--R ROOT +--R 2 +--R (- 12a b + 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--R (- 1296a b + 2592a b - 1296a )%%EO0 +--R + +--R 2 3 +--R (72a b - 72a )%%EO0 + 4b - a +--R / +--R 3 2 4 5 +--R 432a b - 864a b + 432a +--R + +--R 2 +--R (- 12a b + 12a )%%EO0 + 1 +--R / +--R 2 +--R 6a b - 6a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R - +--R ROOT +--R 2 +--R (12a b - 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--R (- 1296a b + 2592a b - 1296a )%%EO0 +--R + +--R 2 3 +--R (72a b - 72a )%%EO0 + 4b - a +--R / +--R 3 2 4 5 +--R 432a b - 864a b + 432a +--R + +--R 2 +--R (- 12a b + 12a )%%EO0 + 1 +--R / +--R 2 +--R 6a b - 6a +--R * +--R log +--R - +--R 6a sin(x) +--R * +--R ROOT +--R 2 +--R (12a b - 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--R (- 1296a b + 2592a b - 1296a )%%EO0 +--R + +--R 2 3 +--R (72a b - 72a )%%EO0 + 4b - a +--R / +--R 3 2 4 5 +--R 432a b - 864a b + 432a +--R + +--R 2 +--R (- 12a b + 12a )%%EO0 + 1 +--R / +--R 2 +--R 6a b - 6a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R +------+ +--R +------+ 6a sin(x)\|4%%EO0 - 2cos(x) +--R \|4%%EO0 log(----------------------------) +--R cos(x) + 1 +--R + +--R +------+ +--R +------+ - 6a sin(x)\|4%%EO0 - 2cos(x) +--R - \|4%%EO0 log(------------------------------) +--R cos(x) + 1 +--R / +--R 2 +--R Type: Union(Expression Integer,...) +--R +--E 357 + +--S 358 of 504 +--Rm0168:= a0168-r0168 +--R +--R +--R (310) +--R +--------------------+ +-------------+ +-----------------+ +--R 6+-+5 | 3+---+2 3+-+ 3+-+ | 3+-+ 3+-+ |3+---+3+-+ 3+-+ +--R 3\|a \|- \|- 1 \|b + \|a \|- \|b + \|a \|\|- 1 \|b + \|a +--R * +--R ROOT +--R 2 +--R (12a b - 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--R (- 1296a b + 2592a b - 1296a )%%EO0 +--R + +--R 2 3 +--R (72a b - 72a )%%EO0 + 4b - a +--R / +--R 3 2 4 5 +--R 432a b - 864a b + 432a +--R + +--R 2 +--R (- 12a b + 12a )%%EO0 + 1 +--R / +--R 2 +--R 6a b - 6a +--R * +--R log +--R 6a sin(x) +--R * +--R ROOT +--R 2 +--R (12a b - 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--R (- 1296a b + 2592a b - 1296a )%%EO0 +--R + +--R 2 3 +--R (72a b - 72a )%%EO0 + 4b - a +--R / +--R 3 2 4 5 +--R 432a b - 864a b + 432a +--R + +--R 2 +--R (- 12a b + 12a )%%EO0 + 1 +--R / +--R 2 +--R 6a b - 6a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R +--------------------+ +-------------+ +-----------------+ +--R 6+-+5 | 3+---+2 3+-+ 3+-+ | 3+-+ 3+-+ |3+---+3+-+ 3+-+ +--R 3\|a \|- \|- 1 \|b + \|a \|- \|b + \|a \|\|- 1 \|b + \|a +--R * +--R ROOT +--R 2 +--R (- 12a b + 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--R (- 1296a b + 2592a b - 1296a )%%EO0 +--R + +--R 2 3 +--R (72a b - 72a )%%EO0 + 4b - a +--R / +--R 3 2 4 5 +--R 432a b - 864a b + 432a +--R + +--R 2 +--R (- 12a b + 12a )%%EO0 + 1 +--R / +--R 2 +--R 6a b - 6a +--R * +--R log +--R 6a sin(x) +--R * +--R ROOT +--R 2 +--R (- 12a b + 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--R (- 1296a b + 2592a b - 1296a )%%EO0 +--R + +--R 2 3 +--R (72a b - 72a )%%EO0 + 4b - a +--R / +--R 3 2 4 5 +--R 432a b - 864a b + 432a +--R + +--R 2 +--R (- 12a b + 12a )%%EO0 + 1 +--R / +--R 2 +--R 6a b - 6a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R - +--R +--------------------+ +-------------+ +-----------------+ +--R 6+-+5 | 3+---+2 3+-+ 3+-+ | 3+-+ 3+-+ |3+---+3+-+ 3+-+ +--R 3\|a \|- \|- 1 \|b + \|a \|- \|b + \|a \|\|- 1 \|b + \|a +--R * +--R ROOT +--R 2 +--R (- 12a b + 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--R (- 1296a b + 2592a b - 1296a )%%EO0 +--R + +--R 2 3 +--R (72a b - 72a )%%EO0 + 4b - a +--R / +--R 3 2 4 5 +--R 432a b - 864a b + 432a +--R + +--R 2 +--R (- 12a b + 12a )%%EO0 + 1 +--R / +--R 2 +--R 6a b - 6a +--R * +--R log +--R - +--R 6a sin(x) +--R * +--R ROOT +--R 2 +--R (- 12a b + 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--R (- 1296a b + 2592a b - 1296a )%%EO0 +--R + +--R 2 3 +--R (72a b - 72a )%%EO0 + 4b - a +--R / +--R 3 2 4 5 +--R 432a b - 864a b + 432a +--R + +--R 2 +--R (- 12a b + 12a )%%EO0 + 1 +--R / +--R 2 +--R 6a b - 6a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R - +--R +--------------------+ +-------------+ +-----------------+ +--R 6+-+5 | 3+---+2 3+-+ 3+-+ | 3+-+ 3+-+ |3+---+3+-+ 3+-+ +--R 3\|a \|- \|- 1 \|b + \|a \|- \|b + \|a \|\|- 1 \|b + \|a +--R * +--R ROOT +--R 2 +--R (12a b - 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--R (- 1296a b + 2592a b - 1296a )%%EO0 +--R + +--R 2 3 +--R (72a b - 72a )%%EO0 + 4b - a +--R / +--R 3 2 4 5 +--R 432a b - 864a b + 432a +--R + +--R 2 +--R (- 12a b + 12a )%%EO0 + 1 +--R / +--R 2 +--R 6a b - 6a +--R * +--R log +--R - +--R 6a sin(x) +--R * +--R ROOT +--R 2 +--R (12a b - 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--R (- 1296a b + 2592a b - 1296a )%%EO0 +--R + +--R 2 3 +--R (72a b - 72a )%%EO0 + 4b - a +--R / +--R 3 2 4 5 +--R 432a b - 864a b + 432a +--R + +--R 2 +--R (- 12a b + 12a )%%EO0 + 1 +--R / +--R 2 +--R 6a b - 6a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R +--------------------+ +-------------+ +-----------------+ +--R 6+-+5 | 3+---+2 3+-+ 3+-+ | 3+-+ 3+-+ |3+---+3+-+ 3+-+ +--R 3\|a \|- \|- 1 \|b + \|a \|- \|b + \|a \|\|- 1 \|b + \|a +--R * +--R +------+ +--R +------+ 6a sin(x)\|4%%EO0 - 2cos(x) +--R \|4%%EO0 log(----------------------------) +--R cos(x) + 1 +--R + +--R - +--R +--------------------+ +-------------+ +-----------------+ +--R 6+-+5 | 3+---+2 3+-+ 3+-+ | 3+-+ 3+-+ |3+---+3+-+ 3+-+ +--R 3\|a \|- \|- 1 \|b + \|a \|- \|b + \|a \|\|- 1 \|b + \|a +--R * +--R +------+ +--R +------+ - 6a sin(x)\|4%%EO0 - 2cos(x) +--R \|4%%EO0 log(------------------------------) +--R cos(x) + 1 +--R + +--R +-------------+ +-----------------+ 6+-+ +--R | 3+-+ 3+-+ |3+---+3+-+ 3+-+ tan(x)\|a +--R - 2\|- \|b + \|a \|\|- 1 \|b + \|a atan(-----------------------) +--R +--------------------+ +--R | 3+---+2 3+-+ 3+-+ +--R \|- \|- 1 \|b + \|a +--R + +--R +--------------------+ +-----------------+ 6+-+ +--R | 3+---+2 3+-+ 3+-+ |3+---+3+-+ 3+-+ tan(x)\|a +--R - 2\|- \|- 1 \|b + \|a \|\|- 1 \|b + \|a atan(----------------) +--R +-------------+ +--R | 3+-+ 3+-+ +--R \|- \|b + \|a +--R + +--R +--------------------+ +-------------+ 6+-+ +--R | 3+---+2 3+-+ 3+-+ | 3+-+ 3+-+ tan(x)\|a +--R - 2\|- \|- 1 \|b + \|a \|- \|b + \|a atan(--------------------) +--R +-----------------+ +--R |3+---+3+-+ 3+-+ +--R \|\|- 1 \|b + \|a +--R / +--R +--------------------+ +-------------+ +-----------------+ +--R 6+-+5 | 3+---+2 3+-+ 3+-+ | 3+-+ 3+-+ |3+---+3+-+ 3+-+ +--R 6\|a \|- \|- 1 \|b + \|a \|- \|b + \|a \|\|- 1 \|b + \|a +--R Type: Expression Integer +--R +--E 358 + +--S 359 of 504 +--Rd0168:= D(m0168,x) +--R +--R +--R (311) +--R 3+---+2 3+---+ 6 6 +--R (3b \|- 1 - 3b\|- 1 + 3b)cos(x) tan(x) +--R + +--R 3+---+2 3+---+ 6 +--R (- 3a \|- 1 + 3a\|- 1 - 3a)sin(x) +--R + +--R 3+---+2 3+---+ 2 4 +--R (- 9a \|- 1 + 9a\|- 1 - 9a)cos(x) sin(x) +--R + +--R 3+---+2 3+---+ 4 2 +--R (- 9a \|- 1 + 9a\|- 1 - 9a)cos(x) sin(x) +--R + +--R 3+---+2 3+---+ 6 +--R ((3b - 3a)\|- 1 + (- 3b + 3a)\|- 1 + 3b - 3a)cos(x) +--R * +--R 4 +--R tan(x) +--R + +--R 3+---+2 3+---+ 6 +--R ((- 6b + 15a)\|- 1 + (6b - 15a)\|- 1 - 6b + 15a)sin(x) +--R + +--R 3+---+2 3+---+ 2 +--R ((- 18b + 45a)\|- 1 + (18b - 45a)\|- 1 - 18b + 45a)cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 3+---+2 3+---+ 4 +--R ((- 18b + 45a)\|- 1 + (18b - 45a)\|- 1 - 18b + 45a)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 3+---+2 3+---+ 6 +--R ((- 6b + 15a)\|- 1 + (6b - 15a)\|- 1 - 6b + 15a)cos(x) +--R * +--R 3+-+6+-+4 +--R \|a \|a +--R + +--R 3+---+2 3+---+ 6 +--R (6a \|- 1 - 6a\|- 1 + 6a)sin(x) +--R + +--R 3+---+2 3+---+ 2 4 +--R (18a \|- 1 - 18a\|- 1 + 18a)cos(x) sin(x) +--R + +--R 3+---+2 3+---+ 4 2 +--R (18a \|- 1 - 18a\|- 1 + 18a)cos(x) sin(x) +--R + +--R 3+---+2 3+---+ 6 +--R ((12b + 6a)\|- 1 + (- 12b - 6a)\|- 1 + 12b + 6a)cos(x) +--R * +--R 4 +--R tan(x) +--R + +--R 3+---+2 3+---+ 6 +--R (- 12a \|- 1 + 12a\|- 1 - 12a)sin(x) +--R + +--R 3+---+2 3+---+ 2 4 +--R (- 36a \|- 1 + 36a\|- 1 - 36a)cos(x) sin(x) +--R + +--R 3+---+2 3+---+ 4 2 +--R (- 36a \|- 1 + 36a\|- 1 - 36a)cos(x) sin(x) +--R + +--R 3+---+2 3+---+ 6 +--R ((12b - 12a)\|- 1 + (- 12b + 12a)\|- 1 + 12b - 12a)cos(x) +--R * +--R 2 +--R tan(x) +--R * +--R 3+-+2 6+-+2 +--R \|a \|a +--R + +--R 2 3+---+2 2 3+---+ 2 +--R ((- 2a b + 20a )\|- 1 + (2a b - 20a )\|- 1 - 2a b + 20a ) +--R * +--R 6 +--R sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R ((- 6a b + 60a )\|- 1 + (6a b - 60a )\|- 1 - 6a b + 60a ) +--R * +--R 2 4 +--R cos(x) sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R ((- 6a b + 60a )\|- 1 + (6a b - 60a )\|- 1 - 6a b + 60a ) +--R * +--R 4 2 +--R cos(x) sin(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 +--R (- b + 8a b + 20a )\|- 1 + (b - 8a b - 20a )\|- 1 - b +--R + +--R 2 +--R 8a b + 20a +--R * +--R 6 +--R cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 2 3+---+2 2 3+---+ 2 6 +--R ((a b - 10a )\|- 1 + (- a b + 10a )\|- 1 + a b - 10a )sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 +--R ((3a b - 30a )\|- 1 + (- 3a b + 30a )\|- 1 + 3a b - 30a )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 4 +--R ((3a b - 30a )\|- 1 + (- 3a b + 30a )\|- 1 + 3a b - 30a )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 +--R (- b + 11a b - 10a )\|- 1 + (b - 11a b + 10a )\|- 1 - b +--R + +--R 2 +--R 11a b - 10a +--R * +--R 6 +--R cos(x) +--R * +--R 3+-+2 +--R \|b +--R + +--R 3+---+2 3+---+ 6 6 +--R (- 3b \|- 1 + 3b\|- 1 - 3b)cos(x) tan(x) +--R + +--R 3+---+2 3+---+ 6 +--R (3a \|- 1 - 3a\|- 1 + 3a)sin(x) +--R + +--R 3+---+2 3+---+ 2 4 +--R (9a \|- 1 - 9a\|- 1 + 9a)cos(x) sin(x) +--R + +--R 3+---+2 3+---+ 4 2 +--R (9a \|- 1 - 9a\|- 1 + 9a)cos(x) sin(x) +--R + +--R 3+---+2 3+---+ 6 +--R ((- 3b + 3a)\|- 1 + (3b - 3a)\|- 1 - 3b + 3a)cos(x) +--R * +--R 4 +--R tan(x) +--R + +--R 3+---+2 3+---+ 6 +--R ((15b - 6a)\|- 1 + (- 15b + 6a)\|- 1 + 15b - 6a)sin(x) +--R + +--R 3+---+2 3+---+ 2 +--R ((45b - 18a)\|- 1 + (- 45b + 18a)\|- 1 + 45b - 18a)cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 3+---+2 3+---+ 4 +--R ((45b - 18a)\|- 1 + (- 45b + 18a)\|- 1 + 45b - 18a)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 3+---+2 3+---+ 6 +--R ((15b - 6a)\|- 1 + (- 15b + 6a)\|- 1 + 15b - 6a)cos(x) +--R * +--R 3+-+2 6+-+4 +--R \|a \|a +--R + +--R 2 3+---+2 2 3+---+ 2 6 +--R ((a b - 4a )\|- 1 + (- a b + 4a )\|- 1 + a b - 4a )sin(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (3a b - 12a )\|- 1 + (- 3a b + 12a )\|- 1 + 3a b +--R + +--R 2 +--R - 12a +--R * +--R 2 4 +--R cos(x) sin(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (3a b - 12a )\|- 1 + (- 3a b + 12a )\|- 1 + 3a b +--R + +--R 2 +--R - 12a +--R * +--R 4 2 +--R cos(x) sin(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ +--R (2b - 7a b - 4a )\|- 1 + (- 2b + 7a b + 4a )\|- 1 +--R + +--R 2 2 +--R 2b - 7a b - 4a +--R * +--R 6 +--R cos(x) +--R * +--R 4 +--R tan(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R ((- 2a b + 8a )\|- 1 + (2a b - 8a )\|- 1 - 2a b + 8a ) +--R * +--R 6 +--R sin(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (- 6a b + 24a )\|- 1 + (6a b - 24a )\|- 1 - 6a b +--R + +--R 2 +--R 24a +--R * +--R 2 4 +--R cos(x) sin(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (- 6a b + 24a )\|- 1 + (6a b - 24a )\|- 1 - 6a b +--R + +--R 2 +--R 24a +--R * +--R 4 2 +--R cos(x) sin(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ +--R (2b - 10a b + 8a )\|- 1 + (- 2b + 10a b - 8a )\|- 1 +--R + +--R 2 2 +--R 2b - 10a b + 8a +--R * +--R 6 +--R cos(x) +--R * +--R 2 +--R tan(x) +--R * +--R 6+-+2 +--R \|a +--R + +--R 2 3+---+2 2 3+---+ +--R (10a b - 10a )\|- 1 + (- 10a b + 10a )\|- 1 + 10a b +--R + +--R 2 +--R - 10a +--R * +--R 6 +--R sin(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (30a b - 30a )\|- 1 + (- 30a b + 30a )\|- 1 + 30a b +--R + +--R 2 +--R - 30a +--R * +--R 2 4 +--R cos(x) sin(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (30a b - 30a )\|- 1 + (- 30a b + 30a )\|- 1 + 30a b +--R + +--R 2 +--R - 30a +--R * +--R 4 2 +--R cos(x) sin(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ +--R (5b + 5a b - 10a )\|- 1 + (- 5b - 5a b + 10a )\|- 1 +--R + +--R 2 2 +--R 5b + 5a b - 10a +--R * +--R 6 +--R cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 2 3+---+2 2 3+---+ 2 6 +--R ((- 5a b + 5a )\|- 1 + (5a b - 5a )\|- 1 - 5a b + 5a )sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R ((- 15a b + 15a )\|- 1 + (15a b - 15a )\|- 1 - 15a b + 15a ) +--R * +--R 2 4 +--R cos(x) sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R ((- 15a b + 15a )\|- 1 + (15a b - 15a )\|- 1 - 15a b + 15a ) +--R * +--R 4 2 +--R cos(x) sin(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ +--R (5b - 10a b + 5a )\|- 1 + (- 5b + 10a b - 5a )\|- 1 +--R + +--R 2 2 +--R 5b - 10a b + 5a +--R * +--R 6 +--R cos(x) +--R * +--R 3+-+ +--R \|a +--R * +--R 3+-+ +--R \|b +--R + +--R 2 6 6 +--R (- 3b + 3a b)cos(x) tan(x) +--R + +--R 2 6 2 2 4 +--R (3a b - 3a )sin(x) + (9a b - 9a )cos(x) sin(x) +--R + +--R 2 4 2 2 2 6 +--R (9a b - 9a )cos(x) sin(x) + (- 3b + 6a b - 3a )cos(x) +--R * +--R 4 +--R tan(x) +--R + +--R 3+---+2 3+---+ 2 2 6 +--R (- 18a b \|- 1 + 18a b\|- 1 + 3b - 24a b + 3a )sin(x) +--R + +--R 3+---+2 3+---+ 2 2 2 4 +--R (- 54a b \|- 1 + 54a b\|- 1 + 9b - 72a b + 9a )cos(x) sin(x) +--R + +--R 3+---+2 3+---+ 2 2 4 2 +--R (- 54a b \|- 1 + 54a b\|- 1 + 9b - 72a b + 9a )cos(x) sin(x) +--R + +--R 3+---+2 3+---+ 2 2 6 +--R (- 18a b \|- 1 + 18a b\|- 1 + 3b - 24a b + 3a )cos(x) +--R * +--R 6+-+4 +--R \|a +--R + +--R 3+---+2 3+---+ 2 6 +--R (- 3a b \|- 1 + 3a b\|- 1 - 6a b + 3a )sin(x) +--R + +--R 3+---+2 3+---+ 2 2 4 +--R (- 9a b \|- 1 + 9a b\|- 1 - 18a b + 9a )cos(x) sin(x) +--R + +--R 3+---+2 3+---+ 2 4 2 +--R (- 9a b \|- 1 + 9a b\|- 1 - 18a b + 9a )cos(x) sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 6 +--R ((- 6b - 3a b)\|- 1 + (6b + 3a b)\|- 1 - 12b + 3a )cos(x) +--R * +--R 4 +--R tan(x) +--R + +--R 3+---+2 3+---+ 2 6 +--R (6a b \|- 1 - 6a b\|- 1 + 12a b - 6a )sin(x) +--R + +--R 3+---+2 3+---+ 2 2 4 +--R (18a b \|- 1 - 18a b\|- 1 + 36a b - 18a )cos(x) sin(x) +--R + +--R 3+---+2 3+---+ 2 4 2 +--R (18a b \|- 1 - 18a b\|- 1 + 36a b - 18a )cos(x) sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (- 6b + 6a b)\|- 1 + (6b - 6a b)\|- 1 - 12b + 18a b +--R + +--R 2 +--R - 6a +--R * +--R 6 +--R cos(x) +--R * +--R 2 +--R tan(x) +--R * +--R 3+-+6+-+2 +--R \|a \|a +--R + +--R 3+---+2 3+---+ 2 6 +--R (- 18a b \|- 1 + 18a b\|- 1 - 24a b + 6a )sin(x) +--R + +--R 3+---+2 3+---+ 2 2 4 +--R (- 54a b \|- 1 + 54a b\|- 1 - 72a b + 18a )cos(x) sin(x) +--R + +--R 3+---+2 3+---+ 2 4 2 +--R (- 54a b \|- 1 + 54a b\|- 1 - 72a b + 18a )cos(x) sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (- 9b - 18a b)\|- 1 + (9b + 18a b)\|- 1 - 12b - 21a b +--R + +--R 2 +--R 6a +--R * +--R 6 +--R cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 3+---+2 3+---+ 2 6 +--R (9a b \|- 1 - 9a b\|- 1 + 12a b - 3a )sin(x) +--R + +--R 3+---+2 3+---+ 2 2 4 +--R (27a b \|- 1 - 27a b\|- 1 + 36a b - 9a )cos(x) sin(x) +--R + +--R 3+---+2 3+---+ 2 4 2 +--R (27a b \|- 1 - 27a b\|- 1 + 36a b - 9a )cos(x) sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 +--R ((- 9b + 9a b)\|- 1 + (9b - 9a b)\|- 1 - 12b + 15a b - 3a ) +--R * +--R 6 +--R cos(x) +--R * +--R 3+-+2 +--R \|a +--R / +--R 2 3+---+2 2 3+---+ 2 6 +--R (3a \|- 1 - 3a \|- 1 + 3a )sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 4 +--R (9a \|- 1 - 9a \|- 1 + 9a )cos(x) sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 4 2 +--R (9a \|- 1 - 9a \|- 1 + 9a )cos(x) sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R ((- 3a b + 3a )\|- 1 + (3a b - 3a )\|- 1 - 3a b + 3a ) +--R * +--R 6 +--R cos(x) +--R * +--R 6 +--R tan(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R ((- 6a b + 15a )\|- 1 + (6a b - 15a )\|- 1 - 6a b + 15a ) +--R * +--R 6 +--R sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R ((- 18a b + 45a )\|- 1 + (18a b - 45a )\|- 1 - 18a b + 45a ) +--R * +--R 2 4 +--R cos(x) sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R ((- 18a b + 45a )\|- 1 + (18a b - 45a )\|- 1 - 18a b + 45a ) +--R * +--R 4 2 +--R cos(x) sin(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ +--R (6b - 21a b + 15a )\|- 1 + (- 6b + 21a b - 15a )\|- 1 +--R + +--R 2 2 +--R 6b - 21a b + 15a +--R * +--R 6 +--R cos(x) +--R * +--R 3+-+6+-+4 +--R \|a \|a +--R + +--R 2 3+---+2 2 3+---+ 2 6 +--R (18a \|- 1 - 18a \|- 1 + 18a )sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 4 +--R (54a \|- 1 - 54a \|- 1 + 54a )cos(x) sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 4 2 +--R (54a \|- 1 - 54a \|- 1 + 54a )cos(x) sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R ((- 18a b + 18a )\|- 1 + (18a b - 18a )\|- 1 - 18a b + 18a ) +--R * +--R 6 +--R cos(x) +--R * +--R 4 3+-+2 6+-+2 +--R tan(x) \|a \|a +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 3 +--R ((- 3a b + 30a )\|- 1 + (3a b - 30a )\|- 1 - 3a b + 30a ) +--R * +--R 6 +--R sin(x) +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 3 +--R ((- 9a b + 90a )\|- 1 + (9a b - 90a )\|- 1 - 9a b + 90a ) +--R * +--R 2 4 +--R cos(x) sin(x) +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 3 +--R ((- 9a b + 90a )\|- 1 + (9a b - 90a )\|- 1 - 9a b + 90a ) +--R * +--R 4 2 +--R cos(x) sin(x) +--R + +--R 2 2 3 3+---+2 +--R (3a b - 33a b + 30a )\|- 1 +--R + +--R 2 2 3 3+---+ 2 2 3 +--R (- 3a b + 33a b - 30a )\|- 1 + 3a b - 33a b + 30a +--R * +--R 6 +--R cos(x) +--R * +--R 2 +--R tan(x) +--R * +--R 3+-+2 +--R \|b +--R + +--R 2 3+---+2 2 3+---+ 2 6 +--R (- 3a \|- 1 + 3a \|- 1 - 3a )sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 4 +--R (- 9a \|- 1 + 9a \|- 1 - 9a )cos(x) sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 4 2 +--R (- 9a \|- 1 + 9a \|- 1 - 9a )cos(x) sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R ((3a b - 3a )\|- 1 + (- 3a b + 3a )\|- 1 + 3a b - 3a ) +--R * +--R 6 +--R cos(x) +--R * +--R 6 +--R tan(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R ((15a b - 6a )\|- 1 + (- 15a b + 6a )\|- 1 + 15a b - 6a ) +--R * +--R 6 +--R sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R ((45a b - 18a )\|- 1 + (- 45a b + 18a )\|- 1 + 45a b - 18a ) +--R * +--R 2 4 +--R cos(x) sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R ((45a b - 18a )\|- 1 + (- 45a b + 18a )\|- 1 + 45a b - 18a ) +--R * +--R 4 2 +--R cos(x) sin(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ +--R (- 15b + 21a b - 6a )\|- 1 + (15b - 21a b + 6a )\|- 1 +--R + +--R 2 2 +--R - 15b + 21a b - 6a +--R * +--R 6 +--R cos(x) +--R * +--R 3+-+2 6+-+4 +--R \|a \|a +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 3 +--R ((3a b - 12a )\|- 1 + (- 3a b + 12a )\|- 1 + 3a b - 12a ) +--R * +--R 6 +--R sin(x) +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 3 +--R ((9a b - 36a )\|- 1 + (- 9a b + 36a )\|- 1 + 9a b - 36a ) +--R * +--R 2 4 +--R cos(x) sin(x) +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 3 +--R ((9a b - 36a )\|- 1 + (- 9a b + 36a )\|- 1 + 9a b - 36a ) +--R * +--R 4 2 +--R cos(x) sin(x) +--R + +--R 2 2 3 3+---+2 +--R (- 3a b + 15a b - 12a )\|- 1 +--R + +--R 2 2 3 3+---+ 2 2 3 +--R (3a b - 15a b + 12a )\|- 1 - 3a b + 15a b - 12a +--R * +--R 6 +--R cos(x) +--R * +--R 4 6+-+2 +--R tan(x) \|a +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 3 +--R ((15a b - 15a )\|- 1 + (- 15a b + 15a )\|- 1 + 15a b - 15a ) +--R * +--R 6 +--R sin(x) +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 3 +--R ((45a b - 45a )\|- 1 + (- 45a b + 45a )\|- 1 + 45a b - 45a ) +--R * +--R 2 4 +--R cos(x) sin(x) +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 3 +--R ((45a b - 45a )\|- 1 + (- 45a b + 45a )\|- 1 + 45a b - 45a ) +--R * +--R 4 2 +--R cos(x) sin(x) +--R + +--R 2 2 3 3+---+2 +--R (- 15a b + 30a b - 15a )\|- 1 +--R + +--R 2 2 3 3+---+ 2 2 3 +--R (15a b - 30a b + 15a )\|- 1 - 15a b + 30a b - 15a +--R * +--R 6 +--R cos(x) +--R * +--R 2 3+-+ +--R tan(x) \|a +--R * +--R 3+-+ +--R \|b +--R + +--R 2 3 6 2 3 2 4 +--R (- 3a b + 3a )sin(x) + (- 9a b + 9a )cos(x) sin(x) +--R + +--R 2 3 4 2 2 2 3 6 +--R (- 9a b + 9a )cos(x) sin(x) + (3a b - 6a b + 3a )cos(x) +--R * +--R 6 +--R tan(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 3 6 +--R (- 18a b \|- 1 + 18a b\|- 1 + 3a b - 24a b + 3a )sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 3 2 4 +--R (- 54a b \|- 1 + 54a b\|- 1 + 9a b - 72a b + 9a )cos(x) sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 3 4 2 +--R (- 54a b \|- 1 + 54a b\|- 1 + 9a b - 72a b + 9a )cos(x) sin(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 3 2 +--R (18a b - 18a b)\|- 1 + (- 18a b + 18a b)\|- 1 - 3b + 27a b +--R + +--R 2 3 +--R - 27a b + 3a +--R * +--R 6 +--R cos(x) +--R * +--R 6+-+4 +--R \|a +--R + +--R 2 3+---+2 2 3+---+ 2 3 6 +--R (- 9a b \|- 1 + 9a b\|- 1 - 18a b + 9a )sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 3 2 4 +--R (- 27a b \|- 1 + 27a b\|- 1 - 54a b + 27a )cos(x) sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 3 4 2 +--R (- 27a b \|- 1 + 27a b\|- 1 - 54a b + 27a )cos(x) sin(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 +--R (9a b - 9a b)\|- 1 + (- 9a b + 9a b)\|- 1 + 18a b - 27a b +--R + +--R 3 +--R 9a +--R * +--R 6 +--R cos(x) +--R * +--R 4 3+-+6+-+2 +--R tan(x) \|a \|a +--R + +--R 2 3+---+2 2 3+---+ 2 3 6 +--R (- 27a b \|- 1 + 27a b\|- 1 - 36a b + 9a )sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 3 2 4 +--R (- 81a b \|- 1 + 81a b\|- 1 - 108a b + 27a )cos(x) sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 3 4 2 +--R (- 81a b \|- 1 + 81a b\|- 1 - 108a b + 27a )cos(x) sin(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 +--R (27a b - 27a b)\|- 1 + (- 27a b + 27a b)\|- 1 + 36a b +--R + +--R 2 3 +--R - 45a b + 9a +--R * +--R 6 +--R cos(x) +--R * +--R 2 3+-+2 +--R tan(x) \|a +--R Type: Expression Integer +--R +--E 359 + +--S 360 of 504 +--Rt0169:= 1/(a-b*cos(x)^8) +--R +--R +--R 1 +--R (312) - ------------- +--R 8 +--R b cos(x) - a +--R Type: Expression Integer +--R +--E 360 + +--S 361 of 504 +--Rr0169:= 1/4*atan(a^(1/8)*tan(x)/(a^(1/4)-b^(1/4))^(1/2))/a^(7/8)/(a^(1/4)-b^(1/4))^(1/2)+1/4*atan(a^(1/8)*tan(x)/(a^(1/4)-%i*b^(1/4))^(1/2))/a^(7/8)/(a^(1/4)-%i*b^(1/4))^(1/2)+1/4*atan(a^(1/8)*tan(x)/(a^(1/4)+%i*b^(1/4))^(1/2))/a^(7/8)/(a^(1/4)+%i*b^(1/4))^(1/2)+1/4*atan(a^(1/8)*tan(x)/(a^(1/4)+b^(1/4))^(1/2))/a^(7/8)/(a^(1/4)+b^(1/4))^(1/2) +--R +--R +--R (313) +--R +---------------+ +-------------+ +-----------+ 8+-+ +--R | 4+-+ 4+-+ | 4+-+ 4+-+ |4+-+ 4+-+ tan(x)\|a +--R \|- %i\|b + \|a \|%i\|b + \|a \|\|b + \|a atan(----------------) +--R +-------------+ +--R | 4+-+ 4+-+ +--R \|- \|b + \|a +--R + +--R +-------------+ +-------------+ +-----------+ 8+-+ +--R | 4+-+ 4+-+ | 4+-+ 4+-+ |4+-+ 4+-+ tan(x)\|a +--R \|- \|b + \|a \|%i\|b + \|a \|\|b + \|a atan(------------------) +--R +---------------+ +--R | 4+-+ 4+-+ +--R \|- %i\|b + \|a +--R + +--R +-------------+ +---------------+ +-----------+ 8+-+ +--R | 4+-+ 4+-+ | 4+-+ 4+-+ |4+-+ 4+-+ tan(x)\|a +--R \|- \|b + \|a \|- %i\|b + \|a \|\|b + \|a atan(----------------) +--R +-------------+ +--R | 4+-+ 4+-+ +--R \|%i\|b + \|a +--R + +--R +-------------+ +---------------+ +-------------+ 8+-+ +--R | 4+-+ 4+-+ | 4+-+ 4+-+ | 4+-+ 4+-+ tan(x)\|a +--R \|- \|b + \|a \|- %i\|b + \|a \|%i\|b + \|a atan(--------------) +--R +-----------+ +--R |4+-+ 4+-+ +--R \|\|b + \|a +--R / +--R +-------------+ +---------------+ +-------------+ +-----------+ +--R 8+-+7 | 4+-+ 4+-+ | 4+-+ 4+-+ | 4+-+ 4+-+ |4+-+ 4+-+ +--R 4\|a \|- \|b + \|a \|- %i\|b + \|a \|%i\|b + \|a \|\|b + \|a +--R Type: Expression Complex Integer +--R +--E 361 + +--S 362 of 504 +--Ra0169:= integrate(t0169,x) +--R +--R +--R (314) +--R ROOT +--R 2 +--R (16a b - 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--R (- 1536a b + 3072a b - 1536a )%%EP1 +--R + +--R 3 2 4 5 2 3 +--R ((- 1024a b + 2048a b - 1024a )%%EP0 + 64a b - 64a ) +--R * +--R %%EP1 +--R + +--R 3 2 4 5 2 +--R (- 1536a b + 3072a b - 1536a )%%EP0 +--R + +--R 2 3 +--R (64a b - 64a )%%EP0 + 3b - a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 2 2 +--R (- 16a b + 16a )%%EP1 + (- 16a b + 16a )%%EP0 + 1 +--R / +--R 2 +--R 8a b - 8a +--R * +--R log +--R 8a sin(x) +--R * +--R ROOT +--R 2 +--R (16a b - 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--R (- 1536a b + 3072a b - 1536a )%%EP1 +--R + +--R 3 2 4 5 +--R (- 1024a b + 2048a b - 1024a )%%EP0 +--R + +--R 2 3 +--R 64a b - 64a +--R * +--R %%EP1 +--R + +--R 3 2 4 5 2 +--R (- 1536a b + 3072a b - 1536a )%%EP0 +--R + +--R 2 3 +--R (64a b - 64a )%%EP0 + 3b - a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 2 2 +--R (- 16a b + 16a )%%EP1 + (- 16a b + 16a )%%EP0 + 1 +--R / +--R 2 +--R 8a b - 8a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R ROOT +--R 2 +--R (- 16a b + 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--R (- 1536a b + 3072a b - 1536a )%%EP1 +--R + +--R 3 2 4 5 2 3 +--R ((- 1024a b + 2048a b - 1024a )%%EP0 + 64a b - 64a ) +--R * +--R %%EP1 +--R + +--R 3 2 4 5 2 +--R (- 1536a b + 3072a b - 1536a )%%EP0 +--R + +--R 2 3 +--R (64a b - 64a )%%EP0 + 3b - a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 2 2 +--R (- 16a b + 16a )%%EP1 + (- 16a b + 16a )%%EP0 + 1 +--R / +--R 2 +--R 8a b - 8a +--R * +--R log +--R 8a sin(x) +--R * +--R ROOT +--R 2 +--R (- 16a b + 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--R (- 1536a b + 3072a b - 1536a )%%EP1 +--R + +--R 3 2 4 5 +--R (- 1024a b + 2048a b - 1024a )%%EP0 +--R + +--R 2 3 +--R 64a b - 64a +--R * +--R %%EP1 +--R + +--R 3 2 4 5 2 +--R (- 1536a b + 3072a b - 1536a )%%EP0 +--R + +--R 2 3 +--R (64a b - 64a )%%EP0 + 3b - a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 2 2 +--R (- 16a b + 16a )%%EP1 + (- 16a b + 16a )%%EP0 + 1 +--R / +--R 2 +--R 8a b - 8a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R - +--R ROOT +--R 2 +--R (- 16a b + 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--R (- 1536a b + 3072a b - 1536a )%%EP1 +--R + +--R 3 2 4 5 2 +--R (- 1024a b + 2048a b - 1024a )%%EP0 + 64a b +--R + +--R 3 +--R - 64a +--R * +--R %%EP1 +--R + +--R 3 2 4 5 2 +--R (- 1536a b + 3072a b - 1536a )%%EP0 +--R + +--R 2 3 +--R (64a b - 64a )%%EP0 + 3b - a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 2 2 +--R (- 16a b + 16a )%%EP1 + (- 16a b + 16a )%%EP0 + 1 +--R / +--R 2 +--R 8a b - 8a +--R * +--R log +--R - +--R 8a sin(x) +--R * +--R ROOT +--R 2 +--R (- 16a b + 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--R (- 1536a b + 3072a b - 1536a )%%EP1 +--R + +--R 3 2 4 5 +--R (- 1024a b + 2048a b - 1024a )%%EP0 +--R + +--R 2 3 +--R 64a b - 64a +--R * +--R %%EP1 +--R + +--R 3 2 4 5 2 +--R (- 1536a b + 3072a b - 1536a )%%EP0 +--R + +--R 2 3 +--R (64a b - 64a )%%EP0 + 3b - a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 2 2 +--R (- 16a b + 16a )%%EP1 + (- 16a b + 16a )%%EP0 + 1 +--R / +--R 2 +--R 8a b - 8a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R - +--R ROOT +--R 2 +--R (16a b - 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--R (- 1536a b + 3072a b - 1536a )%%EP1 +--R + +--R 3 2 4 5 2 +--R (- 1024a b + 2048a b - 1024a )%%EP0 + 64a b +--R + +--R 3 +--R - 64a +--R * +--R %%EP1 +--R + +--R 3 2 4 5 2 +--R (- 1536a b + 3072a b - 1536a )%%EP0 +--R + +--R 2 3 +--R (64a b - 64a )%%EP0 + 3b - a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 2 2 +--R (- 16a b + 16a )%%EP1 + (- 16a b + 16a )%%EP0 + 1 +--R / +--R 2 +--R 8a b - 8a +--R * +--R log +--R - +--R 8a sin(x) +--R * +--R ROOT +--R 2 +--R (16a b - 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--R (- 1536a b + 3072a b - 1536a )%%EP1 +--R + +--R 3 2 4 5 +--R (- 1024a b + 2048a b - 1024a )%%EP0 +--R + +--R 2 3 +--R 64a b - 64a +--R * +--R %%EP1 +--R + +--R 3 2 4 5 2 +--R (- 1536a b + 3072a b - 1536a )%%EP0 +--R + +--R 2 3 +--R (64a b - 64a )%%EP0 + 3b - a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 2 2 +--R (- 16a b + 16a )%%EP1 + (- 16a b + 16a )%%EP0 + 1 +--R / +--R 2 +--R 8a b - 8a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R +------+ +--R +------+ 8a sin(x)\|4%%EP1 - 2cos(x) +--R \|4%%EP1 log(----------------------------) +--R cos(x) + 1 +--R + +--R +------+ +--R +------+ - 8a sin(x)\|4%%EP1 - 2cos(x) +--R - \|4%%EP1 log(------------------------------) +--R cos(x) + 1 +--R + +--R +------+ +--R +------+ 8a sin(x)\|4%%EP0 - 2cos(x) +--R \|4%%EP0 log(----------------------------) +--R cos(x) + 1 +--R + +--R +------+ +--R +------+ - 8a sin(x)\|4%%EP0 - 2cos(x) +--R - \|4%%EP0 log(------------------------------) +--R cos(x) + 1 +--R / +--R 2 +--R Type: Union(Expression Integer,...) +--R +--E 362 + +--S 363 of 504 +--Rm0169:= a0169-r0169 +--R +--R +--R (315) +--R +-------------+ +---------------+ +-------------+ +-----------+ +--R 8+-+7 | 4+-+ 4+-+ | 4+-+ 4+-+ | 4+-+ 4+-+ |4+-+ 4+-+ +--R 2\|a \|- \|b + \|a \|- %i\|b + \|a \|%i\|b + \|a \|\|b + \|a +--R * +--R ROOT +--R 2 +--R (16a b - 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--R (- 1536a b + 3072a b - 1536a )%%EP1 +--R + +--R 3 2 4 5 2 3 +--R ((- 1024a b + 2048a b - 1024a )%%EP0 + 64a b - 64a ) +--R * +--R %%EP1 +--R + +--R 3 2 4 5 2 +--R (- 1536a b + 3072a b - 1536a )%%EP0 +--R + +--R 2 3 +--R (64a b - 64a )%%EP0 + 3b - a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 2 2 +--R (- 16a b + 16a )%%EP1 + (- 16a b + 16a )%%EP0 + 1 +--R / +--R 2 +--R 8a b - 8a +--R * +--R log +--R 8a sin(x) +--R * +--R ROOT +--R 2 +--R (16a b - 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--R (- 1536a b + 3072a b - 1536a )%%EP1 +--R + +--R 3 2 4 5 +--R (- 1024a b + 2048a b - 1024a )%%EP0 +--R + +--R 2 3 +--R 64a b - 64a +--R * +--R %%EP1 +--R + +--R 3 2 4 5 2 +--R (- 1536a b + 3072a b - 1536a )%%EP0 +--R + +--R 2 3 +--R (64a b - 64a )%%EP0 + 3b - a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 2 2 +--R (- 16a b + 16a )%%EP1 + (- 16a b + 16a )%%EP0 + 1 +--R / +--R 2 +--R 8a b - 8a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R +-------------+ +---------------+ +-------------+ +-----------+ +--R 8+-+7 | 4+-+ 4+-+ | 4+-+ 4+-+ | 4+-+ 4+-+ |4+-+ 4+-+ +--R 2\|a \|- \|b + \|a \|- %i\|b + \|a \|%i\|b + \|a \|\|b + \|a +--R * +--R ROOT +--R 2 +--R (- 16a b + 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--R (- 1536a b + 3072a b - 1536a )%%EP1 +--R + +--R 3 2 4 5 2 3 +--R ((- 1024a b + 2048a b - 1024a )%%EP0 + 64a b - 64a ) +--R * +--R %%EP1 +--R + +--R 3 2 4 5 2 +--R (- 1536a b + 3072a b - 1536a )%%EP0 +--R + +--R 2 3 +--R (64a b - 64a )%%EP0 + 3b - a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 2 2 +--R (- 16a b + 16a )%%EP1 + (- 16a b + 16a )%%EP0 + 1 +--R / +--R 2 +--R 8a b - 8a +--R * +--R log +--R 8a sin(x) +--R * +--R ROOT +--R 2 +--R (- 16a b + 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--R (- 1536a b + 3072a b - 1536a )%%EP1 +--R + +--R 3 2 4 5 +--R (- 1024a b + 2048a b - 1024a )%%EP0 +--R + +--R 2 3 +--R 64a b - 64a +--R * +--R %%EP1 +--R + +--R 3 2 4 5 2 +--R (- 1536a b + 3072a b - 1536a )%%EP0 +--R + +--R 2 3 +--R (64a b - 64a )%%EP0 + 3b - a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 2 2 +--R (- 16a b + 16a )%%EP1 + (- 16a b + 16a )%%EP0 + 1 +--R / +--R 2 +--R 8a b - 8a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R - +--R +-------------+ +---------------+ +-------------+ +--R 8+-+7 | 4+-+ 4+-+ | 4+-+ 4+-+ | 4+-+ 4+-+ +--R 2\|a \|- \|b + \|a \|- %i\|b + \|a \|%i\|b + \|a +--R * +--R +-----------+ +--R |4+-+ 4+-+ +--R \|\|b + \|a +--R * +--R ROOT +--R 2 +--R (- 16a b + 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--R (- 1536a b + 3072a b - 1536a )%%EP1 +--R + +--R 3 2 4 5 2 +--R (- 1024a b + 2048a b - 1024a )%%EP0 + 64a b +--R + +--R 3 +--R - 64a +--R * +--R %%EP1 +--R + +--R 3 2 4 5 2 +--R (- 1536a b + 3072a b - 1536a )%%EP0 +--R + +--R 2 3 +--R (64a b - 64a )%%EP0 + 3b - a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 2 2 +--R (- 16a b + 16a )%%EP1 + (- 16a b + 16a )%%EP0 + 1 +--R / +--R 2 +--R 8a b - 8a +--R * +--R log +--R - +--R 8a sin(x) +--R * +--R ROOT +--R 2 +--R (- 16a b + 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--R (- 1536a b + 3072a b - 1536a )%%EP1 +--R + +--R 3 2 4 5 +--R (- 1024a b + 2048a b - 1024a )%%EP0 +--R + +--R 2 3 +--R 64a b - 64a +--R * +--R %%EP1 +--R + +--R 3 2 4 5 2 +--R (- 1536a b + 3072a b - 1536a )%%EP0 +--R + +--R 2 3 +--R (64a b - 64a )%%EP0 + 3b - a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 2 2 +--R (- 16a b + 16a )%%EP1 + (- 16a b + 16a )%%EP0 + 1 +--R / +--R 2 +--R 8a b - 8a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R - +--R +-------------+ +---------------+ +-------------+ +--R 8+-+7 | 4+-+ 4+-+ | 4+-+ 4+-+ | 4+-+ 4+-+ +--R 2\|a \|- \|b + \|a \|- %i\|b + \|a \|%i\|b + \|a +--R * +--R +-----------+ +--R |4+-+ 4+-+ +--R \|\|b + \|a +--R * +--R ROOT +--R 2 +--R (16a b - 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--R (- 1536a b + 3072a b - 1536a )%%EP1 +--R + +--R 3 2 4 5 2 +--R (- 1024a b + 2048a b - 1024a )%%EP0 + 64a b +--R + +--R 3 +--R - 64a +--R * +--R %%EP1 +--R + +--R 3 2 4 5 2 +--R (- 1536a b + 3072a b - 1536a )%%EP0 +--R + +--R 2 3 +--R (64a b - 64a )%%EP0 + 3b - a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 2 2 +--R (- 16a b + 16a )%%EP1 + (- 16a b + 16a )%%EP0 + 1 +--R / +--R 2 +--R 8a b - 8a +--R * +--R log +--R - +--R 8a sin(x) +--R * +--R ROOT +--R 2 +--R (16a b - 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--R (- 1536a b + 3072a b - 1536a )%%EP1 +--R + +--R 3 2 4 5 +--R (- 1024a b + 2048a b - 1024a )%%EP0 +--R + +--R 2 3 +--R 64a b - 64a +--R * +--R %%EP1 +--R + +--R 3 2 4 5 2 +--R (- 1536a b + 3072a b - 1536a )%%EP0 +--R + +--R 2 3 +--R (64a b - 64a )%%EP0 + 3b - a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 2 2 +--R (- 16a b + 16a )%%EP1 + (- 16a b + 16a )%%EP0 + 1 +--R / +--R 2 +--R 8a b - 8a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R +-------------+ +---------------+ +-------------+ +-----------+ +--R 8+-+7 | 4+-+ 4+-+ | 4+-+ 4+-+ | 4+-+ 4+-+ |4+-+ 4+-+ +--R 2\|a \|- \|b + \|a \|- %i\|b + \|a \|%i\|b + \|a \|\|b + \|a +--R * +--R +------+ +--R +------+ 8a sin(x)\|4%%EP1 - 2cos(x) +--R \|4%%EP1 log(----------------------------) +--R cos(x) + 1 +--R + +--R - +--R +-------------+ +---------------+ +-------------+ +--R 8+-+7 | 4+-+ 4+-+ | 4+-+ 4+-+ | 4+-+ 4+-+ +--R 2\|a \|- \|b + \|a \|- %i\|b + \|a \|%i\|b + \|a +--R * +--R +-----------+ +------+ +--R |4+-+ 4+-+ +------+ - 8a sin(x)\|4%%EP1 - 2cos(x) +--R \|\|b + \|a \|4%%EP1 log(------------------------------) +--R cos(x) + 1 +--R + +--R +-------------+ +---------------+ +-------------+ +-----------+ +--R 8+-+7 | 4+-+ 4+-+ | 4+-+ 4+-+ | 4+-+ 4+-+ |4+-+ 4+-+ +--R 2\|a \|- \|b + \|a \|- %i\|b + \|a \|%i\|b + \|a \|\|b + \|a +--R * +--R +------+ +--R +------+ 8a sin(x)\|4%%EP0 - 2cos(x) +--R \|4%%EP0 log(----------------------------) +--R cos(x) + 1 +--R + +--R - +--R +-------------+ +---------------+ +-------------+ +--R 8+-+7 | 4+-+ 4+-+ | 4+-+ 4+-+ | 4+-+ 4+-+ +--R 2\|a \|- \|b + \|a \|- %i\|b + \|a \|%i\|b + \|a +--R * +--R +-----------+ +------+ +--R |4+-+ 4+-+ +------+ - 8a sin(x)\|4%%EP0 - 2cos(x) +--R \|\|b + \|a \|4%%EP0 log(------------------------------) +--R cos(x) + 1 +--R + +--R +---------------+ +-------------+ +-----------+ 8+-+ +--R | 4+-+ 4+-+ | 4+-+ 4+-+ |4+-+ 4+-+ tan(x)\|a +--R - \|- %i\|b + \|a \|%i\|b + \|a \|\|b + \|a atan(----------------) +--R +-------------+ +--R | 4+-+ 4+-+ +--R \|- \|b + \|a +--R + +--R +-------------+ +-------------+ +-----------+ 8+-+ +--R | 4+-+ 4+-+ | 4+-+ 4+-+ |4+-+ 4+-+ tan(x)\|a +--R - \|- \|b + \|a \|%i\|b + \|a \|\|b + \|a atan(------------------) +--R +---------------+ +--R | 4+-+ 4+-+ +--R \|- %i\|b + \|a +--R + +--R +-------------+ +---------------+ +-----------+ 8+-+ +--R | 4+-+ 4+-+ | 4+-+ 4+-+ |4+-+ 4+-+ tan(x)\|a +--R - \|- \|b + \|a \|- %i\|b + \|a \|\|b + \|a atan(----------------) +--R +-------------+ +--R | 4+-+ 4+-+ +--R \|%i\|b + \|a +--R + +--R +-------------+ +---------------+ +-------------+ 8+-+ +--R | 4+-+ 4+-+ | 4+-+ 4+-+ | 4+-+ 4+-+ tan(x)\|a +--R - \|- \|b + \|a \|- %i\|b + \|a \|%i\|b + \|a atan(--------------) +--R +-----------+ +--R |4+-+ 4+-+ +--R \|\|b + \|a +--R / +--R +-------------+ +---------------+ +-------------+ +-----------+ +--R 8+-+7 | 4+-+ 4+-+ | 4+-+ 4+-+ | 4+-+ 4+-+ |4+-+ 4+-+ +--R 4\|a \|- \|b + \|a \|- %i\|b + \|a \|%i\|b + \|a \|\|b + \|a +--R Type: Expression Complex Integer +--R +--E 363 + +--S 364 of 504 +--Rd0169:= D(m0169,x) +--R +--R +--R (316) +--R 8 8 +--R b cos(x) tan(x) +--R + +--R 8 2 6 4 4 +--R - a sin(x) - 4a cos(x) sin(x) - 6a cos(x) sin(x) +--R + +--R 6 2 8 +--R - 4a cos(x) sin(x) + (b - a)cos(x) +--R * +--R 6 +--R tan(x) +--R + +--R 8 2 6 +--R (- b + a)sin(x) + (- 4b + 4a)cos(x) sin(x) +--R + +--R 4 4 6 2 +--R (- 6b + 6a)cos(x) sin(x) + (- 4b + 4a)cos(x) sin(x) +--R + +--R 8 +--R (- b + a)cos(x) +--R * +--R 8+-+6 +--R \|a +--R + +--R 8 2 6 4 4 +--R a sin(x) + 4a cos(x) sin(x) + 6a cos(x) sin(x) +--R + +--R 6 2 8 +--R 4a cos(x) sin(x) + (3b + a)cos(x) +--R * +--R 6 +--R tan(x) +--R + +--R 8 2 6 4 4 +--R - 3a sin(x) - 12a cos(x) sin(x) - 18a cos(x) sin(x) +--R + +--R 6 2 8 +--R - 12a cos(x) sin(x) + (3b - 3a)cos(x) +--R * +--R 4 +--R tan(x) +--R * +--R 4+-+8+-+4 +--R \|a \|a +--R + +--R 8 2 6 4 4 +--R 3a sin(x) + 12a cos(x) sin(x) + 18a cos(x) sin(x) +--R + +--R 6 2 8 +--R 12a cos(x) sin(x) + (3b + 3a)cos(x) +--R * +--R 4 +--R tan(x) +--R + +--R 8 2 6 4 4 +--R - 3a sin(x) - 12a cos(x) sin(x) - 18a cos(x) sin(x) +--R + +--R 6 2 8 +--R - 12a cos(x) sin(x) + (3b - 3a)cos(x) +--R * +--R 2 +--R tan(x) +--R * +--R 4+-+2 8+-+2 +--R \|a \|a +--R + +--R 8 2 6 4 4 +--R 3a sin(x) + 12a cos(x) sin(x) + 18a cos(x) sin(x) +--R + +--R 6 2 8 +--R 12a cos(x) sin(x) + (b + 3a)cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 8 2 6 4 4 +--R - a sin(x) - 4a cos(x) sin(x) - 6a cos(x) sin(x) +--R + +--R 6 2 8 +--R - 4a cos(x) sin(x) + (b - a)cos(x) +--R * +--R 4+-+3 +--R \|a +--R / +--R 2 8 2 2 6 2 4 4 +--R a sin(x) + 4a cos(x) sin(x) + 6a cos(x) sin(x) +--R + +--R 2 6 2 2 8 +--R 4a cos(x) sin(x) + (- a b + a )cos(x) +--R * +--R 8 +--R tan(x) +--R + +--R 2 8 2 2 6 +--R (- a b + a )sin(x) + (- 4a b + 4a )cos(x) sin(x) +--R + +--R 2 4 4 2 6 2 +--R (- 6a b + 6a )cos(x) sin(x) + (- 4a b + 4a )cos(x) sin(x) +--R + +--R 2 2 8 +--R (b - 2a b + a )cos(x) +--R * +--R 8+-+6 +--R \|a +--R + +--R 2 8 2 2 6 2 4 4 +--R 4a sin(x) + 16a cos(x) sin(x) + 24a cos(x) sin(x) +--R + +--R 2 6 2 2 8 +--R 16a cos(x) sin(x) + (- 4a b + 4a )cos(x) +--R * +--R 6 4+-+8+-+4 +--R tan(x) \|a \|a +--R + +--R 2 8 2 2 6 2 4 4 +--R 6a sin(x) + 24a cos(x) sin(x) + 36a cos(x) sin(x) +--R + +--R 2 6 2 2 8 +--R 24a cos(x) sin(x) + (- 6a b + 6a )cos(x) +--R * +--R 4 4+-+2 8+-+2 +--R tan(x) \|a \|a +--R + +--R 2 8 2 2 6 2 4 4 +--R 4a sin(x) + 16a cos(x) sin(x) + 24a cos(x) sin(x) +--R + +--R 2 6 2 2 8 +--R 16a cos(x) sin(x) + (- 4a b + 4a )cos(x) +--R * +--R 2 4+-+3 +--R tan(x) \|a +--R Type: Expression Complex Integer +--R +--E 364 + +--S 365 of 504 +--Rt0170:= 1/(1+cos(x)^3) +--R +--R +--R 1 +--R (317) ----------- +--R 3 +--R cos(x) + 1 +--R Type: Expression Integer +--R +--E 365 + +--S 366 of 504 +--Rr0170:= -2/3*atan((-1)^(2/3)*(1+(-1)^(1/3))^(1/2)*tan(1/2*x))/(1+(-1)^(1/3))^(1/2)+2/3*atan((-1)^(1/3)*(1-(-1)^(2/3))^(1/2)*tan(1/2*x))/(1-(-1)^(2/3))^(1/2)+sin(x)/(3*cos(x)+3) +--R +--R +--R (318) +--R +-------------+ +----------+ +--R | 3+---+2 3+---+2 x |3+---+ +--R (- 2cos(x) - 2)\|- \|- 1 + 1 atan(\|- 1 tan(-)\|\|- 1 + 1 ) +--R 2 +--R + +--R +----------+ +-------------+ +--R |3+---+ 3+---+ x | 3+---+2 +--R (2cos(x) + 2)\|\|- 1 + 1 atan(\|- 1 tan(-)\|- \|- 1 + 1 ) +--R 2 +--R + +--R +-------------+ +----------+ +--R | 3+---+2 |3+---+ +--R sin(x)\|- \|- 1 + 1 \|\|- 1 + 1 +--R / +--R +-------------+ +----------+ +--R | 3+---+2 |3+---+ +--R (3cos(x) + 3)\|- \|- 1 + 1 \|\|- 1 + 1 +--R Type: Expression Integer +--R +--E 366 + +--S 367 of 504 +--Ra0170:= integrate(t0170,x) +--R +--R +--R (319) +--R %pi x 4 %pi x 2 %pi x 2 +--R cos(---)sin(-) + (2cos(---)cos(-) - 2cos(---))sin(-) +--R 12 2 12 2 12 2 +--R + +--R %pi x 4 %pi x 2 %pi +--R cos(---)cos(-) + 2cos(---)cos(-) + cos(---) +--R 12 2 12 2 12 +--R * +--R log +--R %pi 2 4+-+ %pi %pi 2 +-+4+-+ %pi +--R sin(---) + \|3 sin(---) + cos(---) - \|3 \|3 cos(---) +--R 12 12 12 12 +--R + +--R 4+-+2 +--R \|3 +--R * +--R x 4 +--R sin(-) +--R 2 +--R + +--R x 2 %pi 2 4+-+ x 2 %pi +--R (2cos(-) - 2)sin(---) + 2\|3 cos(-) sin(---) +--R 2 12 2 12 +--R + +--R %pi 2 +-+4+-+ %pi 4+-+2 x 2 +--R (2cos(---) - 2\|3 \|3 cos(---) + 2\|3 )cos(-) +--R 12 12 2 +--R + +--R %pi 2 4+-+2 +--R - 2cos(---) + 2\|3 +--R 12 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R +-+4+-+ x %pi 4+-+ %pi x x +--R (4\|3 \|3 cos(-)sin(---) + 4\|3 cos(---)cos(-))sin(-) +--R 2 12 12 2 2 +--R + +--R x 4 x 2 %pi 2 4+-+ x 4 4+-+ %pi +--R (cos(-) + 2cos(-) + 1)sin(---) + (\|3 cos(-) - \|3 )sin(---) +--R 2 2 12 2 12 +--R + +--R %pi 2 +-+4+-+ %pi 4+-+2 x 4 +--R (cos(---) - \|3 \|3 cos(---) + \|3 )cos(-) +--R 12 12 2 +--R + +--R %pi 2 4+-+2 x 2 %pi 2 +-+4+-+ %pi +--R (2cos(---) - 2\|3 )cos(-) + cos(---) + \|3 \|3 cos(---) +--R 12 2 12 12 +--R + +--R 4+-+2 +--R \|3 +--R / +--R x 4 x 2 x 2 x 4 x 2 +--R sin(-) + (2cos(-) - 2)sin(-) + cos(-) + 2cos(-) + 1 +--R 2 2 2 2 2 +--R + +--R %pi x 4 %pi x 2 %pi x 2 +--R - cos(---)sin(-) + (- 2cos(---)cos(-) + 2cos(---))sin(-) +--R 12 2 12 2 12 2 +--R + +--R %pi x 4 %pi x 2 %pi +--R - cos(---)cos(-) - 2cos(---)cos(-) - cos(---) +--R 12 2 12 2 12 +--R * +--R log +--R %pi 2 4+-+ %pi %pi 2 +-+4+-+ %pi +--R sin(---) + \|3 sin(---) + cos(---) - \|3 \|3 cos(---) +--R 12 12 12 12 +--R + +--R 4+-+2 +--R \|3 +--R * +--R x 4 +--R sin(-) +--R 2 +--R + +--R x 2 %pi 2 4+-+ x 2 %pi +--R (2cos(-) - 2)sin(---) + 2\|3 cos(-) sin(---) +--R 2 12 2 12 +--R + +--R %pi 2 +-+4+-+ %pi 4+-+2 x 2 +--R (2cos(---) - 2\|3 \|3 cos(---) + 2\|3 )cos(-) +--R 12 12 2 +--R + +--R %pi 2 4+-+2 +--R - 2cos(---) + 2\|3 +--R 12 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R +-+4+-+ x %pi 4+-+ %pi x x +--R (- 4\|3 \|3 cos(-)sin(---) - 4\|3 cos(---)cos(-))sin(-) +--R 2 12 12 2 2 +--R + +--R x 4 x 2 %pi 2 4+-+ x 4 4+-+ %pi +--R (cos(-) + 2cos(-) + 1)sin(---) + (\|3 cos(-) - \|3 )sin(---) +--R 2 2 12 2 12 +--R + +--R %pi 2 +-+4+-+ %pi 4+-+2 x 4 +--R (cos(---) - \|3 \|3 cos(---) + \|3 )cos(-) +--R 12 12 2 +--R + +--R %pi 2 4+-+2 x 2 %pi 2 +-+4+-+ %pi +--R (2cos(---) - 2\|3 )cos(-) + cos(---) + \|3 \|3 cos(---) +--R 12 2 12 12 +--R + +--R 4+-+2 +--R \|3 +--R / +--R x 4 x 2 x 2 x 4 x 2 +--R sin(-) + (2cos(-) - 2)sin(-) + cos(-) + 2cos(-) + 1 +--R 2 2 2 2 2 +--R + +--R %pi x 4 %pi x 2 %pi x 2 +--R cos(---)sin(-) + (2cos(---)cos(-) - 2cos(---))sin(-) +--R 12 2 12 2 12 2 +--R + +--R %pi x 4 %pi x 2 %pi +--R cos(---)cos(-) + 2cos(---)cos(-) + cos(---) +--R 12 2 12 2 12 +--R * +--R log +--R %pi 2 4+-+ %pi %pi 2 +-+4+-+ %pi +--R sin(---) - \|3 sin(---) + cos(---) + \|3 \|3 cos(---) +--R 12 12 12 12 +--R + +--R 4+-+2 +--R \|3 +--R * +--R x 4 +--R sin(-) +--R 2 +--R + +--R x 2 %pi 2 4+-+ x 2 %pi +--R (2cos(-) - 2)sin(---) - 2\|3 cos(-) sin(---) +--R 2 12 2 12 +--R + +--R %pi 2 +-+4+-+ %pi 4+-+2 x 2 +--R (2cos(---) + 2\|3 \|3 cos(---) + 2\|3 )cos(-) +--R 12 12 2 +--R + +--R %pi 2 4+-+2 +--R - 2cos(---) + 2\|3 +--R 12 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R +-+4+-+ x %pi 4+-+ %pi x x +--R (4\|3 \|3 cos(-)sin(---) + 4\|3 cos(---)cos(-))sin(-) +--R 2 12 12 2 2 +--R + +--R x 4 x 2 %pi 2 +--R (cos(-) + 2cos(-) + 1)sin(---) +--R 2 2 12 +--R + +--R 4+-+ x 4 4+-+ %pi +--R (- \|3 cos(-) + \|3 )sin(---) +--R 2 12 +--R + +--R %pi 2 +-+4+-+ %pi 4+-+2 x 4 +--R (cos(---) + \|3 \|3 cos(---) + \|3 )cos(-) +--R 12 12 2 +--R + +--R %pi 2 4+-+2 x 2 %pi 2 +-+4+-+ %pi +--R (2cos(---) - 2\|3 )cos(-) + cos(---) - \|3 \|3 cos(---) +--R 12 2 12 12 +--R + +--R 4+-+2 +--R \|3 +--R / +--R x 4 x 2 x 2 x 4 x 2 +--R sin(-) + (2cos(-) - 2)sin(-) + cos(-) + 2cos(-) + 1 +--R 2 2 2 2 2 +--R + +--R %pi x 4 %pi x 2 %pi x 2 +--R - cos(---)sin(-) + (- 2cos(---)cos(-) + 2cos(---))sin(-) +--R 12 2 12 2 12 2 +--R + +--R %pi x 4 %pi x 2 %pi +--R - cos(---)cos(-) - 2cos(---)cos(-) - cos(---) +--R 12 2 12 2 12 +--R * +--R log +--R %pi 2 4+-+ %pi %pi 2 +-+4+-+ %pi +--R sin(---) - \|3 sin(---) + cos(---) + \|3 \|3 cos(---) +--R 12 12 12 12 +--R + +--R 4+-+2 +--R \|3 +--R * +--R x 4 +--R sin(-) +--R 2 +--R + +--R x 2 %pi 2 4+-+ x 2 %pi +--R (2cos(-) - 2)sin(---) - 2\|3 cos(-) sin(---) +--R 2 12 2 12 +--R + +--R %pi 2 +-+4+-+ %pi 4+-+2 x 2 +--R (2cos(---) + 2\|3 \|3 cos(---) + 2\|3 )cos(-) +--R 12 12 2 +--R + +--R %pi 2 4+-+2 +--R - 2cos(---) + 2\|3 +--R 12 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R +-+4+-+ x %pi 4+-+ %pi x x +--R (- 4\|3 \|3 cos(-)sin(---) - 4\|3 cos(---)cos(-))sin(-) +--R 2 12 12 2 2 +--R + +--R x 4 x 2 %pi 2 +--R (cos(-) + 2cos(-) + 1)sin(---) +--R 2 2 12 +--R + +--R 4+-+ x 4 4+-+ %pi +--R (- \|3 cos(-) + \|3 )sin(---) +--R 2 12 +--R + +--R %pi 2 +-+4+-+ %pi 4+-+2 x 4 +--R (cos(---) + \|3 \|3 cos(---) + \|3 )cos(-) +--R 12 12 2 +--R + +--R %pi 2 4+-+2 x 2 %pi 2 +-+4+-+ %pi +--R (2cos(---) - 2\|3 )cos(-) + cos(---) - \|3 \|3 cos(---) +--R 12 2 12 12 +--R + +--R 4+-+2 +--R \|3 +--R / +--R x 4 x 2 x 2 x 4 x 2 +--R sin(-) + (2cos(-) - 2)sin(-) + cos(-) + 2cos(-) + 1 +--R 2 2 2 2 2 +--R + +--R %pi x 4 x 2 %pi x 2 +--R 2sin(---)sin(-) + (4cos(-) - 4)sin(---)sin(-) +--R 12 2 2 12 2 +--R + +--R x 4 x 2 %pi +--R (2cos(-) + 4cos(-) + 2)sin(---) +--R 2 2 12 +--R * +--R atan +--R %pi +-+ %pi 4+-+ x 4 +--R (sin(---) - \|3 cos(---) + 2\|3 )sin(-) +--R 12 12 2 +--R + +--R x 2 %pi +-+ %pi 4+-+ x 2 +--R (2cos(-) - 2)sin(---) + (- 2\|3 cos(---) + 4\|3 )cos(-) +--R 2 12 12 2 +--R + +--R +-+ %pi +--R 2\|3 cos(---) +--R 12 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R x 4 x 2 %pi +--R (cos(-) + 2cos(-) + 1)sin(---) +--R 2 2 12 +--R + +--R +-+ %pi 4+-+ x 4 +-+ %pi x 2 +--R (- \|3 cos(---) + 2\|3 )cos(-) - 2\|3 cos(---)cos(-) +--R 12 2 12 2 +--R + +--R +-+ %pi 4+-+ +--R - \|3 cos(---) - 2\|3 +--R 12 +--R / +--R +-+ %pi %pi x 4 +--R (\|3 sin(---) + cos(---))sin(-) +--R 12 12 2 +--R + +--R +-+ x 2 +-+ %pi %pi x 2 +--R (2\|3 cos(-) - 2\|3 )sin(---) + 2cos(---)cos(-) +--R 2 12 12 2 +--R + +--R %pi +--R - 2cos(---) +--R 12 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R 4+-+ x x +--R - 8\|3 cos(-)sin(-) +--R 2 2 +--R + +--R +-+ x 4 +-+ x 2 +-+ %pi %pi x 4 +--R (\|3 cos(-) + 2\|3 cos(-) + \|3 )sin(---) + cos(---)cos(-) +--R 2 2 12 12 2 +--R + +--R %pi x 2 %pi +--R 2cos(---)cos(-) + cos(---) +--R 12 2 12 +--R + +--R %pi x 4 x 2 %pi x 2 +--R - 2sin(---)sin(-) + (- 4cos(-) + 4)sin(---)sin(-) +--R 12 2 2 12 2 +--R + +--R x 4 x 2 %pi +--R (- 2cos(-) - 4cos(-) - 2)sin(---) +--R 2 2 12 +--R * +--R atan +--R %pi +-+ %pi 4+-+ x 4 +--R (sin(---) - \|3 cos(---) + 2\|3 )sin(-) +--R 12 12 2 +--R + +--R x 2 %pi +-+ %pi 4+-+ x 2 +--R (2cos(-) - 2)sin(---) + (- 2\|3 cos(---) + 4\|3 )cos(-) +--R 2 12 12 2 +--R + +--R +-+ %pi +--R 2\|3 cos(---) +--R 12 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R x 4 x 2 %pi +--R (cos(-) + 2cos(-) + 1)sin(---) +--R 2 2 12 +--R + +--R +-+ %pi 4+-+ x 4 +-+ %pi x 2 +--R (- \|3 cos(---) + 2\|3 )cos(-) - 2\|3 cos(---)cos(-) +--R 12 2 12 2 +--R + +--R +-+ %pi 4+-+ +--R - \|3 cos(---) - 2\|3 +--R 12 +--R / +--R +-+ %pi %pi x 4 +--R (\|3 sin(---) + cos(---))sin(-) +--R 12 12 2 +--R + +--R +-+ x 2 +-+ %pi %pi x 2 +--R (2\|3 cos(-) - 2\|3 )sin(---) + 2cos(---)cos(-) +--R 2 12 12 2 +--R + +--R %pi +--R - 2cos(---) +--R 12 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R 4+-+ x x +-+ x 4 +-+ x 2 +-+ %pi +--R 8\|3 cos(-)sin(-) + (\|3 cos(-) + 2\|3 cos(-) + \|3 )sin(---) +--R 2 2 2 2 12 +--R + +--R %pi x 4 %pi x 2 %pi +--R cos(---)cos(-) + 2cos(---)cos(-) + cos(---) +--R 12 2 12 2 12 +--R + +--R %pi x 4 x 2 %pi x 2 +--R 2sin(---)sin(-) + (4cos(-) - 4)sin(---)sin(-) +--R 12 2 2 12 2 +--R + +--R x 4 x 2 %pi +--R (2cos(-) + 4cos(-) + 2)sin(---) +--R 2 2 12 +--R * +--R atan +--R %pi +-+ %pi 4+-+ x 4 +--R (sin(---) - \|3 cos(---) - 2\|3 )sin(-) +--R 12 12 2 +--R + +--R x 2 %pi +-+ %pi 4+-+ x 2 +--R (2cos(-) - 2)sin(---) + (- 2\|3 cos(---) - 4\|3 )cos(-) +--R 2 12 12 2 +--R + +--R +-+ %pi +--R 2\|3 cos(---) +--R 12 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R x 4 x 2 %pi +--R (cos(-) + 2cos(-) + 1)sin(---) +--R 2 2 12 +--R + +--R +-+ %pi 4+-+ x 4 +-+ %pi x 2 +--R (- \|3 cos(---) - 2\|3 )cos(-) - 2\|3 cos(---)cos(-) +--R 12 2 12 2 +--R + +--R +-+ %pi 4+-+ +--R - \|3 cos(---) + 2\|3 +--R 12 +--R / +--R +-+ %pi %pi x 4 +--R (\|3 sin(---) + cos(---))sin(-) +--R 12 12 2 +--R + +--R +-+ x 2 +-+ %pi %pi x 2 +--R (2\|3 cos(-) - 2\|3 )sin(---) + 2cos(---)cos(-) +--R 2 12 12 2 +--R + +--R %pi +--R - 2cos(---) +--R 12 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R 4+-+ x x +--R - 8\|3 cos(-)sin(-) +--R 2 2 +--R + +--R +-+ x 4 +-+ x 2 +-+ %pi %pi x 4 +--R (\|3 cos(-) + 2\|3 cos(-) + \|3 )sin(---) + cos(---)cos(-) +--R 2 2 12 12 2 +--R + +--R %pi x 2 %pi +--R 2cos(---)cos(-) + cos(---) +--R 12 2 12 +--R + +--R %pi x 4 x 2 %pi x 2 +--R - 2sin(---)sin(-) + (- 4cos(-) + 4)sin(---)sin(-) +--R 12 2 2 12 2 +--R + +--R x 4 x 2 %pi +--R (- 2cos(-) - 4cos(-) - 2)sin(---) +--R 2 2 12 +--R * +--R atan +--R %pi +-+ %pi 4+-+ x 4 +--R (sin(---) - \|3 cos(---) - 2\|3 )sin(-) +--R 12 12 2 +--R + +--R x 2 %pi +-+ %pi 4+-+ x 2 +--R (2cos(-) - 2)sin(---) + (- 2\|3 cos(---) - 4\|3 )cos(-) +--R 2 12 12 2 +--R + +--R +-+ %pi +--R 2\|3 cos(---) +--R 12 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R x 4 x 2 %pi +--R (cos(-) + 2cos(-) + 1)sin(---) +--R 2 2 12 +--R + +--R +-+ %pi 4+-+ x 4 +-+ %pi x 2 +--R (- \|3 cos(---) - 2\|3 )cos(-) - 2\|3 cos(---)cos(-) +--R 12 2 12 2 +--R + +--R +-+ %pi 4+-+ +--R - \|3 cos(---) + 2\|3 +--R 12 +--R / +--R +-+ %pi %pi x 4 +--R (\|3 sin(---) + cos(---))sin(-) +--R 12 12 2 +--R + +--R +-+ x 2 +-+ %pi %pi x 2 +--R (2\|3 cos(-) - 2\|3 )sin(---) + 2cos(---)cos(-) +--R 2 12 12 2 +--R + +--R %pi +--R - 2cos(---) +--R 12 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R 4+-+ x x +-+ x 4 +-+ x 2 +-+ %pi +--R 8\|3 cos(-)sin(-) + (\|3 cos(-) + 2\|3 cos(-) + \|3 )sin(---) +--R 2 2 2 2 12 +--R + +--R %pi x 4 %pi x 2 %pi +--R cos(---)cos(-) + 2cos(---)cos(-) + cos(---) +--R 12 2 12 2 12 +--R + +--R 4+-+ x x +--R 8\|3 cos(-)sin(-) +--R 2 2 +--R / +--R 4+-+ x 4 4+-+ x 2 4+-+ x 2 4+-+ x 4 +--R 6\|3 sin(-) + (12\|3 cos(-) - 12\|3 )sin(-) + 6\|3 cos(-) +--R 2 2 2 2 +--R + +--R 4+-+ x 2 4+-+ +--R 12\|3 cos(-) + 6\|3 +--R 2 +--R Type: Union(Expression Integer,...) +--R +--R +--R +--E 367 + +--S 368 of 504 +--Rt0171:= 1/(1+cos(x)^4) +--R +--R +--R 1 +--R (320) ----------- +--R 4 +--R cos(x) + 1 +--R Type: Expression Integer +--R +--E 368 + +--S 369 of 504 +--Rr0171:= 1/2*atan(tan(x)/(1-%i)^(1/2))/(1-%i)^(1/2)+1/2*atan(tan(x)/(1+%i)^(1/2))/(1+%i)^(1/2) +--R +--R +--R +------+ tan(x) +------+ tan(x) +--R \|1 + %i atan(---------) + \|1 - %i atan(---------) +--R +------+ +------+ +--R \|1 - %i \|1 + %i +--R (321) --------------------------------------------------- +--R +------+ +------+ +--R 2\|1 - %i \|1 + %i +--R Type: Expression Complex Integer +--R +--E 369 + +--S 370 of 504 +--Ra0171:= integrate(t0171,x) +--R +--R +--R (322) +--R 4+-+ %pi +--R \|2 cos(---) +--R 8 +--R * +--R log +--R x 4 +-+4+-+ %pi x x 3 +--R sin(-) + 2\|2 \|2 cos(---)cos(-)sin(-) +--R 2 8 2 2 +--R + +--R 4+-+2 x 2 %pi 2 4+-+2 %pi 2 x 2 x 2 +--R (2\|2 cos(-) sin(---) + (2\|2 cos(---) - 2)cos(-) )sin(-) +--R 2 8 8 2 2 +--R + +--R +-+4+-+ %pi x 3 x x 4 +--R - 2\|2 \|2 cos(---)cos(-) sin(-) + cos(-) +--R 8 2 2 2 +--R / +--R x 4 x 2 x 2 x 4 x 2 +--R sin(-) + (- 2cos(-) - 2)sin(-) + cos(-) + 2cos(-) + 1 +--R 2 2 2 2 2 +--R + +--R - +--R 4+-+ %pi +--R \|2 cos(---) +--R 8 +--R * +--R log +--R x 4 +-+4+-+ %pi x x 3 +--R sin(-) - 2\|2 \|2 cos(---)cos(-)sin(-) +--R 2 8 2 2 +--R + +--R 4+-+2 x 2 %pi 2 4+-+2 %pi 2 x 2 +--R (2\|2 cos(-) sin(---) + (2\|2 cos(---) - 2)cos(-) ) +--R 2 8 8 2 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R +-+4+-+ %pi x 3 x x 4 +--R 2\|2 \|2 cos(---)cos(-) sin(-) + cos(-) +--R 8 2 2 2 +--R / +--R x 4 x 2 x 2 x 4 x 2 +--R sin(-) + (- 2cos(-) - 2)sin(-) + cos(-) + 2cos(-) + 1 +--R 2 2 2 2 2 +--R + +--R - +--R 4+-+ %pi +--R 2\|2 sin(---) +--R 8 +--R * +--R 4+-+ x %pi x +--R 2\|2 cos(-)sin(---)sin(-) +--R 2 8 2 +--R atan(-----------------------------------------------------) +--R +-+ x 2 4+-+ %pi x x +-+ x 2 +--R \|2 sin(-) - 2\|2 cos(---)cos(-)sin(-) - \|2 cos(-) +--R 2 8 2 2 2 +--R + +--R 4+-+ x %pi x +--R 2\|2 cos(-)sin(---)sin(-) +--R 4+-+ %pi 2 8 2 +--R - 2\|2 sin(---)atan(-----------------------------------------------------) +--R 8 +-+ x 2 4+-+ %pi x x +-+ x 2 +--R \|2 sin(-) + 2\|2 cos(---)cos(-)sin(-) - \|2 cos(-) +--R 2 8 2 2 2 +--R / +--R +-+ +--R 4\|2 +--R Type: Union(Expression Integer,...) +--R +--E 370 + +--S 371 of 504 +--Rm0171:= a0171-r0171 +--R +--R +--R (323) +--R +------+ +------+4+-+ %pi +--R \|1 - %i \|1 + %i \|2 cos(---) +--R 8 +--R * +--R log +--R x 4 +-+4+-+ %pi x x 3 +--R sin(-) + 2\|2 \|2 cos(---)cos(-)sin(-) +--R 2 8 2 2 +--R + +--R 4+-+2 x 2 %pi 2 4+-+2 %pi 2 x 2 x 2 +--R (2\|2 cos(-) sin(---) + (2\|2 cos(---) - 2)cos(-) )sin(-) +--R 2 8 8 2 2 +--R + +--R +-+4+-+ %pi x 3 x x 4 +--R - 2\|2 \|2 cos(---)cos(-) sin(-) + cos(-) +--R 8 2 2 2 +--R / +--R x 4 x 2 x 2 x 4 x 2 +--R sin(-) + (- 2cos(-) - 2)sin(-) + cos(-) + 2cos(-) + 1 +--R 2 2 2 2 2 +--R + +--R - +--R +------+ +------+4+-+ %pi +--R \|1 - %i \|1 + %i \|2 cos(---) +--R 8 +--R * +--R log +--R x 4 +-+4+-+ %pi x x 3 +--R sin(-) - 2\|2 \|2 cos(---)cos(-)sin(-) +--R 2 8 2 2 +--R + +--R 4+-+2 x 2 %pi 2 4+-+2 %pi 2 x 2 +--R (2\|2 cos(-) sin(---) + (2\|2 cos(---) - 2)cos(-) ) +--R 2 8 8 2 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R +-+4+-+ %pi x 3 x x 4 +--R 2\|2 \|2 cos(---)cos(-) sin(-) + cos(-) +--R 8 2 2 2 +--R / +--R x 4 x 2 x 2 x 4 x 2 +--R sin(-) + (- 2cos(-) - 2)sin(-) + cos(-) + 2cos(-) + 1 +--R 2 2 2 2 2 +--R + +--R +------+ +-+ tan(x) +------+ +-+ tan(x) +--R - 2\|1 + %i \|2 atan(---------) - 2\|1 - %i \|2 atan(---------) +--R +------+ +------+ +--R \|1 - %i \|1 + %i +--R + +--R - +--R +------+ +------+4+-+ %pi +--R 2\|1 - %i \|1 + %i \|2 sin(---) +--R 8 +--R * +--R 4+-+ x %pi x +--R 2\|2 cos(-)sin(---)sin(-) +--R 2 8 2 +--R atan(-----------------------------------------------------) +--R +-+ x 2 4+-+ %pi x x +-+ x 2 +--R \|2 sin(-) - 2\|2 cos(---)cos(-)sin(-) - \|2 cos(-) +--R 2 8 2 2 2 +--R + +--R - +--R +------+ +------+4+-+ %pi +--R 2\|1 - %i \|1 + %i \|2 sin(---) +--R 8 +--R * +--R 4+-+ x %pi x +--R 2\|2 cos(-)sin(---)sin(-) +--R 2 8 2 +--R atan(-----------------------------------------------------) +--R +-+ x 2 4+-+ %pi x x +-+ x 2 +--R \|2 sin(-) + 2\|2 cos(---)cos(-)sin(-) - \|2 cos(-) +--R 2 8 2 2 2 +--R / +--R +------+ +------+ +-+ +--R 4\|1 - %i \|1 + %i \|2 +--R Type: Expression Complex Integer +--R +--E 371 + +--S 372 of 504 +--Rd0171:= D(m0171,x) +--R +--R +--R (324) +--R 4+-+2 %pi 2 4+-+2 %pi 2 x 16 +--R (\|2 sin(---) - \|2 cos(---) - 2)sin(-) +--R 8 8 2 +--R + +--R x 2 %pi 4 %pi 2 4+-+2 x 2 %pi 2 +--R 12cos(-) sin(---) + (- 8cos(---) - 20\|2 )cos(-) sin(---) +--R 2 8 8 2 8 +--R + +--R %pi 4 4+-+2 %pi 2 x 2 +--R (12cos(---) + 20\|2 cos(---) + 16)cos(-) +--R 8 8 2 +--R * +--R x 14 +--R sin(-) +--R 2 +--R + +--R 4+-+2 x 4 %pi 6 +--R 24\|2 cos(-) sin(---) +--R 2 8 +--R + +--R 4+-+2 %pi 2 x 4 %pi 4 +--R (24\|2 cos(---) - 120)cos(-) sin(---) +--R 8 2 8 +--R + +--R 4+-+2 %pi 4 %pi 2 4+-+2 x 4 %pi 2 +--R (- 24\|2 cos(---) + 80cos(---) + 100\|2 )cos(-) sin(---) +--R 8 8 2 8 +--R + +--R 4+-+2 %pi 6 %pi 4 4+-+2 %pi 2 x 4 +--R (- 24\|2 cos(---) - 120cos(---) - 100\|2 cos(---) - 56)cos(-) +--R 8 8 8 2 +--R * +--R x 12 +--R sin(-) +--R 2 +--R + +--R x 6 %pi 8 %pi 2 4+-+2 x 6 %pi 6 +--R 32cos(-) sin(---) + (128cos(---) - 128\|2 )cos(-) sin(---) +--R 2 8 8 2 8 +--R + +--R %pi 4 4+-+2 %pi 2 x 6 %pi 4 +--R (192cos(---) - 128\|2 cos(---) + 372)cos(-) sin(---) +--R 8 8 2 8 +--R + +--R %pi 6 4+-+2 %pi 4 %pi 2 4+-+2 +--R (128cos(---) + 128\|2 cos(---) - 248cos(---) - 236\|2 ) +--R 8 8 8 +--R * +--R x 6 %pi 2 +--R cos(-) sin(---) +--R 2 8 +--R + +--R %pi 8 4+-+2 %pi 6 %pi 4 +--R 32cos(---) + 128\|2 cos(---) + 372cos(---) +--R 8 8 8 +--R + +--R 4+-+2 %pi 2 +--R 236\|2 cos(---) + 112 +--R 8 +--R * +--R x 6 +--R cos(-) +--R 2 +--R * +--R x 10 +--R sin(-) +--R 2 +--R + +--R x 8 %pi 8 +--R - 64cos(-) sin(---) +--R 2 8 +--R + +--R %pi 2 4+-+2 x 8 %pi 6 +--R (- 256cos(---) + 208\|2 )cos(-) sin(---) +--R 8 2 8 +--R + +--R %pi 4 4+-+2 %pi 2 x 8 %pi 4 +--R (- 384cos(---) + 208\|2 cos(---) - 528)cos(-) sin(---) +--R 8 8 2 8 +--R + +--R %pi 6 4+-+2 %pi 4 %pi 2 4+-+2 +--R (- 256cos(---) - 208\|2 cos(---) + 352cos(---) + 310\|2 ) +--R 8 8 8 +--R * +--R x 8 %pi 2 +--R cos(-) sin(---) +--R 2 8 +--R + +--R %pi 8 4+-+2 %pi 6 %pi 4 +--R - 64cos(---) - 208\|2 cos(---) - 528cos(---) +--R 8 8 8 +--R + +--R 4+-+2 %pi 2 +--R - 310\|2 cos(---) - 140 +--R 8 +--R * +--R x 8 +--R cos(-) +--R 2 +--R * +--R x 8 +--R sin(-) +--R 2 +--R + +--R x 10 %pi 8 %pi 2 4+-+2 x 10 %pi 6 +--R 32cos(-) sin(---) + (128cos(---) - 128\|2 )cos(-) sin(---) +--R 2 8 8 2 8 +--R + +--R %pi 4 4+-+2 %pi 2 x 10 %pi 4 +--R (192cos(---) - 128\|2 cos(---) + 372)cos(-) sin(---) +--R 8 8 2 8 +--R + +--R %pi 6 4+-+2 %pi 4 %pi 2 4+-+2 +--R (128cos(---) + 128\|2 cos(---) - 248cos(---) - 236\|2 ) +--R 8 8 8 +--R * +--R x 10 %pi 2 +--R cos(-) sin(---) +--R 2 8 +--R + +--R %pi 8 4+-+2 %pi 6 %pi 4 +--R 32cos(---) + 128\|2 cos(---) + 372cos(---) +--R 8 8 8 +--R + +--R 4+-+2 %pi 2 +--R 236\|2 cos(---) + 112 +--R 8 +--R * +--R x 10 +--R cos(-) +--R 2 +--R * +--R x 6 +--R sin(-) +--R 2 +--R + +--R 4+-+2 x 12 %pi 6 +--R 24\|2 cos(-) sin(---) +--R 2 8 +--R + +--R 4+-+2 %pi 2 x 12 %pi 4 +--R (24\|2 cos(---) - 120)cos(-) sin(---) +--R 8 2 8 +--R + +--R 4+-+2 %pi 4 %pi 2 4+-+2 x 12 %pi 2 +--R (- 24\|2 cos(---) + 80cos(---) + 100\|2 )cos(-) sin(---) +--R 8 8 2 8 +--R + +--R 4+-+2 %pi 6 %pi 4 4+-+2 %pi 2 +--R (- 24\|2 cos(---) - 120cos(---) - 100\|2 cos(---) - 56) +--R 8 8 8 +--R * +--R x 12 +--R cos(-) +--R 2 +--R * +--R x 4 +--R sin(-) +--R 2 +--R + +--R x 14 %pi 4 %pi 2 4+-+2 x 14 %pi 2 +--R 12cos(-) sin(---) + (- 8cos(---) - 20\|2 )cos(-) sin(---) +--R 2 8 8 2 8 +--R + +--R %pi 4 4+-+2 %pi 2 x 14 +--R (12cos(---) + 20\|2 cos(---) + 16)cos(-) +--R 8 8 2 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R 4+-+2 x 16 %pi 2 4+-+2 %pi 2 x 16 +--R \|2 cos(-) sin(---) + (- \|2 cos(---) - 2)cos(-) +--R 2 8 8 2 +--R * +--R 4 +--R tan(x) +--R + +--R 4+-+2 %pi 2 4+-+2 %pi 2 x 16 +--R (2\|2 sin(---) - 2\|2 cos(---) - 4)sin(-) +--R 8 8 2 +--R + +--R x 2 %pi 4 %pi 2 4+-+2 x 2 %pi 2 +--R 24cos(-) sin(---) + (- 16cos(---) - 40\|2 )cos(-) sin(---) +--R 2 8 8 2 8 +--R + +--R %pi 4 4+-+2 %pi 2 x 2 +--R (24cos(---) + 40\|2 cos(---) + 32)cos(-) +--R 8 8 2 +--R * +--R x 14 +--R sin(-) +--R 2 +--R + +--R 4+-+2 x 4 %pi 6 +--R 48\|2 cos(-) sin(---) +--R 2 8 +--R + +--R 4+-+2 %pi 2 x 4 %pi 4 +--R (48\|2 cos(---) - 240)cos(-) sin(---) +--R 8 2 8 +--R + +--R 4+-+2 %pi 4 %pi 2 4+-+2 x 4 %pi 2 +--R (- 48\|2 cos(---) + 160cos(---) + 200\|2 )cos(-) sin(---) +--R 8 8 2 8 +--R + +--R 4+-+2 %pi 6 %pi 4 4+-+2 %pi 2 +--R (- 48\|2 cos(---) - 240cos(---) - 200\|2 cos(---) - 112) +--R 8 8 8 +--R * +--R x 4 +--R cos(-) +--R 2 +--R * +--R x 12 +--R sin(-) +--R 2 +--R + +--R x 6 %pi 8 %pi 2 4+-+2 x 6 %pi 6 +--R 64cos(-) sin(---) + (256cos(---) - 256\|2 )cos(-) sin(---) +--R 2 8 8 2 8 +--R + +--R %pi 4 4+-+2 %pi 2 x 6 %pi 4 +--R (384cos(---) - 256\|2 cos(---) + 744)cos(-) sin(---) +--R 8 8 2 8 +--R + +--R %pi 6 4+-+2 %pi 4 %pi 2 4+-+2 +--R (256cos(---) + 256\|2 cos(---) - 496cos(---) - 472\|2 ) +--R 8 8 8 +--R * +--R x 6 %pi 2 +--R cos(-) sin(---) +--R 2 8 +--R + +--R %pi 8 4+-+2 %pi 6 %pi 4 +--R 64cos(---) + 256\|2 cos(---) + 744cos(---) +--R 8 8 8 +--R + +--R 4+-+2 %pi 2 +--R 472\|2 cos(---) + 224 +--R 8 +--R * +--R x 6 +--R cos(-) +--R 2 +--R * +--R x 10 +--R sin(-) +--R 2 +--R + +--R x 8 %pi 8 +--R - 128cos(-) sin(---) +--R 2 8 +--R + +--R %pi 2 4+-+2 x 8 %pi 6 +--R (- 512cos(---) + 416\|2 )cos(-) sin(---) +--R 8 2 8 +--R + +--R %pi 4 4+-+2 %pi 2 x 8 %pi 4 +--R (- 768cos(---) + 416\|2 cos(---) - 1056)cos(-) sin(---) +--R 8 8 2 8 +--R + +--R %pi 6 4+-+2 %pi 4 %pi 2 4+-+2 +--R (- 512cos(---) - 416\|2 cos(---) + 704cos(---) + 620\|2 ) +--R 8 8 8 +--R * +--R x 8 %pi 2 +--R cos(-) sin(---) +--R 2 8 +--R + +--R %pi 8 4+-+2 %pi 6 %pi 4 +--R - 128cos(---) - 416\|2 cos(---) - 1056cos(---) +--R 8 8 8 +--R + +--R 4+-+2 %pi 2 +--R - 620\|2 cos(---) - 280 +--R 8 +--R * +--R x 8 +--R cos(-) +--R 2 +--R * +--R x 8 +--R sin(-) +--R 2 +--R + +--R x 10 %pi 8 %pi 2 4+-+2 x 10 %pi 6 +--R 64cos(-) sin(---) + (256cos(---) - 256\|2 )cos(-) sin(---) +--R 2 8 8 2 8 +--R + +--R %pi 4 4+-+2 %pi 2 x 10 %pi 4 +--R (384cos(---) - 256\|2 cos(---) + 744)cos(-) sin(---) +--R 8 8 2 8 +--R + +--R %pi 6 4+-+2 %pi 4 %pi 2 4+-+2 +--R (256cos(---) + 256\|2 cos(---) - 496cos(---) - 472\|2 ) +--R 8 8 8 +--R * +--R x 10 %pi 2 +--R cos(-) sin(---) +--R 2 8 +--R + +--R %pi 8 4+-+2 %pi 6 %pi 4 +--R 64cos(---) + 256\|2 cos(---) + 744cos(---) +--R 8 8 8 +--R + +--R 4+-+2 %pi 2 +--R 472\|2 cos(---) + 224 +--R 8 +--R * +--R x 10 +--R cos(-) +--R 2 +--R * +--R x 6 +--R sin(-) +--R 2 +--R + +--R 4+-+2 x 12 %pi 6 +--R 48\|2 cos(-) sin(---) +--R 2 8 +--R + +--R 4+-+2 %pi 2 x 12 %pi 4 +--R (48\|2 cos(---) - 240)cos(-) sin(---) +--R 8 2 8 +--R + +--R 4+-+2 %pi 4 %pi 2 4+-+2 x 12 %pi 2 +--R (- 48\|2 cos(---) + 160cos(---) + 200\|2 )cos(-) sin(---) +--R 8 8 2 8 +--R + +--R 4+-+2 %pi 6 %pi 4 4+-+2 %pi 2 +--R (- 48\|2 cos(---) - 240cos(---) - 200\|2 cos(---) - 112) +--R 8 8 8 +--R * +--R x 12 +--R cos(-) +--R 2 +--R * +--R x 4 +--R sin(-) +--R 2 +--R + +--R x 14 %pi 4 %pi 2 4+-+2 x 14 %pi 2 +--R 24cos(-) sin(---) + (- 16cos(---) - 40\|2 )cos(-) sin(---) +--R 2 8 8 2 8 +--R + +--R %pi 4 4+-+2 %pi 2 x 14 +--R (24cos(---) + 40\|2 cos(---) + 32)cos(-) +--R 8 8 2 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R 4+-+2 x 16 %pi 2 4+-+2 %pi 2 x 16 +--R 2\|2 cos(-) sin(---) + (- 2\|2 cos(---) - 4)cos(-) +--R 2 8 8 2 +--R * +--R 2 +--R tan(x) +--R + +--R 4+-+2 %pi 2 4+-+2 %pi 2 x 16 +--R (2\|2 sin(---) - 2\|2 cos(---) - 2)sin(-) +--R 8 8 2 +--R + +--R x 2 %pi 4 %pi 2 4+-+2 x 2 %pi 2 +--R 24cos(-) sin(---) + (- 16cos(---) - 24\|2 )cos(-) sin(---) +--R 2 8 8 2 8 +--R + +--R %pi 4 4+-+2 %pi 2 x 2 +--R (24cos(---) + 24\|2 cos(---) + 16)cos(-) +--R 8 8 2 +--R * +--R x 14 +--R sin(-) +--R 2 +--R + +--R 4+-+2 x 4 %pi 6 4+-+2 %pi 2 x 4 %pi 4 +--R 48\|2 cos(-) sin(---) + (48\|2 cos(---) - 144)cos(-) sin(---) +--R 2 8 8 2 8 +--R + +--R 4+-+2 %pi 4 %pi 2 4+-+2 x 4 %pi 2 +--R (- 48\|2 cos(---) + 96cos(---) + 104\|2 )cos(-) sin(---) +--R 8 8 2 8 +--R + +--R 4+-+2 %pi 6 %pi 4 4+-+2 %pi 2 x 4 +--R (- 48\|2 cos(---) - 144cos(---) - 104\|2 cos(---) - 56)cos(-) +--R 8 8 8 2 +--R * +--R x 12 +--R sin(-) +--R 2 +--R + +--R x 6 %pi 8 %pi 2 4+-+2 x 6 %pi 6 +--R 64cos(-) sin(---) + (256cos(---) - 128\|2 )cos(-) sin(---) +--R 2 8 8 2 8 +--R + +--R %pi 4 4+-+2 %pi 2 x 6 %pi 4 +--R (384cos(---) - 128\|2 cos(---) + 360)cos(-) sin(---) +--R 8 8 2 8 +--R + +--R %pi 6 4+-+2 %pi 4 %pi 2 4+-+2 x 6 +--R (256cos(---) + 128\|2 cos(---) - 240cos(---) - 232\|2 )cos(-) +--R 8 8 8 2 +--R * +--R %pi 2 +--R sin(---) +--R 8 +--R + +--R %pi 8 4+-+2 %pi 6 %pi 4 +--R 64cos(---) + 128\|2 cos(---) + 360cos(---) +--R 8 8 8 +--R + +--R 4+-+2 %pi 2 +--R 232\|2 cos(---) + 112 +--R 8 +--R * +--R x 6 +--R cos(-) +--R 2 +--R * +--R x 10 +--R sin(-) +--R 2 +--R + +--R 4+-+2 x 8 %pi 6 4+-+2 %pi 2 x 8 %pi 4 +--R 160\|2 cos(-) sin(---) + (160\|2 cos(---) - 480)cos(-) sin(---) +--R 2 8 8 2 8 +--R + +--R 4+-+2 %pi 4 %pi 2 4+-+2 x 8 %pi 2 +--R (- 160\|2 cos(---) + 320cos(---) + 300\|2 )cos(-) sin(---) +--R 8 8 2 8 +--R + +--R 4+-+2 %pi 6 %pi 4 4+-+2 %pi 2 x 8 +--R (- 160\|2 cos(---) - 480cos(---) - 300\|2 cos(---) - 140)cos(-) +--R 8 8 8 2 +--R * +--R x 8 +--R sin(-) +--R 2 +--R + +--R x 10 %pi 8 %pi 2 4+-+2 x 10 %pi 6 +--R 64cos(-) sin(---) + (256cos(---) - 128\|2 )cos(-) sin(---) +--R 2 8 8 2 8 +--R + +--R %pi 4 4+-+2 %pi 2 x 10 %pi 4 +--R (384cos(---) - 128\|2 cos(---) + 360)cos(-) sin(---) +--R 8 8 2 8 +--R + +--R %pi 6 4+-+2 %pi 4 %pi 2 4+-+2 +--R (256cos(---) + 128\|2 cos(---) - 240cos(---) - 232\|2 ) +--R 8 8 8 +--R * +--R x 10 %pi 2 +--R cos(-) sin(---) +--R 2 8 +--R + +--R %pi 8 4+-+2 %pi 6 %pi 4 +--R 64cos(---) + 128\|2 cos(---) + 360cos(---) +--R 8 8 8 +--R + +--R 4+-+2 %pi 2 +--R 232\|2 cos(---) + 112 +--R 8 +--R * +--R x 10 +--R cos(-) +--R 2 +--R * +--R x 6 +--R sin(-) +--R 2 +--R + +--R 4+-+2 x 12 %pi 6 4+-+2 %pi 2 x 12 %pi 4 +--R 48\|2 cos(-) sin(---) + (48\|2 cos(---) - 144)cos(-) sin(---) +--R 2 8 8 2 8 +--R + +--R 4+-+2 %pi 4 %pi 2 4+-+2 x 12 %pi 2 +--R (- 48\|2 cos(---) + 96cos(---) + 104\|2 )cos(-) sin(---) +--R 8 8 2 8 +--R + +--R 4+-+2 %pi 6 %pi 4 4+-+2 %pi 2 x 12 +--R (- 48\|2 cos(---) - 144cos(---) - 104\|2 cos(---) - 56)cos(-) +--R 8 8 8 2 +--R * +--R x 4 +--R sin(-) +--R 2 +--R + +--R x 14 %pi 4 %pi 2 4+-+2 x 14 %pi 2 +--R 24cos(-) sin(---) + (- 16cos(---) - 24\|2 )cos(-) sin(---) +--R 2 8 8 2 8 +--R + +--R %pi 4 4+-+2 %pi 2 x 14 +--R (24cos(---) + 24\|2 cos(---) + 16)cos(-) +--R 8 8 2 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R 4+-+2 x 16 %pi 2 4+-+2 %pi 2 x 16 +--R 2\|2 cos(-) sin(---) + (- 2\|2 cos(---) - 2)cos(-) +--R 2 8 8 2 +--R / +--R x 16 +--R 2sin(-) +--R 2 +--R + +--R 4+-+2 x 2 %pi 2 4+-+2 %pi 2 x 2 x 14 +--R (16\|2 cos(-) sin(---) + (- 16\|2 cos(---) - 16)cos(-) )sin(-) +--R 2 8 8 2 2 +--R + +--R x 4 %pi 4 %pi 2 4+-+2 x 4 %pi 2 +--R 96cos(-) sin(---) + (- 64cos(---) - 96\|2 )cos(-) sin(---) +--R 2 8 8 2 8 +--R + +--R %pi 4 4+-+2 %pi 2 x 4 +--R (96cos(---) + 96\|2 cos(---) + 56)cos(-) +--R 8 8 2 +--R * +--R x 12 +--R sin(-) +--R 2 +--R + +--R 4+-+2 x 6 %pi 6 +--R 128\|2 cos(-) sin(---) +--R 2 8 +--R + +--R 4+-+2 %pi 2 x 6 %pi 4 +--R (128\|2 cos(---) - 384)cos(-) sin(---) +--R 8 2 8 +--R + +--R 4+-+2 %pi 4 %pi 2 4+-+2 x 6 %pi 2 +--R (- 128\|2 cos(---) + 256cos(---) + 240\|2 )cos(-) sin(---) +--R 8 8 2 8 +--R + +--R 4+-+2 %pi 6 %pi 4 4+-+2 %pi 2 +--R (- 128\|2 cos(---) - 384cos(---) - 240\|2 cos(---) - 112) +--R 8 8 8 +--R * +--R x 6 +--R cos(-) +--R 2 +--R * +--R x 10 +--R sin(-) +--R 2 +--R + +--R x 8 %pi 8 %pi 2 4+-+2 x 8 %pi 6 +--R 128cos(-) sin(---) + (512cos(---) - 256\|2 )cos(-) sin(---) +--R 2 8 8 2 8 +--R + +--R %pi 4 4+-+2 %pi 2 x 8 %pi 4 +--R (768cos(---) - 256\|2 cos(---) + 576)cos(-) sin(---) +--R 8 8 2 8 +--R + +--R %pi 6 4+-+2 %pi 4 %pi 2 4+-+2 +--R (512cos(---) + 256\|2 cos(---) - 384cos(---) - 320\|2 ) +--R 8 8 8 +--R * +--R x 8 %pi 2 +--R cos(-) sin(---) +--R 2 8 +--R + +--R %pi 8 4+-+2 %pi 6 %pi 4 +--R 128cos(---) + 256\|2 cos(---) + 576cos(---) +--R 8 8 8 +--R + +--R 4+-+2 %pi 2 +--R 320\|2 cos(---) + 140 +--R 8 +--R * +--R x 8 +--R cos(-) +--R 2 +--R * +--R x 8 +--R sin(-) +--R 2 +--R + +--R 4+-+2 x 10 %pi 6 +--R 128\|2 cos(-) sin(---) +--R 2 8 +--R + +--R 4+-+2 %pi 2 x 10 %pi 4 +--R (128\|2 cos(---) - 384)cos(-) sin(---) +--R 8 2 8 +--R + +--R 4+-+2 %pi 4 %pi 2 4+-+2 x 10 %pi 2 +--R (- 128\|2 cos(---) + 256cos(---) + 240\|2 )cos(-) sin(---) +--R 8 8 2 8 +--R + +--R 4+-+2 %pi 6 %pi 4 4+-+2 %pi 2 +--R (- 128\|2 cos(---) - 384cos(---) - 240\|2 cos(---) - 112) +--R 8 8 8 +--R * +--R x 10 +--R cos(-) +--R 2 +--R * +--R x 6 +--R sin(-) +--R 2 +--R + +--R x 12 %pi 4 %pi 2 4+-+2 x 12 %pi 2 +--R 96cos(-) sin(---) + (- 64cos(---) - 96\|2 )cos(-) sin(---) +--R 2 8 8 2 8 +--R + +--R %pi 4 4+-+2 %pi 2 x 12 +--R (96cos(---) + 96\|2 cos(---) + 56)cos(-) +--R 8 8 2 +--R * +--R x 4 +--R sin(-) +--R 2 +--R + +--R 4+-+2 x 14 %pi 2 4+-+2 %pi 2 x 14 x 2 +--R (16\|2 cos(-) sin(---) + (- 16\|2 cos(---) - 16)cos(-) )sin(-) +--R 2 8 8 2 2 +--R + +--R x 16 +--R 2cos(-) +--R 2 +--R * +--R 4 +--R tan(x) +--R + +--R x 16 +--R 4sin(-) +--R 2 +--R + +--R 4+-+2 x 2 %pi 2 4+-+2 %pi 2 x 2 x 14 +--R (32\|2 cos(-) sin(---) + (- 32\|2 cos(---) - 32)cos(-) )sin(-) +--R 2 8 8 2 2 +--R + +--R x 4 %pi 4 %pi 2 4+-+2 x 4 %pi 2 +--R 192cos(-) sin(---) + (- 128cos(---) - 192\|2 )cos(-) sin(---) +--R 2 8 8 2 8 +--R + +--R %pi 4 4+-+2 %pi 2 x 4 +--R (192cos(---) + 192\|2 cos(---) + 112)cos(-) +--R 8 8 2 +--R * +--R x 12 +--R sin(-) +--R 2 +--R + +--R 4+-+2 x 6 %pi 6 +--R 256\|2 cos(-) sin(---) +--R 2 8 +--R + +--R 4+-+2 %pi 2 x 6 %pi 4 +--R (256\|2 cos(---) - 768)cos(-) sin(---) +--R 8 2 8 +--R + +--R 4+-+2 %pi 4 %pi 2 4+-+2 x 6 %pi 2 +--R (- 256\|2 cos(---) + 512cos(---) + 480\|2 )cos(-) sin(---) +--R 8 8 2 8 +--R + +--R 4+-+2 %pi 6 %pi 4 4+-+2 %pi 2 +--R (- 256\|2 cos(---) - 768cos(---) - 480\|2 cos(---) - 224) +--R 8 8 8 +--R * +--R x 6 +--R cos(-) +--R 2 +--R * +--R x 10 +--R sin(-) +--R 2 +--R + +--R x 8 %pi 8 %pi 2 4+-+2 x 8 %pi 6 +--R 256cos(-) sin(---) + (1024cos(---) - 512\|2 )cos(-) sin(---) +--R 2 8 8 2 8 +--R + +--R %pi 4 4+-+2 %pi 2 x 8 %pi 4 +--R (1536cos(---) - 512\|2 cos(---) + 1152)cos(-) sin(---) +--R 8 8 2 8 +--R + +--R %pi 6 4+-+2 %pi 4 %pi 2 4+-+2 +--R (1024cos(---) + 512\|2 cos(---) - 768cos(---) - 640\|2 ) +--R 8 8 8 +--R * +--R x 8 %pi 2 +--R cos(-) sin(---) +--R 2 8 +--R + +--R %pi 8 4+-+2 %pi 6 %pi 4 +--R 256cos(---) + 512\|2 cos(---) + 1152cos(---) +--R 8 8 8 +--R + +--R 4+-+2 %pi 2 +--R 640\|2 cos(---) + 280 +--R 8 +--R * +--R x 8 +--R cos(-) +--R 2 +--R * +--R x 8 +--R sin(-) +--R 2 +--R + +--R 4+-+2 x 10 %pi 6 +--R 256\|2 cos(-) sin(---) +--R 2 8 +--R + +--R 4+-+2 %pi 2 x 10 %pi 4 +--R (256\|2 cos(---) - 768)cos(-) sin(---) +--R 8 2 8 +--R + +--R 4+-+2 %pi 4 %pi 2 4+-+2 x 10 %pi 2 +--R (- 256\|2 cos(---) + 512cos(---) + 480\|2 )cos(-) sin(---) +--R 8 8 2 8 +--R + +--R 4+-+2 %pi 6 %pi 4 4+-+2 %pi 2 +--R (- 256\|2 cos(---) - 768cos(---) - 480\|2 cos(---) - 224) +--R 8 8 8 +--R * +--R x 10 +--R cos(-) +--R 2 +--R * +--R x 6 +--R sin(-) +--R 2 +--R + +--R x 12 %pi 4 +--R 192cos(-) sin(---) +--R 2 8 +--R + +--R %pi 2 4+-+2 x 12 %pi 2 +--R (- 128cos(---) - 192\|2 )cos(-) sin(---) +--R 8 2 8 +--R + +--R %pi 4 4+-+2 %pi 2 x 12 +--R (192cos(---) + 192\|2 cos(---) + 112)cos(-) +--R 8 8 2 +--R * +--R x 4 +--R sin(-) +--R 2 +--R + +--R 4+-+2 x 14 %pi 2 4+-+2 %pi 2 x 14 x 2 +--R (32\|2 cos(-) sin(---) + (- 32\|2 cos(---) - 32)cos(-) )sin(-) +--R 2 8 8 2 2 +--R + +--R x 16 +--R 4cos(-) +--R 2 +--R * +--R 2 +--R tan(x) +--R + +--R x 16 +--R 4sin(-) +--R 2 +--R + +--R 4+-+2 x 2 %pi 2 4+-+2 %pi 2 x 2 x 14 +--R (32\|2 cos(-) sin(---) + (- 32\|2 cos(---) - 32)cos(-) )sin(-) +--R 2 8 8 2 2 +--R + +--R x 4 %pi 4 %pi 2 4+-+2 x 4 %pi 2 +--R 192cos(-) sin(---) + (- 128cos(---) - 192\|2 )cos(-) sin(---) +--R 2 8 8 2 8 +--R + +--R %pi 4 4+-+2 %pi 2 x 4 +--R (192cos(---) + 192\|2 cos(---) + 112)cos(-) +--R 8 8 2 +--R * +--R x 12 +--R sin(-) +--R 2 +--R + +--R 4+-+2 x 6 %pi 6 4+-+2 %pi 2 x 6 %pi 4 +--R 256\|2 cos(-) sin(---) + (256\|2 cos(---) - 768)cos(-) sin(---) +--R 2 8 8 2 8 +--R + +--R 4+-+2 %pi 4 %pi 2 4+-+2 x 6 %pi 2 +--R (- 256\|2 cos(---) + 512cos(---) + 480\|2 )cos(-) sin(---) +--R 8 8 2 8 +--R + +--R 4+-+2 %pi 6 %pi 4 4+-+2 %pi 2 x 6 +--R (- 256\|2 cos(---) - 768cos(---) - 480\|2 cos(---) - 224)cos(-) +--R 8 8 8 2 +--R * +--R x 10 +--R sin(-) +--R 2 +--R + +--R x 8 %pi 8 %pi 2 4+-+2 x 8 %pi 6 +--R 256cos(-) sin(---) + (1024cos(---) - 512\|2 )cos(-) sin(---) +--R 2 8 8 2 8 +--R + +--R %pi 4 4+-+2 %pi 2 x 8 %pi 4 +--R (1536cos(---) - 512\|2 cos(---) + 1152)cos(-) sin(---) +--R 8 8 2 8 +--R + +--R %pi 6 4+-+2 %pi 4 %pi 2 4+-+2 +--R (1024cos(---) + 512\|2 cos(---) - 768cos(---) - 640\|2 ) +--R 8 8 8 +--R * +--R x 8 %pi 2 +--R cos(-) sin(---) +--R 2 8 +--R + +--R %pi 8 4+-+2 %pi 6 %pi 4 +--R 256cos(---) + 512\|2 cos(---) + 1152cos(---) +--R 8 8 8 +--R + +--R 4+-+2 %pi 2 +--R 640\|2 cos(---) + 280 +--R 8 +--R * +--R x 8 +--R cos(-) +--R 2 +--R * +--R x 8 +--R sin(-) +--R 2 +--R + +--R 4+-+2 x 10 %pi 6 +--R 256\|2 cos(-) sin(---) +--R 2 8 +--R + +--R 4+-+2 %pi 2 x 10 %pi 4 +--R (256\|2 cos(---) - 768)cos(-) sin(---) +--R 8 2 8 +--R + +--R 4+-+2 %pi 4 %pi 2 4+-+2 x 10 %pi 2 +--R (- 256\|2 cos(---) + 512cos(---) + 480\|2 )cos(-) sin(---) +--R 8 8 2 8 +--R + +--R 4+-+2 %pi 6 %pi 4 4+-+2 %pi 2 x 10 +--R (- 256\|2 cos(---) - 768cos(---) - 480\|2 cos(---) - 224)cos(-) +--R 8 8 8 2 +--R * +--R x 6 +--R sin(-) +--R 2 +--R + +--R x 12 %pi 4 %pi 2 4+-+2 x 12 %pi 2 +--R 192cos(-) sin(---) + (- 128cos(---) - 192\|2 )cos(-) sin(---) +--R 2 8 8 2 8 +--R + +--R %pi 4 4+-+2 %pi 2 x 12 +--R (192cos(---) + 192\|2 cos(---) + 112)cos(-) +--R 8 8 2 +--R * +--R x 4 +--R sin(-) +--R 2 +--R + +--R 4+-+2 x 14 %pi 2 4+-+2 %pi 2 x 14 x 2 +--R (32\|2 cos(-) sin(---) + (- 32\|2 cos(---) - 32)cos(-) )sin(-) +--R 2 8 8 2 2 +--R + +--R x 16 +--R 4cos(-) +--R 2 +--R Type: Expression Complex Integer +--R +--E 372 + +--S 373 of 504 +--Rt0172:= 1/(1+cos(x)^8) +--R +--R +--R 1 +--R (325) ----------- +--R 8 +--R cos(x) + 1 +--R Type: Expression Integer +--R +--E 373 + +--S 374 of 504 +--Rr0172:= 1/4*atan(tan(x)/(1-(-1)^(1/4))^(1/2))/(1-(-1)^(1/4))^(1/2)+1/4*atan(tan(x)/(1+(-1)^(1/4))^(1/2))/(1+(-1)^(1/4))^(1/2)+1/4*atan(tan(x)/(1-(-1)^(3/4))^(1/2))/(1-(-1)^(3/4))^(1/2)+1/4*atan(tan(x)/(1+(-1)^(3/4))^(1/2))/(1+(-1)^(3/4))^(1/2) +--R +--R +--R (326) +--R +-----------------+ +-----------------+ +-----------------+ +--R | +-+ +---+ | +-+ +---+ | +-+ +---+ +--R |\|2 - \|- 1 + 1 |\|2 + \|- 1 - 1 |\|2 + \|- 1 + 1 +--R |----------------- |----------------- |----------------- +--R | +-+ | +-+ | +-+ +--R \| \|2 \| \|2 \| \|2 +--R * +--R tan(x) +--R atan(--------------------) +--R +-----------------+ +--R | +-+ +---+ +--R |\|2 - \|- 1 - 1 +--R |----------------- +--R | +-+ +--R \| \|2 +--R + +--R +-----------------+ +-----------------+ +-----------------+ +--R | +-+ +---+ | +-+ +---+ | +-+ +---+ +--R |\|2 - \|- 1 - 1 |\|2 + \|- 1 - 1 |\|2 + \|- 1 + 1 +--R |----------------- |----------------- |----------------- +--R | +-+ | +-+ | +-+ +--R \| \|2 \| \|2 \| \|2 +--R * +--R tan(x) +--R atan(--------------------) +--R +-----------------+ +--R | +-+ +---+ +--R |\|2 - \|- 1 + 1 +--R |----------------- +--R | +-+ +--R \| \|2 +--R + +--R +-----------------+ +-----------------+ +-----------------+ +--R | +-+ +---+ | +-+ +---+ | +-+ +---+ +--R |\|2 - \|- 1 - 1 |\|2 - \|- 1 + 1 |\|2 + \|- 1 + 1 +--R |----------------- |----------------- |----------------- +--R | +-+ | +-+ | +-+ +--R \| \|2 \| \|2 \| \|2 +--R * +--R tan(x) +--R atan(--------------------) +--R +-----------------+ +--R | +-+ +---+ +--R |\|2 + \|- 1 - 1 +--R |----------------- +--R | +-+ +--R \| \|2 +--R + +--R +-----------------+ +-----------------+ +-----------------+ +--R | +-+ +---+ | +-+ +---+ | +-+ +---+ +--R |\|2 - \|- 1 - 1 |\|2 - \|- 1 + 1 |\|2 + \|- 1 - 1 +--R |----------------- |----------------- |----------------- +--R | +-+ | +-+ | +-+ +--R \| \|2 \| \|2 \| \|2 +--R * +--R tan(x) +--R atan(--------------------) +--R +-----------------+ +--R | +-+ +---+ +--R |\|2 + \|- 1 + 1 +--R |----------------- +--R | +-+ +--R \| \|2 +--R / +--R +-----------------+ +-----------------+ +-----------------+ +--R | +-+ +---+ | +-+ +---+ | +-+ +---+ +--R |\|2 - \|- 1 - 1 |\|2 - \|- 1 + 1 |\|2 + \|- 1 - 1 +--R 4 |----------------- |----------------- |----------------- +--R | +-+ | +-+ | +-+ +--R \| \|2 \| \|2 \| \|2 +--R * +--R +-----------------+ +--R | +-+ +---+ +--R |\|2 + \|- 1 + 1 +--R |----------------- +--R | +-+ +--R \| \|2 +--R Type: Expression Integer +--R +--E 374 + +--S 375 of 504 +--Ra0172:= integrate(t0172,x) +--R +--R +--R (327) +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R * +--R log +--R x 8 x 2 x 6 x 4 x 4 +--R sin(-) + 4cos(-) sin(-) + (6cos(-) - 2)sin(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 2 x 2 x 8 x 4 +--R (4cos(-) + 12cos(-) )sin(-) + cos(-) - 2cos(-) + 1 +--R 2 2 2 2 2 +--R * +--R +---------+ 2 +--R | +-+ +--R |3\|2 + 4 +--R +---------+2 atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ x 8 +-+ x 2 x 6 +-+ x 4 x 4 +--R 2\|2 sin(-) + 8\|2 cos(-) sin(-) + 12\|2 cos(-) sin(-) +--R 2 2 2 2 2 +--R + +--R +-+ x 6 x 2 +-+ x 8 +-+ +--R 8\|2 cos(-) sin(-) + 2\|2 cos(-) - 2\|2 +--R 2 2 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R x 8 x 2 x 6 x 4 x 4 +--R sin(-) + 4cos(-) sin(-) + (6cos(-) - 2)sin(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 2 x 2 x 8 x 4 +--R (4cos(-) + 12cos(-) )sin(-) + cos(-) - 2cos(-) + 1 +--R 2 2 2 2 2 +--R * +--R +---------+ 2 +--R | +-+ +--R |3\|2 + 4 +--R +---------+2 atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +---------+ +--R | +-+ +--R +-+ x x 3 +-+ x 3 x |4\|2 + 4 +--R (16\|2 cos(-)sin(-) - 16\|2 cos(-) sin(-)) |--------- +--R 2 2 2 2 4| +-+ +--R \| \|2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R atan(64 |--------- ) +--R | +-+ +--R \| 4096\|2 +--R cos(--------------------) +--R 2 +--R + +--R x 8 x 2 x 6 x 4 x 4 +--R 2sin(-) + 8cos(-) sin(-) + (12cos(-) + 4)sin(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 2 x 2 x 8 x 4 +--R (8cos(-) - 24cos(-) )sin(-) + 2cos(-) + 4cos(-) + 2 +--R 2 2 2 2 2 +--R / +--R x 8 x 2 x 6 +--R sin(-) + (4cos(-) - 4)sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 x 4 +--R (6cos(-) - 4cos(-) + 6)sin(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 x 2 x 8 x 6 +--R (4cos(-) + 4cos(-) - 4cos(-) - 4)sin(-) + cos(-) + 4cos(-) +--R 2 2 2 2 2 2 +--R + +--R x 4 x 2 +--R 6cos(-) + 4cos(-) + 1 +--R 2 2 +--R + +--R - +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R * +--R log +--R x 8 x 2 x 6 x 4 x 4 +--R sin(-) + 4cos(-) sin(-) + (6cos(-) - 2)sin(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 2 x 2 x 8 x 4 +--R (4cos(-) + 12cos(-) )sin(-) + cos(-) - 2cos(-) + 1 +--R 2 2 2 2 2 +--R * +--R +---------+ 2 +--R | +-+ +--R |3\|2 + 4 +--R +---------+2 atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ x 8 +-+ x 2 x 6 +-+ x 4 x 4 +--R 2\|2 sin(-) + 8\|2 cos(-) sin(-) + 12\|2 cos(-) sin(-) +--R 2 2 2 2 2 +--R + +--R +-+ x 6 x 2 +-+ x 8 +-+ +--R 8\|2 cos(-) sin(-) + 2\|2 cos(-) - 2\|2 +--R 2 2 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R x 8 x 2 x 6 x 4 x 4 +--R sin(-) + 4cos(-) sin(-) + (6cos(-) - 2)sin(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 2 x 2 x 8 x 4 +--R (4cos(-) + 12cos(-) )sin(-) + cos(-) - 2cos(-) + 1 +--R 2 2 2 2 2 +--R * +--R +---------+ 2 +--R | +-+ +--R |3\|2 + 4 +--R +---------+2 atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +---------+ +--R | +-+ +--R +-+ x x 3 +-+ x 3 x |4\|2 + 4 +--R (- 16\|2 cos(-)sin(-) + 16\|2 cos(-) sin(-)) |--------- +--R 2 2 2 2 4| +-+ +--R \| \|2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R atan(64 |--------- ) +--R | +-+ +--R \| 4096\|2 +--R cos(--------------------) +--R 2 +--R + +--R x 8 x 2 x 6 x 4 x 4 +--R 2sin(-) + 8cos(-) sin(-) + (12cos(-) + 4)sin(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 2 x 2 x 8 x 4 +--R (8cos(-) - 24cos(-) )sin(-) + 2cos(-) + 4cos(-) + 2 +--R 2 2 2 2 2 +--R / +--R x 8 x 2 x 6 +--R sin(-) + (4cos(-) - 4)sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 x 4 +--R (6cos(-) - 4cos(-) + 6)sin(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 x 2 x 8 +--R (4cos(-) + 4cos(-) - 4cos(-) - 4)sin(-) + cos(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 4 x 2 +--R 4cos(-) + 6cos(-) + 4cos(-) + 1 +--R 2 2 2 +--R + +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R * +--R log +--R x 8 x 2 x 6 x 4 x 4 +--R sin(-) + 4cos(-) sin(-) + (6cos(-) - 2)sin(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 2 x 2 x 8 x 4 +--R (4cos(-) + 12cos(-) )sin(-) + cos(-) - 2cos(-) + 1 +--R 2 2 2 2 2 +--R * +--R +---------+ 2 +--R | +-+ +--R |3\|2 + 4 +--R +---------+2 atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ x 8 +-+ x 2 x 6 +-+ x 4 x 4 +--R - 2\|2 sin(-) - 8\|2 cos(-) sin(-) - 12\|2 cos(-) sin(-) +--R 2 2 2 2 2 +--R + +--R +-+ x 6 x 2 +-+ x 8 +-+ +--R - 8\|2 cos(-) sin(-) - 2\|2 cos(-) + 2\|2 +--R 2 2 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R x 8 x 2 x 6 x 4 x 4 +--R sin(-) + 4cos(-) sin(-) + (6cos(-) - 2)sin(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 2 x 2 x 8 x 4 +--R (4cos(-) + 12cos(-) )sin(-) + cos(-) - 2cos(-) + 1 +--R 2 2 2 2 2 +--R * +--R +---------+ 2 +--R | +-+ +--R |3\|2 + 4 +--R +---------+2 atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +---------+ +--R | +-+ +--R +-+ x x 3 +-+ x 3 x |4\|2 + 4 +--R (16\|2 cos(-)sin(-) - 16\|2 cos(-) sin(-)) |--------- +--R 2 2 2 2 4| +-+ +--R \| \|2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R atan(64 |--------- ) +--R | +-+ +--R \| 4096\|2 +--R cos(--------------------) +--R 2 +--R + +--R x 8 x 2 x 6 x 4 x 4 +--R 2sin(-) + 8cos(-) sin(-) + (12cos(-) + 4)sin(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 2 x 2 x 8 x 4 +--R (8cos(-) - 24cos(-) )sin(-) + 2cos(-) + 4cos(-) + 2 +--R 2 2 2 2 2 +--R / +--R x 8 x 2 x 6 +--R sin(-) + (4cos(-) - 4)sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 x 4 +--R (6cos(-) - 4cos(-) + 6)sin(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 x 2 x 8 x 6 +--R (4cos(-) + 4cos(-) - 4cos(-) - 4)sin(-) + cos(-) + 4cos(-) +--R 2 2 2 2 2 2 +--R + +--R x 4 x 2 +--R 6cos(-) + 4cos(-) + 1 +--R 2 2 +--R + +--R - +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R * +--R log +--R x 8 x 2 x 6 x 4 x 4 +--R sin(-) + 4cos(-) sin(-) + (6cos(-) - 2)sin(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 2 x 2 x 8 x 4 +--R (4cos(-) + 12cos(-) )sin(-) + cos(-) - 2cos(-) + 1 +--R 2 2 2 2 2 +--R * +--R +---------+ 2 +--R | +-+ +--R |3\|2 + 4 +--R +---------+2 atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ x 8 +-+ x 2 x 6 +--R - 2\|2 sin(-) - 8\|2 cos(-) sin(-) +--R 2 2 2 +--R + +--R +-+ x 4 x 4 +-+ x 6 x 2 +--R - 12\|2 cos(-) sin(-) - 8\|2 cos(-) sin(-) +--R 2 2 2 2 +--R + +--R +-+ x 8 +-+ +--R - 2\|2 cos(-) + 2\|2 +--R 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R x 8 x 2 x 6 x 4 x 4 +--R sin(-) + 4cos(-) sin(-) + (6cos(-) - 2)sin(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 2 x 2 x 8 x 4 +--R (4cos(-) + 12cos(-) )sin(-) + cos(-) - 2cos(-) + 1 +--R 2 2 2 2 2 +--R * +--R +---------+ 2 +--R | +-+ +--R |3\|2 + 4 +--R +---------+2 atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +---------+ +--R | +-+ +--R +-+ x x 3 +-+ x 3 x |4\|2 + 4 +--R (- 16\|2 cos(-)sin(-) + 16\|2 cos(-) sin(-)) |--------- +--R 2 2 2 2 4| +-+ +--R \| \|2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R atan(64 |--------- ) +--R | +-+ +--R \| 4096\|2 +--R cos(--------------------) +--R 2 +--R + +--R x 8 x 2 x 6 x 4 x 4 +--R 2sin(-) + 8cos(-) sin(-) + (12cos(-) + 4)sin(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 2 x 2 x 8 x 4 +--R (8cos(-) - 24cos(-) )sin(-) + 2cos(-) + 4cos(-) + 2 +--R 2 2 2 2 2 +--R / +--R x 8 x 2 x 6 +--R sin(-) + (4cos(-) - 4)sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 x 4 +--R (6cos(-) - 4cos(-) + 6)sin(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 x 2 x 8 +--R (4cos(-) + 4cos(-) - 4cos(-) - 4)sin(-) + cos(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 4 x 2 +--R 4cos(-) + 6cos(-) + 4cos(-) + 1 +--R 2 2 2 +--R + +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R * +--R log +--R x 8 x 2 x 6 x 4 x 4 +--R sin(-) + 4cos(-) sin(-) + (6cos(-) - 2)sin(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 2 x 2 x 8 x 4 +--R (4cos(-) + 12cos(-) )sin(-) + cos(-) - 2cos(-) + 1 +--R 2 2 2 2 2 +--R * +--R +---------+ 2 +--R | +-+ +--R |3\|2 - 4 +--R +---------+2 atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ x 8 +-+ x 2 x 6 +-+ x 4 x 4 +--R 2\|2 sin(-) + 8\|2 cos(-) sin(-) + 12\|2 cos(-) sin(-) +--R 2 2 2 2 2 +--R + +--R +-+ x 6 x 2 +-+ x 8 +-+ +--R 8\|2 cos(-) sin(-) + 2\|2 cos(-) - 2\|2 +--R 2 2 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R x 8 x 2 x 6 x 4 x 4 +--R sin(-) + 4cos(-) sin(-) + (6cos(-) - 2)sin(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 2 x 2 x 8 x 4 +--R (4cos(-) + 12cos(-) )sin(-) + cos(-) - 2cos(-) + 1 +--R 2 2 2 2 2 +--R * +--R +---------+ 2 +--R | +-+ +--R |3\|2 - 4 +--R +---------+2 atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +---------+ +--R | +-+ +--R +-+ x x 3 +-+ x 3 x |4\|2 - 4 +--R (16\|2 cos(-)sin(-) - 16\|2 cos(-) sin(-)) |--------- +--R 2 2 2 2 4| +-+ +--R \| \|2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R atan(64 |--------- ) +--R | +-+ +--R \| 4096\|2 +--R cos(--------------------) +--R 2 +--R + +--R x 8 x 2 x 6 x 4 x 4 +--R 2sin(-) + 8cos(-) sin(-) + (12cos(-) + 4)sin(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 2 x 2 x 8 x 4 +--R (8cos(-) - 24cos(-) )sin(-) + 2cos(-) + 4cos(-) + 2 +--R 2 2 2 2 2 +--R / +--R x 8 x 2 x 6 +--R sin(-) + (4cos(-) - 4)sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 x 4 +--R (6cos(-) - 4cos(-) + 6)sin(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 x 2 x 8 x 6 +--R (4cos(-) + 4cos(-) - 4cos(-) - 4)sin(-) + cos(-) + 4cos(-) +--R 2 2 2 2 2 2 +--R + +--R x 4 x 2 +--R 6cos(-) + 4cos(-) + 1 +--R 2 2 +--R + +--R - +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R * +--R log +--R x 8 x 2 x 6 x 4 x 4 +--R sin(-) + 4cos(-) sin(-) + (6cos(-) - 2)sin(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 2 x 2 x 8 x 4 +--R (4cos(-) + 12cos(-) )sin(-) + cos(-) - 2cos(-) + 1 +--R 2 2 2 2 2 +--R * +--R +---------+ 2 +--R | +-+ +--R |3\|2 - 4 +--R +---------+2 atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ x 8 +-+ x 2 x 6 +-+ x 4 x 4 +--R 2\|2 sin(-) + 8\|2 cos(-) sin(-) + 12\|2 cos(-) sin(-) +--R 2 2 2 2 2 +--R + +--R +-+ x 6 x 2 +-+ x 8 +-+ +--R 8\|2 cos(-) sin(-) + 2\|2 cos(-) - 2\|2 +--R 2 2 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R x 8 x 2 x 6 x 4 x 4 +--R sin(-) + 4cos(-) sin(-) + (6cos(-) - 2)sin(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 2 x 2 x 8 x 4 +--R (4cos(-) + 12cos(-) )sin(-) + cos(-) - 2cos(-) + 1 +--R 2 2 2 2 2 +--R * +--R +---------+ 2 +--R | +-+ +--R |3\|2 - 4 +--R +---------+2 atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +---------+ +--R | +-+ +--R +-+ x x 3 +-+ x 3 x |4\|2 - 4 +--R (- 16\|2 cos(-)sin(-) + 16\|2 cos(-) sin(-)) |--------- +--R 2 2 2 2 4| +-+ +--R \| \|2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R atan(64 |--------- ) +--R | +-+ +--R \| 4096\|2 +--R cos(--------------------) +--R 2 +--R + +--R x 8 x 2 x 6 x 4 x 4 +--R 2sin(-) + 8cos(-) sin(-) + (12cos(-) + 4)sin(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 2 x 2 x 8 x 4 +--R (8cos(-) - 24cos(-) )sin(-) + 2cos(-) + 4cos(-) + 2 +--R 2 2 2 2 2 +--R / +--R x 8 x 2 x 6 +--R sin(-) + (4cos(-) - 4)sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 x 4 +--R (6cos(-) - 4cos(-) + 6)sin(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 x 2 x 8 +--R (4cos(-) + 4cos(-) - 4cos(-) - 4)sin(-) + cos(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 4 x 2 +--R 4cos(-) + 6cos(-) + 4cos(-) + 1 +--R 2 2 2 +--R + +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R * +--R log +--R x 8 x 2 x 6 x 4 x 4 +--R sin(-) + 4cos(-) sin(-) + (6cos(-) - 2)sin(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 2 x 2 x 8 x 4 +--R (4cos(-) + 12cos(-) )sin(-) + cos(-) - 2cos(-) + 1 +--R 2 2 2 2 2 +--R * +--R +---------+ 2 +--R | +-+ +--R |3\|2 - 4 +--R +---------+2 atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ x 8 +-+ x 2 x 6 +-+ x 4 x 4 +--R - 2\|2 sin(-) - 8\|2 cos(-) sin(-) - 12\|2 cos(-) sin(-) +--R 2 2 2 2 2 +--R + +--R +-+ x 6 x 2 +-+ x 8 +-+ +--R - 8\|2 cos(-) sin(-) - 2\|2 cos(-) + 2\|2 +--R 2 2 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R x 8 x 2 x 6 x 4 x 4 +--R sin(-) + 4cos(-) sin(-) + (6cos(-) - 2)sin(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 2 x 2 x 8 x 4 +--R (4cos(-) + 12cos(-) )sin(-) + cos(-) - 2cos(-) + 1 +--R 2 2 2 2 2 +--R * +--R +---------+ 2 +--R | +-+ +--R |3\|2 - 4 +--R +---------+2 atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +---------+ +--R | +-+ +--R +-+ x x 3 +-+ x 3 x |4\|2 - 4 +--R (16\|2 cos(-)sin(-) - 16\|2 cos(-) sin(-)) |--------- +--R 2 2 2 2 4| +-+ +--R \| \|2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R atan(64 |--------- ) +--R | +-+ +--R \| 4096\|2 +--R cos(--------------------) +--R 2 +--R + +--R x 8 x 2 x 6 x 4 x 4 +--R 2sin(-) + 8cos(-) sin(-) + (12cos(-) + 4)sin(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 2 x 2 x 8 x 4 +--R (8cos(-) - 24cos(-) )sin(-) + 2cos(-) + 4cos(-) + 2 +--R 2 2 2 2 2 +--R / +--R x 8 x 2 x 6 +--R sin(-) + (4cos(-) - 4)sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 x 4 +--R (6cos(-) - 4cos(-) + 6)sin(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 x 2 x 8 x 6 +--R (4cos(-) + 4cos(-) - 4cos(-) - 4)sin(-) + cos(-) + 4cos(-) +--R 2 2 2 2 2 2 +--R + +--R x 4 x 2 +--R 6cos(-) + 4cos(-) + 1 +--R 2 2 +--R + +--R - +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R * +--R log +--R x 8 x 2 x 6 x 4 x 4 +--R sin(-) + 4cos(-) sin(-) + (6cos(-) - 2)sin(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 2 x 2 x 8 x 4 +--R (4cos(-) + 12cos(-) )sin(-) + cos(-) - 2cos(-) + 1 +--R 2 2 2 2 2 +--R * +--R +---------+ 2 +--R | +-+ +--R |3\|2 - 4 +--R +---------+2 atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ x 8 +-+ x 2 x 6 +--R - 2\|2 sin(-) - 8\|2 cos(-) sin(-) +--R 2 2 2 +--R + +--R +-+ x 4 x 4 +-+ x 6 x 2 +--R - 12\|2 cos(-) sin(-) - 8\|2 cos(-) sin(-) +--R 2 2 2 2 +--R + +--R +-+ x 8 +-+ +--R - 2\|2 cos(-) + 2\|2 +--R 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R x 8 x 2 x 6 x 4 x 4 +--R sin(-) + 4cos(-) sin(-) + (6cos(-) - 2)sin(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 2 x 2 x 8 x 4 +--R (4cos(-) + 12cos(-) )sin(-) + cos(-) - 2cos(-) + 1 +--R 2 2 2 2 2 +--R * +--R +---------+ 2 +--R | +-+ +--R |3\|2 - 4 +--R +---------+2 atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +---------+ +--R | +-+ +--R +-+ x x 3 +-+ x 3 x |4\|2 - 4 +--R (- 16\|2 cos(-)sin(-) + 16\|2 cos(-) sin(-)) |--------- +--R 2 2 2 2 4| +-+ +--R \| \|2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R atan(64 |--------- ) +--R | +-+ +--R \| 4096\|2 +--R cos(--------------------) +--R 2 +--R + +--R x 8 x 2 x 6 x 4 x 4 +--R 2sin(-) + 8cos(-) sin(-) + (12cos(-) + 4)sin(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 2 x 2 x 8 x 4 +--R (8cos(-) - 24cos(-) )sin(-) + 2cos(-) + 4cos(-) + 2 +--R 2 2 2 2 2 +--R / +--R x 8 x 2 x 6 +--R sin(-) + (4cos(-) - 4)sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 x 4 +--R (6cos(-) - 4cos(-) + 6)sin(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 x 2 x 8 +--R (4cos(-) + 4cos(-) - 4cos(-) - 4)sin(-) + cos(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 4 x 2 +--R 4cos(-) + 6cos(-) + 4cos(-) + 1 +--R 2 2 2 +--R + +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R 2 |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R * +--R atan +--R +-+ x x 5 +-+ x 3 +-+ x x 3 +--R 4\|2 cos(-)sin(-) + (8\|2 cos(-) - 8\|2 cos(-))sin(-) +--R 2 2 2 2 2 +--R + +--R +-+ x 5 +-+ x 3 +-+ x x +--R (4\|2 cos(-) + 8\|2 cos(-) + 4\|2 cos(-))sin(-) +--R 2 2 2 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ x 8 +-+ x 2 +-+ x 6 +--R \|2 sin(-) + (4\|2 cos(-) - 2\|2 )sin(-) +--R 2 2 2 +--R + +--R +-+ x 4 +-+ x 2 x 4 +--R (6\|2 cos(-) - 2\|2 cos(-) )sin(-) +--R 2 2 2 +--R + +--R +-+ x 6 +-+ x 4 +-+ x 2 +-+ x 8 +--R (4\|2 cos(-) + 2\|2 cos(-) + 2\|2 )sin(-) + \|2 cos(-) +--R 2 2 2 2 +--R + +--R +-+ x 6 +-+ x 2 +-+ +--R 2\|2 cos(-) - 2\|2 cos(-) - \|2 +--R 2 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R x x 5 x 3 x 3 x 5 x x +--R 8cos(-)sin(-) + 16cos(-) sin(-) + (8cos(-) - 8cos(-))sin(-) +--R 2 2 2 2 2 2 2 +--R / +--R +-+ x 8 +-+ x 2 +-+ x 6 +--R \|2 sin(-) + (4\|2 cos(-) - 2\|2 )sin(-) +--R 2 2 2 +--R + +--R +-+ x 4 +-+ x 2 x 4 +--R (6\|2 cos(-) - 2\|2 cos(-) )sin(-) +--R 2 2 2 +--R + +--R +-+ x 6 +-+ x 4 +-+ x 2 +-+ x 8 +--R (4\|2 cos(-) + 2\|2 cos(-) + 2\|2 )sin(-) + \|2 cos(-) +--R 2 2 2 2 +--R + +--R +-+ x 6 +-+ x 2 +-+ +--R 2\|2 cos(-) - 2\|2 cos(-) - \|2 +--R 2 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ x x 5 +-+ x 3 +-+ x x 3 +--R - 4\|2 cos(-)sin(-) + (- 8\|2 cos(-) + 8\|2 cos(-))sin(-) +--R 2 2 2 2 2 +--R + +--R +-+ x 5 +-+ x 3 +-+ x x +--R (- 4\|2 cos(-) - 8\|2 cos(-) - 4\|2 cos(-))sin(-) +--R 2 2 2 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R x 8 x 2 x 6 +--R 2sin(-) + (8cos(-) - 4)sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 x 4 +--R (12cos(-) - 4cos(-) + 4)sin(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 x 2 x 8 +--R (8cos(-) + 4cos(-) - 24cos(-) - 4)sin(-) + 2cos(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 4 x 2 +--R 4cos(-) + 4cos(-) + 4cos(-) + 2 +--R 2 2 2 +--R + +--R - +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R 2 |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R * +--R atan +--R +-+ x x 5 +-+ x 3 +-+ x x 3 +--R 4\|2 cos(-)sin(-) + (8\|2 cos(-) - 8\|2 cos(-))sin(-) +--R 2 2 2 2 2 +--R + +--R +-+ x 5 +-+ x 3 +-+ x x +--R (4\|2 cos(-) + 8\|2 cos(-) + 4\|2 cos(-))sin(-) +--R 2 2 2 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ x 8 +-+ x 2 +-+ x 6 +--R \|2 sin(-) + (4\|2 cos(-) - 2\|2 )sin(-) +--R 2 2 2 +--R + +--R +-+ x 4 +-+ x 2 x 4 +--R (6\|2 cos(-) - 2\|2 cos(-) )sin(-) +--R 2 2 2 +--R + +--R +-+ x 6 +-+ x 4 +-+ x 2 +--R (4\|2 cos(-) + 2\|2 cos(-) + 2\|2 )sin(-) +--R 2 2 2 +--R + +--R +-+ x 8 +-+ x 6 +-+ x 2 +-+ +--R \|2 cos(-) + 2\|2 cos(-) - 2\|2 cos(-) - \|2 +--R 2 2 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R x x 5 x 3 x 3 +--R - 8cos(-)sin(-) - 16cos(-) sin(-) +--R 2 2 2 2 +--R + +--R x 5 x x +--R (- 8cos(-) + 8cos(-))sin(-) +--R 2 2 2 +--R / +--R +-+ x 8 +-+ x 2 +-+ x 6 +--R \|2 sin(-) + (4\|2 cos(-) - 2\|2 )sin(-) +--R 2 2 2 +--R + +--R +-+ x 4 +-+ x 2 x 4 +--R (6\|2 cos(-) - 2\|2 cos(-) )sin(-) +--R 2 2 2 +--R + +--R +-+ x 6 +-+ x 4 +-+ x 2 +--R (4\|2 cos(-) + 2\|2 cos(-) + 2\|2 )sin(-) +--R 2 2 2 +--R + +--R +-+ x 8 +-+ x 6 +-+ x 2 +-+ +--R \|2 cos(-) + 2\|2 cos(-) - 2\|2 cos(-) - \|2 +--R 2 2 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ x x 5 +--R - 4\|2 cos(-)sin(-) +--R 2 2 +--R + +--R +-+ x 3 +-+ x x 3 +--R (- 8\|2 cos(-) + 8\|2 cos(-))sin(-) +--R 2 2 2 +--R + +--R +-+ x 5 +-+ x 3 +-+ x x +--R (- 4\|2 cos(-) - 8\|2 cos(-) - 4\|2 cos(-))sin(-) +--R 2 2 2 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R x 8 x 2 x 6 +--R - 2sin(-) + (- 8cos(-) + 4)sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 x 4 +--R (- 12cos(-) + 4cos(-) - 4)sin(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 x 2 x 8 +--R (- 8cos(-) - 4cos(-) + 24cos(-) + 4)sin(-) - 2cos(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 4 x 2 +--R - 4cos(-) - 4cos(-) - 4cos(-) - 2 +--R 2 2 2 +--R + +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R 2 |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R * +--R atan +--R +-+ x x 5 +-+ x 3 +-+ x x 3 +--R 4\|2 cos(-)sin(-) + (8\|2 cos(-) - 8\|2 cos(-))sin(-) +--R 2 2 2 2 2 +--R + +--R +-+ x 5 +-+ x 3 +-+ x x +--R (4\|2 cos(-) + 8\|2 cos(-) + 4\|2 cos(-))sin(-) +--R 2 2 2 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ x 8 +-+ x 2 +-+ x 6 +--R \|2 sin(-) + (4\|2 cos(-) - 2\|2 )sin(-) +--R 2 2 2 +--R + +--R +-+ x 4 +-+ x 2 x 4 +--R (6\|2 cos(-) - 2\|2 cos(-) )sin(-) +--R 2 2 2 +--R + +--R +-+ x 6 +-+ x 4 +-+ x 2 +-+ x 8 +--R (4\|2 cos(-) + 2\|2 cos(-) + 2\|2 )sin(-) + \|2 cos(-) +--R 2 2 2 2 +--R + +--R +-+ x 6 +-+ x 2 +-+ +--R 2\|2 cos(-) - 2\|2 cos(-) - \|2 +--R 2 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R x x 5 x 3 x 3 x 5 x x +--R 8cos(-)sin(-) + 16cos(-) sin(-) + (8cos(-) - 8cos(-))sin(-) +--R 2 2 2 2 2 2 2 +--R / +--R +-+ x 8 +-+ x 2 +-+ x 6 +--R \|2 sin(-) + (4\|2 cos(-) - 2\|2 )sin(-) +--R 2 2 2 +--R + +--R +-+ x 4 +-+ x 2 x 4 +--R (6\|2 cos(-) - 2\|2 cos(-) )sin(-) +--R 2 2 2 +--R + +--R +-+ x 6 +-+ x 4 +-+ x 2 +-+ x 8 +--R (4\|2 cos(-) + 2\|2 cos(-) + 2\|2 )sin(-) + \|2 cos(-) +--R 2 2 2 2 +--R + +--R +-+ x 6 +-+ x 2 +-+ +--R 2\|2 cos(-) - 2\|2 cos(-) - \|2 +--R 2 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ x x 5 +-+ x 3 +-+ x x 3 +--R - 4\|2 cos(-)sin(-) + (- 8\|2 cos(-) + 8\|2 cos(-))sin(-) +--R 2 2 2 2 2 +--R + +--R +-+ x 5 +-+ x 3 +-+ x x +--R (- 4\|2 cos(-) - 8\|2 cos(-) - 4\|2 cos(-))sin(-) +--R 2 2 2 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R x 8 x 2 x 6 +--R 2sin(-) + (8cos(-) - 4)sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 x 4 +--R (12cos(-) - 4cos(-) + 4)sin(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 x 2 x 8 +--R (8cos(-) + 4cos(-) - 24cos(-) - 4)sin(-) + 2cos(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 4 x 2 +--R 4cos(-) + 4cos(-) + 4cos(-) + 2 +--R 2 2 2 +--R + +--R - +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R 2 |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R * +--R atan +--R +-+ x x 5 +-+ x 3 +-+ x x 3 +--R 4\|2 cos(-)sin(-) + (8\|2 cos(-) - 8\|2 cos(-))sin(-) +--R 2 2 2 2 2 +--R + +--R +-+ x 5 +-+ x 3 +-+ x x +--R (4\|2 cos(-) + 8\|2 cos(-) + 4\|2 cos(-))sin(-) +--R 2 2 2 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ x 8 +-+ x 2 +-+ x 6 +--R \|2 sin(-) + (4\|2 cos(-) - 2\|2 )sin(-) +--R 2 2 2 +--R + +--R +-+ x 4 +-+ x 2 x 4 +--R (6\|2 cos(-) - 2\|2 cos(-) )sin(-) +--R 2 2 2 +--R + +--R +-+ x 6 +-+ x 4 +-+ x 2 +--R (4\|2 cos(-) + 2\|2 cos(-) + 2\|2 )sin(-) +--R 2 2 2 +--R + +--R +-+ x 8 +-+ x 6 +-+ x 2 +-+ +--R \|2 cos(-) + 2\|2 cos(-) - 2\|2 cos(-) - \|2 +--R 2 2 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R x x 5 x 3 x 3 +--R - 8cos(-)sin(-) - 16cos(-) sin(-) +--R 2 2 2 2 +--R + +--R x 5 x x +--R (- 8cos(-) + 8cos(-))sin(-) +--R 2 2 2 +--R / +--R +-+ x 8 +-+ x 2 +-+ x 6 +--R \|2 sin(-) + (4\|2 cos(-) - 2\|2 )sin(-) +--R 2 2 2 +--R + +--R +-+ x 4 +-+ x 2 x 4 +--R (6\|2 cos(-) - 2\|2 cos(-) )sin(-) +--R 2 2 2 +--R + +--R +-+ x 6 +-+ x 4 +-+ x 2 +--R (4\|2 cos(-) + 2\|2 cos(-) + 2\|2 )sin(-) +--R 2 2 2 +--R + +--R +-+ x 8 +-+ x 6 +-+ x 2 +-+ +--R \|2 cos(-) + 2\|2 cos(-) - 2\|2 cos(-) - \|2 +--R 2 2 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ x x 5 +--R - 4\|2 cos(-)sin(-) +--R 2 2 +--R + +--R +-+ x 3 +-+ x x 3 +--R (- 8\|2 cos(-) + 8\|2 cos(-))sin(-) +--R 2 2 2 +--R + +--R +-+ x 5 +-+ x 3 +-+ x x +--R (- 4\|2 cos(-) - 8\|2 cos(-) - 4\|2 cos(-))sin(-) +--R 2 2 2 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R x 8 x 2 x 6 +--R - 2sin(-) + (- 8cos(-) + 4)sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 x 4 +--R (- 12cos(-) + 4cos(-) - 4)sin(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 x 2 x 8 +--R (- 8cos(-) - 4cos(-) + 24cos(-) + 4)sin(-) - 2cos(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 4 x 2 +--R - 4cos(-) - 4cos(-) - 4cos(-) - 2 +--R 2 2 2 +--R + +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R 2 |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R * +--R atan +--R +-+ x x 5 +-+ x 3 +-+ x x 3 +--R 4\|2 cos(-)sin(-) + (8\|2 cos(-) - 8\|2 cos(-))sin(-) +--R 2 2 2 2 2 +--R + +--R +-+ x 5 +-+ x 3 +-+ x x +--R (4\|2 cos(-) + 8\|2 cos(-) + 4\|2 cos(-))sin(-) +--R 2 2 2 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ x 8 +-+ x 2 +-+ x 6 +--R - \|2 sin(-) + (- 4\|2 cos(-) + 2\|2 )sin(-) +--R 2 2 2 +--R + +--R +-+ x 4 +-+ x 2 x 4 +--R (- 6\|2 cos(-) + 2\|2 cos(-) )sin(-) +--R 2 2 2 +--R + +--R +-+ x 6 +-+ x 4 +-+ x 2 +-+ x 8 +--R (- 4\|2 cos(-) - 2\|2 cos(-) - 2\|2 )sin(-) - \|2 cos(-) +--R 2 2 2 2 +--R + +--R +-+ x 6 +-+ x 2 +-+ +--R - 2\|2 cos(-) + 2\|2 cos(-) + \|2 +--R 2 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R x x 5 x 3 x 3 x 5 x x +--R 8cos(-)sin(-) + 16cos(-) sin(-) + (8cos(-) - 8cos(-))sin(-) +--R 2 2 2 2 2 2 2 +--R / +--R +-+ x 8 +-+ x 2 +-+ x 6 +--R \|2 sin(-) + (4\|2 cos(-) - 2\|2 )sin(-) +--R 2 2 2 +--R + +--R +-+ x 4 +-+ x 2 x 4 +--R (6\|2 cos(-) - 2\|2 cos(-) )sin(-) +--R 2 2 2 +--R + +--R +-+ x 6 +-+ x 4 +-+ x 2 +-+ x 8 +--R (4\|2 cos(-) + 2\|2 cos(-) + 2\|2 )sin(-) + \|2 cos(-) +--R 2 2 2 2 +--R + +--R +-+ x 6 +-+ x 2 +-+ +--R 2\|2 cos(-) - 2\|2 cos(-) - \|2 +--R 2 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ x x 5 +-+ x 3 +-+ x x 3 +--R 4\|2 cos(-)sin(-) + (8\|2 cos(-) - 8\|2 cos(-))sin(-) +--R 2 2 2 2 2 +--R + +--R +-+ x 5 +-+ x 3 +-+ x x +--R (4\|2 cos(-) + 8\|2 cos(-) + 4\|2 cos(-))sin(-) +--R 2 2 2 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R x 8 x 2 x 6 +--R 2sin(-) + (8cos(-) - 4)sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 x 4 +--R (12cos(-) - 4cos(-) + 4)sin(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 x 2 x 8 +--R (8cos(-) + 4cos(-) - 24cos(-) - 4)sin(-) + 2cos(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 4 x 2 +--R 4cos(-) + 4cos(-) + 4cos(-) + 2 +--R 2 2 2 +--R + +--R - +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R 2 |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R * +--R atan +--R +-+ x x 5 +-+ x 3 +-+ x x 3 +--R 4\|2 cos(-)sin(-) + (8\|2 cos(-) - 8\|2 cos(-))sin(-) +--R 2 2 2 2 2 +--R + +--R +-+ x 5 +-+ x 3 +-+ x x +--R (4\|2 cos(-) + 8\|2 cos(-) + 4\|2 cos(-))sin(-) +--R 2 2 2 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ x 8 +-+ x 2 +-+ x 6 +--R - \|2 sin(-) + (- 4\|2 cos(-) + 2\|2 )sin(-) +--R 2 2 2 +--R + +--R +-+ x 4 +-+ x 2 x 4 +--R (- 6\|2 cos(-) + 2\|2 cos(-) )sin(-) +--R 2 2 2 +--R + +--R +-+ x 6 +-+ x 4 +-+ x 2 +--R (- 4\|2 cos(-) - 2\|2 cos(-) - 2\|2 )sin(-) +--R 2 2 2 +--R + +--R +-+ x 8 +-+ x 6 +-+ x 2 +-+ +--R - \|2 cos(-) - 2\|2 cos(-) + 2\|2 cos(-) + \|2 +--R 2 2 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R x x 5 x 3 x 3 +--R - 8cos(-)sin(-) - 16cos(-) sin(-) +--R 2 2 2 2 +--R + +--R x 5 x x +--R (- 8cos(-) + 8cos(-))sin(-) +--R 2 2 2 +--R / +--R +-+ x 8 +-+ x 2 +-+ x 6 +--R \|2 sin(-) + (4\|2 cos(-) - 2\|2 )sin(-) +--R 2 2 2 +--R + +--R +-+ x 4 +-+ x 2 x 4 +--R (6\|2 cos(-) - 2\|2 cos(-) )sin(-) +--R 2 2 2 +--R + +--R +-+ x 6 +-+ x 4 +-+ x 2 +--R (4\|2 cos(-) + 2\|2 cos(-) + 2\|2 )sin(-) +--R 2 2 2 +--R + +--R +-+ x 8 +-+ x 6 +-+ x 2 +-+ +--R \|2 cos(-) + 2\|2 cos(-) - 2\|2 cos(-) - \|2 +--R 2 2 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ x x 5 +-+ x 3 +-+ x x 3 +--R 4\|2 cos(-)sin(-) + (8\|2 cos(-) - 8\|2 cos(-))sin(-) +--R 2 2 2 2 2 +--R + +--R +-+ x 5 +-+ x 3 +-+ x x +--R (4\|2 cos(-) + 8\|2 cos(-) + 4\|2 cos(-))sin(-) +--R 2 2 2 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R x 8 x 2 x 6 +--R - 2sin(-) + (- 8cos(-) + 4)sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 x 4 +--R (- 12cos(-) + 4cos(-) - 4)sin(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 x 2 x 8 +--R (- 8cos(-) - 4cos(-) + 24cos(-) + 4)sin(-) - 2cos(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 4 x 2 +--R - 4cos(-) - 4cos(-) - 4cos(-) - 2 +--R 2 2 2 +--R + +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R 2 |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R * +--R atan +--R +-+ x x 5 +-+ x 3 +-+ x x 3 +--R 4\|2 cos(-)sin(-) + (8\|2 cos(-) - 8\|2 cos(-))sin(-) +--R 2 2 2 2 2 +--R + +--R +-+ x 5 +-+ x 3 +-+ x x +--R (4\|2 cos(-) + 8\|2 cos(-) + 4\|2 cos(-))sin(-) +--R 2 2 2 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ x 8 +-+ x 2 +-+ x 6 +--R - \|2 sin(-) + (- 4\|2 cos(-) + 2\|2 )sin(-) +--R 2 2 2 +--R + +--R +-+ x 4 +-+ x 2 x 4 +--R (- 6\|2 cos(-) + 2\|2 cos(-) )sin(-) +--R 2 2 2 +--R + +--R +-+ x 6 +-+ x 4 +-+ x 2 +-+ x 8 +--R (- 4\|2 cos(-) - 2\|2 cos(-) - 2\|2 )sin(-) - \|2 cos(-) +--R 2 2 2 2 +--R + +--R +-+ x 6 +-+ x 2 +-+ +--R - 2\|2 cos(-) + 2\|2 cos(-) + \|2 +--R 2 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R x x 5 x 3 x 3 x 5 x x +--R 8cos(-)sin(-) + 16cos(-) sin(-) + (8cos(-) - 8cos(-))sin(-) +--R 2 2 2 2 2 2 2 +--R / +--R +-+ x 8 +-+ x 2 +-+ x 6 +--R \|2 sin(-) + (4\|2 cos(-) - 2\|2 )sin(-) +--R 2 2 2 +--R + +--R +-+ x 4 +-+ x 2 x 4 +--R (6\|2 cos(-) - 2\|2 cos(-) )sin(-) +--R 2 2 2 +--R + +--R +-+ x 6 +-+ x 4 +-+ x 2 +-+ x 8 +--R (4\|2 cos(-) + 2\|2 cos(-) + 2\|2 )sin(-) + \|2 cos(-) +--R 2 2 2 2 +--R + +--R +-+ x 6 +-+ x 2 +-+ +--R 2\|2 cos(-) - 2\|2 cos(-) - \|2 +--R 2 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ x x 5 +-+ x 3 +-+ x x 3 +--R 4\|2 cos(-)sin(-) + (8\|2 cos(-) - 8\|2 cos(-))sin(-) +--R 2 2 2 2 2 +--R + +--R +-+ x 5 +-+ x 3 +-+ x x +--R (4\|2 cos(-) + 8\|2 cos(-) + 4\|2 cos(-))sin(-) +--R 2 2 2 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R x 8 x 2 x 6 +--R 2sin(-) + (8cos(-) - 4)sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 x 4 +--R (12cos(-) - 4cos(-) + 4)sin(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 x 2 x 8 +--R (8cos(-) + 4cos(-) - 24cos(-) - 4)sin(-) + 2cos(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 4 x 2 +--R 4cos(-) + 4cos(-) + 4cos(-) + 2 +--R 2 2 2 +--R + +--R - +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R 2 |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R * +--R atan +--R +-+ x x 5 +-+ x 3 +-+ x x 3 +--R 4\|2 cos(-)sin(-) + (8\|2 cos(-) - 8\|2 cos(-))sin(-) +--R 2 2 2 2 2 +--R + +--R +-+ x 5 +-+ x 3 +-+ x x +--R (4\|2 cos(-) + 8\|2 cos(-) + 4\|2 cos(-))sin(-) +--R 2 2 2 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ x 8 +-+ x 2 +-+ x 6 +--R - \|2 sin(-) + (- 4\|2 cos(-) + 2\|2 )sin(-) +--R 2 2 2 +--R + +--R +-+ x 4 +-+ x 2 x 4 +--R (- 6\|2 cos(-) + 2\|2 cos(-) )sin(-) +--R 2 2 2 +--R + +--R +-+ x 6 +-+ x 4 +-+ x 2 +--R (- 4\|2 cos(-) - 2\|2 cos(-) - 2\|2 )sin(-) +--R 2 2 2 +--R + +--R +-+ x 8 +-+ x 6 +-+ x 2 +-+ +--R - \|2 cos(-) - 2\|2 cos(-) + 2\|2 cos(-) + \|2 +--R 2 2 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R x x 5 x 3 x 3 +--R - 8cos(-)sin(-) - 16cos(-) sin(-) +--R 2 2 2 2 +--R + +--R x 5 x x +--R (- 8cos(-) + 8cos(-))sin(-) +--R 2 2 2 +--R / +--R +-+ x 8 +-+ x 2 +-+ x 6 +--R \|2 sin(-) + (4\|2 cos(-) - 2\|2 )sin(-) +--R 2 2 2 +--R + +--R +-+ x 4 +-+ x 2 x 4 +--R (6\|2 cos(-) - 2\|2 cos(-) )sin(-) +--R 2 2 2 +--R + +--R +-+ x 6 +-+ x 4 +-+ x 2 +--R (4\|2 cos(-) + 2\|2 cos(-) + 2\|2 )sin(-) +--R 2 2 2 +--R + +--R +-+ x 8 +-+ x 6 +-+ x 2 +-+ +--R \|2 cos(-) + 2\|2 cos(-) - 2\|2 cos(-) - \|2 +--R 2 2 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ x x 5 +-+ x 3 +-+ x x 3 +--R 4\|2 cos(-)sin(-) + (8\|2 cos(-) - 8\|2 cos(-))sin(-) +--R 2 2 2 2 2 +--R + +--R +-+ x 5 +-+ x 3 +-+ x x +--R (4\|2 cos(-) + 8\|2 cos(-) + 4\|2 cos(-))sin(-) +--R 2 2 2 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R x 8 x 2 x 6 +--R - 2sin(-) + (- 8cos(-) + 4)sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 x 4 +--R (- 12cos(-) + 4cos(-) - 4)sin(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 x 2 x 8 +--R (- 8cos(-) - 4cos(-) + 24cos(-) + 4)sin(-) - 2cos(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 4 x 2 +--R - 4cos(-) - 4cos(-) - 4cos(-) - 2 +--R 2 2 2 +--R / +--R +-+ +--R 16\|2 +--R Type: Union(Expression Integer,...) +--R +--R +--R +--E 375 + +--S 376 of 504 +--Rt0173:= 1/(1-cos(x)^3) +--R +--R +--R 1 +--R (328) - ----------- +--R 3 +--R cos(x) - 1 +--R Type: Expression Integer +--R +--E 376 + +--S 377 of 504 +--Rr0173:= 2/3*atan((1-(-1)^(1/3))*tan(1/2*x)/(1-(-1)^(2/3))^(1/2))/(1-(-1)^(2/3))^(1/2)+2/3*atan((1+(-1)^(2/3))*tan(1/2*x)/(1+(-1)^(1/3))^(1/2))/(1+(-1)^(1/3))^(1/2)-sin(x)/(3-3*cos(x)) +--R +--R +--R (329) +--R 3+---+ x +--R +----------+ (\|- 1 - 1)tan(-) +--R |3+---+ 2 +--R (- 2cos(x) + 2)\|\|- 1 + 1 atan(------------------) +--R +-------------+ +--R | 3+---+2 +--R \|- \|- 1 + 1 +--R + +--R 3+---+2 x +--R +-------------+ (\|- 1 + 1)tan(-) +--R | 3+---+2 2 +--R (2cos(x) - 2)\|- \|- 1 + 1 atan(-------------------) +--R +----------+ +--R |3+---+ +--R \|\|- 1 + 1 +--R + +--R +-------------+ +----------+ +--R | 3+---+2 |3+---+ +--R sin(x)\|- \|- 1 + 1 \|\|- 1 + 1 +--R / +--R +-------------+ +----------+ +--R | 3+---+2 |3+---+ +--R (3cos(x) - 3)\|- \|- 1 + 1 \|\|- 1 + 1 +--R Type: Expression Integer +--R +--E 377 + +--S 378 of 504 +--Ra0173:= integrate(t0173,x) +--R +--R +--R (330) +--R %pi x 4 %pi x 2 %pi x 2 +--R - cos(---)sin(-) + (- 2cos(---)cos(-) - 2cos(---))sin(-) +--R 12 2 12 2 12 2 +--R + +--R %pi x 4 %pi x 2 %pi +--R - cos(---)cos(-) + 2cos(---)cos(-) - cos(---) +--R 12 2 12 2 12 +--R * +--R log +--R %pi 2 4+-+ %pi %pi 2 +-+4+-+ %pi +--R 3sin(---) + 3\|3 sin(---) + 3cos(---) + \|3 \|3 cos(---) +--R 12 12 12 12 +--R + +--R 4+-+2 +--R \|3 +--R * +--R x 4 +--R sin(-) +--R 2 +--R + +--R x 2 %pi 2 4+-+ x 2 %pi +--R (6cos(-) - 6)sin(---) + 6\|3 cos(-) sin(---) +--R 2 12 2 12 +--R + +--R %pi 2 +-+4+-+ %pi 4+-+2 x 2 +--R (6cos(---) + 2\|3 \|3 cos(---) + 2\|3 )cos(-) +--R 12 12 2 +--R + +--R %pi 2 4+-+2 +--R - 6cos(---) + 2\|3 +--R 12 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R +-+4+-+ x %pi 4+-+ %pi x x +--R (4\|3 \|3 cos(-)sin(---) - 12\|3 cos(---)cos(-))sin(-) +--R 2 12 12 2 2 +--R + +--R x 4 x 2 %pi 2 +--R (3cos(-) + 6cos(-) + 3)sin(---) +--R 2 2 12 +--R + +--R 4+-+ x 4 4+-+ %pi +--R (3\|3 cos(-) - 3\|3 )sin(---) +--R 2 12 +--R + +--R %pi 2 +-+4+-+ %pi 4+-+2 x 4 +--R (3cos(---) + \|3 \|3 cos(---) + \|3 )cos(-) +--R 12 12 2 +--R + +--R %pi 2 4+-+2 x 2 %pi 2 +-+4+-+ %pi +--R (6cos(---) - 2\|3 )cos(-) + 3cos(---) - \|3 \|3 cos(---) +--R 12 2 12 12 +--R + +--R 4+-+2 +--R \|3 +--R / +--R x 4 x 2 x 2 x 4 x 2 +--R sin(-) + (2cos(-) - 2)sin(-) + cos(-) + 2cos(-) + 1 +--R 2 2 2 2 2 +--R + +--R %pi x 4 %pi x 2 %pi x 2 +--R cos(---)sin(-) + (2cos(---)cos(-) + 2cos(---))sin(-) +--R 12 2 12 2 12 2 +--R + +--R %pi x 4 %pi x 2 %pi +--R cos(---)cos(-) - 2cos(---)cos(-) + cos(---) +--R 12 2 12 2 12 +--R * +--R log +--R %pi 2 4+-+ %pi %pi 2 +-+4+-+ %pi +--R 3sin(---) + 3\|3 sin(---) + 3cos(---) + \|3 \|3 cos(---) +--R 12 12 12 12 +--R + +--R 4+-+2 +--R \|3 +--R * +--R x 4 +--R sin(-) +--R 2 +--R + +--R x 2 %pi 2 4+-+ x 2 %pi +--R (6cos(-) - 6)sin(---) + 6\|3 cos(-) sin(---) +--R 2 12 2 12 +--R + +--R %pi 2 +-+4+-+ %pi 4+-+2 x 2 +--R (6cos(---) + 2\|3 \|3 cos(---) + 2\|3 )cos(-) +--R 12 12 2 +--R + +--R %pi 2 4+-+2 +--R - 6cos(---) + 2\|3 +--R 12 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R +-+4+-+ x %pi 4+-+ %pi x x +--R (- 4\|3 \|3 cos(-)sin(---) + 12\|3 cos(---)cos(-))sin(-) +--R 2 12 12 2 2 +--R + +--R x 4 x 2 %pi 2 +--R (3cos(-) + 6cos(-) + 3)sin(---) +--R 2 2 12 +--R + +--R 4+-+ x 4 4+-+ %pi +--R (3\|3 cos(-) - 3\|3 )sin(---) +--R 2 12 +--R + +--R %pi 2 +-+4+-+ %pi 4+-+2 x 4 +--R (3cos(---) + \|3 \|3 cos(---) + \|3 )cos(-) +--R 12 12 2 +--R + +--R %pi 2 4+-+2 x 2 %pi 2 +-+4+-+ %pi +--R (6cos(---) - 2\|3 )cos(-) + 3cos(---) - \|3 \|3 cos(---) +--R 12 2 12 12 +--R + +--R 4+-+2 +--R \|3 +--R / +--R x 4 x 2 x 2 x 4 x 2 +--R sin(-) + (2cos(-) - 2)sin(-) + cos(-) + 2cos(-) + 1 +--R 2 2 2 2 2 +--R + +--R %pi x 4 %pi x 2 %pi x 2 +--R - cos(---)sin(-) + (- 2cos(---)cos(-) - 2cos(---))sin(-) +--R 12 2 12 2 12 2 +--R + +--R %pi x 4 %pi x 2 %pi +--R - cos(---)cos(-) + 2cos(---)cos(-) - cos(---) +--R 12 2 12 2 12 +--R * +--R log +--R %pi 2 4+-+ %pi %pi 2 +-+4+-+ %pi +--R 3sin(---) - 3\|3 sin(---) + 3cos(---) - \|3 \|3 cos(---) +--R 12 12 12 12 +--R + +--R 4+-+2 +--R \|3 +--R * +--R x 4 +--R sin(-) +--R 2 +--R + +--R x 2 %pi 2 4+-+ x 2 %pi +--R (6cos(-) - 6)sin(---) - 6\|3 cos(-) sin(---) +--R 2 12 2 12 +--R + +--R %pi 2 +-+4+-+ %pi 4+-+2 x 2 +--R (6cos(---) - 2\|3 \|3 cos(---) + 2\|3 )cos(-) +--R 12 12 2 +--R + +--R %pi 2 4+-+2 +--R - 6cos(---) + 2\|3 +--R 12 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R +-+4+-+ x %pi 4+-+ %pi x x +--R (4\|3 \|3 cos(-)sin(---) - 12\|3 cos(---)cos(-))sin(-) +--R 2 12 12 2 2 +--R + +--R x 4 x 2 %pi 2 +--R (3cos(-) + 6cos(-) + 3)sin(---) +--R 2 2 12 +--R + +--R 4+-+ x 4 4+-+ %pi +--R (- 3\|3 cos(-) + 3\|3 )sin(---) +--R 2 12 +--R + +--R %pi 2 +-+4+-+ %pi 4+-+2 x 4 +--R (3cos(---) - \|3 \|3 cos(---) + \|3 )cos(-) +--R 12 12 2 +--R + +--R %pi 2 4+-+2 x 2 %pi 2 +-+4+-+ %pi +--R (6cos(---) - 2\|3 )cos(-) + 3cos(---) + \|3 \|3 cos(---) +--R 12 2 12 12 +--R + +--R 4+-+2 +--R \|3 +--R / +--R x 4 x 2 x 2 x 4 x 2 +--R sin(-) + (2cos(-) - 2)sin(-) + cos(-) + 2cos(-) + 1 +--R 2 2 2 2 2 +--R + +--R %pi x 4 %pi x 2 %pi x 2 +--R cos(---)sin(-) + (2cos(---)cos(-) + 2cos(---))sin(-) +--R 12 2 12 2 12 2 +--R + +--R %pi x 4 %pi x 2 %pi +--R cos(---)cos(-) - 2cos(---)cos(-) + cos(---) +--R 12 2 12 2 12 +--R * +--R log +--R %pi 2 4+-+ %pi %pi 2 +-+4+-+ %pi +--R 3sin(---) - 3\|3 sin(---) + 3cos(---) - \|3 \|3 cos(---) +--R 12 12 12 12 +--R + +--R 4+-+2 +--R \|3 +--R * +--R x 4 +--R sin(-) +--R 2 +--R + +--R x 2 %pi 2 4+-+ x 2 %pi +--R (6cos(-) - 6)sin(---) - 6\|3 cos(-) sin(---) +--R 2 12 2 12 +--R + +--R %pi 2 +-+4+-+ %pi 4+-+2 x 2 +--R (6cos(---) - 2\|3 \|3 cos(---) + 2\|3 )cos(-) +--R 12 12 2 +--R + +--R %pi 2 4+-+2 +--R - 6cos(---) + 2\|3 +--R 12 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R +-+4+-+ x %pi 4+-+ %pi x x +--R (- 4\|3 \|3 cos(-)sin(---) + 12\|3 cos(---)cos(-))sin(-) +--R 2 12 12 2 2 +--R + +--R x 4 x 2 %pi 2 +--R (3cos(-) + 6cos(-) + 3)sin(---) +--R 2 2 12 +--R + +--R 4+-+ x 4 4+-+ %pi +--R (- 3\|3 cos(-) + 3\|3 )sin(---) +--R 2 12 +--R + +--R %pi 2 +-+4+-+ %pi 4+-+2 x 4 +--R (3cos(---) - \|3 \|3 cos(---) + \|3 )cos(-) +--R 12 12 2 +--R + +--R %pi 2 4+-+2 x 2 %pi 2 +-+4+-+ %pi +--R (6cos(---) - 2\|3 )cos(-) + 3cos(---) + \|3 \|3 cos(---) +--R 12 2 12 12 +--R + +--R 4+-+2 +--R \|3 +--R / +--R x 4 x 2 x 2 x 4 x 2 +--R sin(-) + (2cos(-) - 2)sin(-) + cos(-) + 2cos(-) + 1 +--R 2 2 2 2 2 +--R + +--R %pi x 4 x 2 %pi x 2 +--R 2sin(---)sin(-) + (4cos(-) + 4)sin(---)sin(-) +--R 12 2 2 12 2 +--R + +--R x 4 x 2 %pi +--R (2cos(-) - 4cos(-) + 2)sin(---) +--R 2 2 12 +--R * +--R atan +--R %pi +-+ %pi 4+-+ x 4 +--R (3sin(---) + \|3 cos(---) + 2\|3 )sin(-) +--R 12 12 2 +--R + +--R x 2 %pi +-+ %pi 4+-+ x 2 +--R (6cos(-) - 6)sin(---) + (2\|3 cos(---) + 4\|3 )cos(-) +--R 2 12 12 2 +--R + +--R +-+ %pi +--R - 2\|3 cos(---) +--R 12 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R x 4 x 2 %pi +--R (3cos(-) + 6cos(-) + 3)sin(---) +--R 2 2 12 +--R + +--R +-+ %pi 4+-+ x 4 +-+ %pi x 2 +--R (\|3 cos(---) + 2\|3 )cos(-) + 2\|3 cos(---)cos(-) +--R 12 2 12 2 +--R + +--R +-+ %pi 4+-+ +--R \|3 cos(---) - 2\|3 +--R 12 +--R / +--R +-+ %pi %pi x 4 +--R (\|3 sin(---) - 3cos(---))sin(-) +--R 12 12 2 +--R + +--R +-+ x 2 +-+ %pi %pi x 2 +--R (2\|3 cos(-) - 2\|3 )sin(---) - 6cos(---)cos(-) +--R 2 12 12 2 +--R + +--R %pi +--R 6cos(---) +--R 12 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R 4+-+ x x +--R - 8\|3 cos(-)sin(-) +--R 2 2 +--R + +--R +-+ x 4 +-+ x 2 +-+ %pi %pi x 4 +--R (\|3 cos(-) + 2\|3 cos(-) + \|3 )sin(---) - 3cos(---)cos(-) +--R 2 2 12 12 2 +--R + +--R %pi x 2 %pi +--R - 6cos(---)cos(-) - 3cos(---) +--R 12 2 12 +--R + +--R %pi x 4 x 2 %pi x 2 +--R - 2sin(---)sin(-) + (- 4cos(-) - 4)sin(---)sin(-) +--R 12 2 2 12 2 +--R + +--R x 4 x 2 %pi +--R (- 2cos(-) + 4cos(-) - 2)sin(---) +--R 2 2 12 +--R * +--R atan +--R %pi +-+ %pi 4+-+ x 4 +--R (3sin(---) + \|3 cos(---) + 2\|3 )sin(-) +--R 12 12 2 +--R + +--R x 2 %pi +-+ %pi 4+-+ x 2 +--R (6cos(-) - 6)sin(---) + (2\|3 cos(---) + 4\|3 )cos(-) +--R 2 12 12 2 +--R + +--R +-+ %pi +--R - 2\|3 cos(---) +--R 12 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R x 4 x 2 %pi +--R (3cos(-) + 6cos(-) + 3)sin(---) +--R 2 2 12 +--R + +--R +-+ %pi 4+-+ x 4 +-+ %pi x 2 +--R (\|3 cos(---) + 2\|3 )cos(-) + 2\|3 cos(---)cos(-) +--R 12 2 12 2 +--R + +--R +-+ %pi 4+-+ +--R \|3 cos(---) - 2\|3 +--R 12 +--R / +--R +-+ %pi %pi x 4 +--R (\|3 sin(---) - 3cos(---))sin(-) +--R 12 12 2 +--R + +--R +-+ x 2 +-+ %pi %pi x 2 +--R (2\|3 cos(-) - 2\|3 )sin(---) - 6cos(---)cos(-) +--R 2 12 12 2 +--R + +--R %pi +--R 6cos(---) +--R 12 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R 4+-+ x x +-+ x 4 +-+ x 2 +-+ %pi +--R 8\|3 cos(-)sin(-) + (\|3 cos(-) + 2\|3 cos(-) + \|3 )sin(---) +--R 2 2 2 2 12 +--R + +--R %pi x 4 %pi x 2 %pi +--R - 3cos(---)cos(-) - 6cos(---)cos(-) - 3cos(---) +--R 12 2 12 2 12 +--R + +--R %pi x 4 x 2 %pi x 2 +--R 2sin(---)sin(-) + (4cos(-) + 4)sin(---)sin(-) +--R 12 2 2 12 2 +--R + +--R x 4 x 2 %pi +--R (2cos(-) - 4cos(-) + 2)sin(---) +--R 2 2 12 +--R * +--R atan +--R %pi +-+ %pi 4+-+ x 4 +--R (3sin(---) + \|3 cos(---) - 2\|3 )sin(-) +--R 12 12 2 +--R + +--R x 2 %pi +-+ %pi 4+-+ x 2 +--R (6cos(-) - 6)sin(---) + (2\|3 cos(---) - 4\|3 )cos(-) +--R 2 12 12 2 +--R + +--R +-+ %pi +--R - 2\|3 cos(---) +--R 12 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R x 4 x 2 %pi +--R (3cos(-) + 6cos(-) + 3)sin(---) +--R 2 2 12 +--R + +--R +-+ %pi 4+-+ x 4 +-+ %pi x 2 +--R (\|3 cos(---) - 2\|3 )cos(-) + 2\|3 cos(---)cos(-) +--R 12 2 12 2 +--R + +--R +-+ %pi 4+-+ +--R \|3 cos(---) + 2\|3 +--R 12 +--R / +--R +-+ %pi %pi x 4 +--R (\|3 sin(---) - 3cos(---))sin(-) +--R 12 12 2 +--R + +--R +-+ x 2 +-+ %pi %pi x 2 +--R (2\|3 cos(-) - 2\|3 )sin(---) - 6cos(---)cos(-) +--R 2 12 12 2 +--R + +--R %pi +--R 6cos(---) +--R 12 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R 4+-+ x x +--R - 8\|3 cos(-)sin(-) +--R 2 2 +--R + +--R +-+ x 4 +-+ x 2 +-+ %pi %pi x 4 +--R (\|3 cos(-) + 2\|3 cos(-) + \|3 )sin(---) - 3cos(---)cos(-) +--R 2 2 12 12 2 +--R + +--R %pi x 2 %pi +--R - 6cos(---)cos(-) - 3cos(---) +--R 12 2 12 +--R + +--R %pi x 4 x 2 %pi x 2 +--R - 2sin(---)sin(-) + (- 4cos(-) - 4)sin(---)sin(-) +--R 12 2 2 12 2 +--R + +--R x 4 x 2 %pi +--R (- 2cos(-) + 4cos(-) - 2)sin(---) +--R 2 2 12 +--R * +--R atan +--R %pi +-+ %pi 4+-+ x 4 +--R (3sin(---) + \|3 cos(---) - 2\|3 )sin(-) +--R 12 12 2 +--R + +--R x 2 %pi +-+ %pi 4+-+ x 2 +--R (6cos(-) - 6)sin(---) + (2\|3 cos(---) - 4\|3 )cos(-) +--R 2 12 12 2 +--R + +--R +-+ %pi +--R - 2\|3 cos(---) +--R 12 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R x 4 x 2 %pi +--R (3cos(-) + 6cos(-) + 3)sin(---) +--R 2 2 12 +--R + +--R +-+ %pi 4+-+ x 4 +-+ %pi x 2 +--R (\|3 cos(---) - 2\|3 )cos(-) + 2\|3 cos(---)cos(-) +--R 12 2 12 2 +--R + +--R +-+ %pi 4+-+ +--R \|3 cos(---) + 2\|3 +--R 12 +--R / +--R +-+ %pi %pi x 4 +--R (\|3 sin(---) - 3cos(---))sin(-) +--R 12 12 2 +--R + +--R +-+ x 2 +-+ %pi %pi x 2 +--R (2\|3 cos(-) - 2\|3 )sin(---) - 6cos(---)cos(-) +--R 2 12 12 2 +--R + +--R %pi +--R 6cos(---) +--R 12 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R 4+-+ x x +-+ x 4 +-+ x 2 +-+ %pi +--R 8\|3 cos(-)sin(-) + (\|3 cos(-) + 2\|3 cos(-) + \|3 )sin(---) +--R 2 2 2 2 12 +--R + +--R %pi x 4 %pi x 2 %pi +--R - 3cos(---)cos(-) - 6cos(---)cos(-) - 3cos(---) +--R 12 2 12 2 12 +--R + +--R 4+-+ x x +--R - 8\|3 cos(-)sin(-) +--R 2 2 +--R / +--R 4+-+ x 4 4+-+ x 2 4+-+ x 2 4+-+ x 4 +--R 6\|3 sin(-) + (12\|3 cos(-) + 12\|3 )sin(-) + 6\|3 cos(-) +--R 2 2 2 2 +--R + +--R 4+-+ x 2 4+-+ +--R - 12\|3 cos(-) + 6\|3 +--R 2 +--R Type: Union(Expression Integer,...) +--R +--R +--R +--E 378 + +--S 379 of 504 +--Rt0174:= 1/(1-cos(x)^6) +--R +--R +--R 1 +--R (331) - ----------- +--R 6 +--R cos(x) - 1 +--R Type: Expression Integer +--R +--E 379 + +--S 380 of 504 +--Rr0174:= 1/3*atan(tan(x)/(1+(-1)^(1/3))^(1/2))/(1+(-1)^(1/3))^(1/2)+1/3*atan(tan(x)/(1-(-1)^(2/3))^(1/2))/(1-(-1)^(2/3))^(1/2)-1/3*cot(x) +--R +--R +--R (332) +--R +----------+ +-------------+ +--R |3+---+ tan(x) | 3+---+2 tan(x) +--R \|\|- 1 + 1 atan(----------------) + \|- \|- 1 + 1 atan(-------------) +--R +-------------+ +----------+ +--R | 3+---+2 |3+---+ +--R \|- \|- 1 + 1 \|\|- 1 + 1 +--R + +--R +-------------+ +----------+ +--R | 3+---+2 |3+---+ +--R - cot(x)\|- \|- 1 + 1 \|\|- 1 + 1 +--R / +--R +-------------+ +----------+ +--R | 3+---+2 |3+---+ +--R 3\|- \|- 1 + 1 \|\|- 1 + 1 +--R Type: Expression Integer +--R +--E 380 + +--S 381 of 504 +--Ra0174:= integrate(t0174,x) +--R +--R +--R (333) +--R %pi x 8 %pi x 2 x 6 +--R cos(---)sin(-) + 4cos(---)cos(-) sin(-) +--R 12 2 12 2 2 +--R + +--R %pi x 4 %pi x 4 +--R (6cos(---)cos(-) - 2cos(---))sin(-) +--R 12 2 12 2 +--R + +--R %pi x 6 %pi x 2 x 2 %pi x 8 +--R (4cos(---)cos(-) + 12cos(---)cos(-) )sin(-) + cos(---)cos(-) +--R 12 2 12 2 2 12 2 +--R + +--R %pi x 4 %pi +--R - 2cos(---)cos(-) + cos(---) +--R 12 2 12 +--R * +--R log +--R %pi 2 4+-+ %pi %pi 2 4+-+2 x 8 +--R (sin(---) + 2\|3 sin(---) + cos(---) + \|3 )sin(-) +--R 12 12 12 2 +--R + +--R x 2 %pi 2 4+-+ x 2 %pi +--R 4cos(-) sin(---) + 8\|3 cos(-) sin(---) +--R 2 12 2 12 +--R + +--R %pi 2 4+-+2 x 2 +--R (4cos(---) + 4\|3 )cos(-) +--R 12 2 +--R * +--R x 6 +--R sin(-) +--R 2 +--R + +--R x 4 %pi 2 4+-+ x 4 %pi +--R (6cos(-) - 2)sin(---) + 12\|3 cos(-) sin(---) +--R 2 12 2 12 +--R + +--R %pi 2 4+-+2 x 4 %pi 2 4+-+2 +--R (6cos(---) + 6\|3 )cos(-) - 2cos(---) + 2\|3 +--R 12 2 12 +--R * +--R x 4 +--R sin(-) +--R 2 +--R + +--R 4+-+ %pi x x 3 +--R 16\|3 cos(---)cos(-)sin(-) +--R 12 2 2 +--R + +--R x 6 x 2 %pi 2 4+-+ x 6 %pi +--R (4cos(-) + 12cos(-) )sin(---) + 8\|3 cos(-) sin(---) +--R 2 2 12 2 12 +--R + +--R %pi 2 4+-+2 x 6 %pi 2 4+-+2 x 2 +--R (4cos(---) + 4\|3 )cos(-) + (12cos(---) - 12\|3 )cos(-) +--R 12 2 12 2 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R 4+-+ %pi x 3 x +--R - 16\|3 cos(---)cos(-) sin(-) +--R 12 2 2 +--R + +--R x 8 x 4 %pi 2 +--R (cos(-) - 2cos(-) + 1)sin(---) +--R 2 2 12 +--R + +--R 4+-+ x 8 4+-+ %pi %pi 2 4+-+2 x 8 +--R (2\|3 cos(-) - 2\|3 )sin(---) + (cos(---) + \|3 )cos(-) +--R 2 12 12 2 +--R + +--R %pi 2 4+-+2 x 4 %pi 2 4+-+2 +--R (- 2cos(---) + 2\|3 )cos(-) + cos(---) + \|3 +--R 12 2 12 +--R / +--R x 8 x 2 x 6 +--R sin(-) + (4cos(-) - 4)sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 x 4 +--R (6cos(-) - 4cos(-) + 6)sin(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 x 2 x 8 x 6 +--R (4cos(-) + 4cos(-) - 4cos(-) - 4)sin(-) + cos(-) + 4cos(-) +--R 2 2 2 2 2 2 +--R + +--R x 4 x 2 +--R 6cos(-) + 4cos(-) + 1 +--R 2 2 +--R + +--R %pi x 8 %pi x 2 x 6 +--R - cos(---)sin(-) - 4cos(---)cos(-) sin(-) +--R 12 2 12 2 2 +--R + +--R %pi x 4 %pi x 4 +--R (- 6cos(---)cos(-) + 2cos(---))sin(-) +--R 12 2 12 2 +--R + +--R %pi x 6 %pi x 2 x 2 %pi x 8 +--R (- 4cos(---)cos(-) - 12cos(---)cos(-) )sin(-) - cos(---)cos(-) +--R 12 2 12 2 2 12 2 +--R + +--R %pi x 4 %pi +--R 2cos(---)cos(-) - cos(---) +--R 12 2 12 +--R * +--R log +--R %pi 2 4+-+ %pi %pi 2 4+-+2 x 8 +--R (sin(---) + 2\|3 sin(---) + cos(---) + \|3 )sin(-) +--R 12 12 12 2 +--R + +--R x 2 %pi 2 4+-+ x 2 %pi +--R 4cos(-) sin(---) + 8\|3 cos(-) sin(---) +--R 2 12 2 12 +--R + +--R %pi 2 4+-+2 x 2 +--R (4cos(---) + 4\|3 )cos(-) +--R 12 2 +--R * +--R x 6 +--R sin(-) +--R 2 +--R + +--R x 4 %pi 2 4+-+ x 4 %pi +--R (6cos(-) - 2)sin(---) + 12\|3 cos(-) sin(---) +--R 2 12 2 12 +--R + +--R %pi 2 4+-+2 x 4 %pi 2 4+-+2 +--R (6cos(---) + 6\|3 )cos(-) - 2cos(---) + 2\|3 +--R 12 2 12 +--R * +--R x 4 +--R sin(-) +--R 2 +--R + +--R 4+-+ %pi x x 3 +--R - 16\|3 cos(---)cos(-)sin(-) +--R 12 2 2 +--R + +--R x 6 x 2 %pi 2 4+-+ x 6 %pi +--R (4cos(-) + 12cos(-) )sin(---) + 8\|3 cos(-) sin(---) +--R 2 2 12 2 12 +--R + +--R %pi 2 4+-+2 x 6 %pi 2 4+-+2 x 2 +--R (4cos(---) + 4\|3 )cos(-) + (12cos(---) - 12\|3 )cos(-) +--R 12 2 12 2 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R 4+-+ %pi x 3 x x 8 x 4 %pi 2 +--R 16\|3 cos(---)cos(-) sin(-) + (cos(-) - 2cos(-) + 1)sin(---) +--R 12 2 2 2 2 12 +--R + +--R 4+-+ x 8 4+-+ %pi %pi 2 4+-+2 x 8 +--R (2\|3 cos(-) - 2\|3 )sin(---) + (cos(---) + \|3 )cos(-) +--R 2 12 12 2 +--R + +--R %pi 2 4+-+2 x 4 %pi 2 4+-+2 +--R (- 2cos(---) + 2\|3 )cos(-) + cos(---) + \|3 +--R 12 2 12 +--R / +--R x 8 x 2 x 6 +--R sin(-) + (4cos(-) - 4)sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 x 4 +--R (6cos(-) - 4cos(-) + 6)sin(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 x 2 x 8 x 6 +--R (4cos(-) + 4cos(-) - 4cos(-) - 4)sin(-) + cos(-) + 4cos(-) +--R 2 2 2 2 2 2 +--R + +--R x 4 x 2 +--R 6cos(-) + 4cos(-) + 1 +--R 2 2 +--R + +--R %pi x 8 %pi x 2 x 6 +--R cos(---)sin(-) + 4cos(---)cos(-) sin(-) +--R 12 2 12 2 2 +--R + +--R %pi x 4 %pi x 4 +--R (6cos(---)cos(-) - 2cos(---))sin(-) +--R 12 2 12 2 +--R + +--R %pi x 6 %pi x 2 x 2 %pi x 8 +--R (4cos(---)cos(-) + 12cos(---)cos(-) )sin(-) + cos(---)cos(-) +--R 12 2 12 2 2 12 2 +--R + +--R %pi x 4 %pi +--R - 2cos(---)cos(-) + cos(---) +--R 12 2 12 +--R * +--R log +--R %pi 2 4+-+ %pi %pi 2 4+-+2 x 8 +--R (sin(---) - 2\|3 sin(---) + cos(---) + \|3 )sin(-) +--R 12 12 12 2 +--R + +--R x 2 %pi 2 4+-+ x 2 %pi +--R 4cos(-) sin(---) - 8\|3 cos(-) sin(---) +--R 2 12 2 12 +--R + +--R %pi 2 4+-+2 x 2 +--R (4cos(---) + 4\|3 )cos(-) +--R 12 2 +--R * +--R x 6 +--R sin(-) +--R 2 +--R + +--R x 4 %pi 2 4+-+ x 4 %pi +--R (6cos(-) - 2)sin(---) - 12\|3 cos(-) sin(---) +--R 2 12 2 12 +--R + +--R %pi 2 4+-+2 x 4 %pi 2 4+-+2 +--R (6cos(---) + 6\|3 )cos(-) - 2cos(---) + 2\|3 +--R 12 2 12 +--R * +--R x 4 +--R sin(-) +--R 2 +--R + +--R 4+-+ %pi x x 3 +--R 16\|3 cos(---)cos(-)sin(-) +--R 12 2 2 +--R + +--R x 6 x 2 %pi 2 4+-+ x 6 %pi +--R (4cos(-) + 12cos(-) )sin(---) - 8\|3 cos(-) sin(---) +--R 2 2 12 2 12 +--R + +--R %pi 2 4+-+2 x 6 %pi 2 4+-+2 x 2 +--R (4cos(---) + 4\|3 )cos(-) + (12cos(---) - 12\|3 )cos(-) +--R 12 2 12 2 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R 4+-+ %pi x 3 x +--R - 16\|3 cos(---)cos(-) sin(-) +--R 12 2 2 +--R + +--R x 8 x 4 %pi 2 +--R (cos(-) - 2cos(-) + 1)sin(---) +--R 2 2 12 +--R + +--R 4+-+ x 8 4+-+ %pi %pi 2 4+-+2 x 8 +--R (- 2\|3 cos(-) + 2\|3 )sin(---) + (cos(---) + \|3 )cos(-) +--R 2 12 12 2 +--R + +--R %pi 2 4+-+2 x 4 %pi 2 4+-+2 +--R (- 2cos(---) + 2\|3 )cos(-) + cos(---) + \|3 +--R 12 2 12 +--R / +--R x 8 x 2 x 6 +--R sin(-) + (4cos(-) - 4)sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 x 4 +--R (6cos(-) - 4cos(-) + 6)sin(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 x 2 x 8 x 6 +--R (4cos(-) + 4cos(-) - 4cos(-) - 4)sin(-) + cos(-) + 4cos(-) +--R 2 2 2 2 2 2 +--R + +--R x 4 x 2 +--R 6cos(-) + 4cos(-) + 1 +--R 2 2 +--R + +--R %pi x 8 %pi x 2 x 6 +--R - cos(---)sin(-) - 4cos(---)cos(-) sin(-) +--R 12 2 12 2 2 +--R + +--R %pi x 4 %pi x 4 +--R (- 6cos(---)cos(-) + 2cos(---))sin(-) +--R 12 2 12 2 +--R + +--R %pi x 6 %pi x 2 x 2 %pi x 8 +--R (- 4cos(---)cos(-) - 12cos(---)cos(-) )sin(-) - cos(---)cos(-) +--R 12 2 12 2 2 12 2 +--R + +--R %pi x 4 %pi +--R 2cos(---)cos(-) - cos(---) +--R 12 2 12 +--R * +--R log +--R %pi 2 4+-+ %pi %pi 2 4+-+2 x 8 +--R (sin(---) - 2\|3 sin(---) + cos(---) + \|3 )sin(-) +--R 12 12 12 2 +--R + +--R x 2 %pi 2 4+-+ x 2 %pi +--R 4cos(-) sin(---) - 8\|3 cos(-) sin(---) +--R 2 12 2 12 +--R + +--R %pi 2 4+-+2 x 2 +--R (4cos(---) + 4\|3 )cos(-) +--R 12 2 +--R * +--R x 6 +--R sin(-) +--R 2 +--R + +--R x 4 %pi 2 4+-+ x 4 %pi +--R (6cos(-) - 2)sin(---) - 12\|3 cos(-) sin(---) +--R 2 12 2 12 +--R + +--R %pi 2 4+-+2 x 4 %pi 2 4+-+2 +--R (6cos(---) + 6\|3 )cos(-) - 2cos(---) + 2\|3 +--R 12 2 12 +--R * +--R x 4 +--R sin(-) +--R 2 +--R + +--R 4+-+ %pi x x 3 +--R - 16\|3 cos(---)cos(-)sin(-) +--R 12 2 2 +--R + +--R x 6 x 2 %pi 2 4+-+ x 6 %pi +--R (4cos(-) + 12cos(-) )sin(---) - 8\|3 cos(-) sin(---) +--R 2 2 12 2 12 +--R + +--R %pi 2 4+-+2 x 6 %pi 2 4+-+2 x 2 +--R (4cos(---) + 4\|3 )cos(-) + (12cos(---) - 12\|3 )cos(-) +--R 12 2 12 2 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R 4+-+ %pi x 3 x x 8 x 4 %pi 2 +--R 16\|3 cos(---)cos(-) sin(-) + (cos(-) - 2cos(-) + 1)sin(---) +--R 12 2 2 2 2 12 +--R + +--R 4+-+ x 8 4+-+ %pi %pi 2 4+-+2 x 8 +--R (- 2\|3 cos(-) + 2\|3 )sin(---) + (cos(---) + \|3 )cos(-) +--R 2 12 12 2 +--R + +--R %pi 2 4+-+2 x 4 %pi 2 4+-+2 +--R (- 2cos(---) + 2\|3 )cos(-) + cos(---) + \|3 +--R 12 2 12 +--R / +--R x 8 x 2 x 6 +--R sin(-) + (4cos(-) - 4)sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 x 4 +--R (6cos(-) - 4cos(-) + 6)sin(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 x 2 x 8 x 6 +--R (4cos(-) + 4cos(-) - 4cos(-) - 4)sin(-) + cos(-) + 4cos(-) +--R 2 2 2 2 2 2 +--R + +--R x 4 x 2 +--R 6cos(-) + 4cos(-) + 1 +--R 2 2 +--R + +--R %pi x 8 x 2 %pi x 6 +--R - 2sin(---)sin(-) - 8cos(-) sin(---)sin(-) +--R 12 2 2 12 2 +--R + +--R x 4 %pi x 4 +--R (- 12cos(-) + 4)sin(---)sin(-) +--R 2 12 2 +--R + +--R x 6 x 2 %pi x 2 +--R (- 8cos(-) - 24cos(-) )sin(---)sin(-) +--R 2 2 12 2 +--R + +--R x 8 x 4 %pi +--R (- 2cos(-) + 4cos(-) - 2)sin(---) +--R 2 2 12 +--R * +--R atan +--R %pi x 8 %pi x 2 %pi x 6 +--R cos(---)sin(-) + (4cos(---)cos(-) - 2cos(---))sin(-) +--R 12 2 12 2 12 2 +--R + +--R x %pi 4+-+ x x 5 +--R (4cos(-)sin(---) - 4\|3 cos(-))sin(-) +--R 2 12 2 2 +--R + +--R %pi x 4 %pi x 2 x 4 +--R (6cos(---)cos(-) - 2cos(---)cos(-) )sin(-) +--R 12 2 12 2 2 +--R + +--R x 3 x %pi 4+-+ x 3 x 3 +--R ((8cos(-) - 8cos(-))sin(---) - 8\|3 cos(-) )sin(-) +--R 2 2 12 2 2 +--R + +--R %pi x 6 %pi x 4 %pi x 2 +--R (4cos(---)cos(-) + 2cos(---)cos(-) + 2cos(---))sin(-) +--R 12 2 12 2 12 2 +--R + +--R x 5 x 3 x %pi 4+-+ x 5 +--R (4cos(-) + 8cos(-) + 4cos(-))sin(---) - 4\|3 cos(-) +--R 2 2 2 12 2 +--R + +--R 4+-+ x +--R 4\|3 cos(-) +--R 2 +--R * +--R x +--R sin(-) +--R 2 +--R + +--R %pi x 8 %pi x 6 %pi x 2 %pi +--R cos(---)cos(-) + 2cos(---)cos(-) - 2cos(---)cos(-) - cos(---) +--R 12 2 12 2 12 2 12 +--R / +--R %pi 4+-+ x 8 +--R (sin(---) - \|3 )sin(-) +--R 12 2 +--R + +--R x 2 %pi 4+-+ x 2 4+-+ x 6 +--R ((4cos(-) - 2)sin(---) - 4\|3 cos(-) + 2\|3 )sin(-) +--R 2 12 2 2 +--R + +--R %pi x x 5 +--R - 4cos(---)cos(-)sin(-) +--R 12 2 2 +--R + +--R x 4 x 2 %pi 4+-+ x 4 4+-+ x 2 +--R (6cos(-) - 2cos(-) )sin(---) - 6\|3 cos(-) + 2\|3 cos(-) +--R 2 2 12 2 2 +--R + +--R 4+-+ +--R - 2\|3 +--R * +--R x 4 +--R sin(-) +--R 2 +--R + +--R %pi x 3 %pi x x 3 +--R (- 8cos(---)cos(-) + 8cos(---)cos(-))sin(-) +--R 12 2 12 2 2 +--R + +--R x 6 x 4 %pi 4+-+ x 6 +--R (4cos(-) + 2cos(-) + 2)sin(---) - 4\|3 cos(-) +--R 2 2 12 2 +--R + +--R 4+-+ x 4 4+-+ x 2 4+-+ +--R - 2\|3 cos(-) + 12\|3 cos(-) + 2\|3 +--R 2 2 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R %pi x 5 %pi x 3 %pi x x +--R (- 4cos(---)cos(-) - 8cos(---)cos(-) - 4cos(---)cos(-))sin(-) +--R 12 2 12 2 12 2 2 +--R + +--R x 8 x 6 x 2 %pi 4+-+ x 8 +--R (cos(-) + 2cos(-) - 2cos(-) - 1)sin(---) - \|3 cos(-) +--R 2 2 2 12 2 +--R + +--R 4+-+ x 6 4+-+ x 4 4+-+ x 2 4+-+ +--R - 2\|3 cos(-) - 2\|3 cos(-) - 2\|3 cos(-) - \|3 +--R 2 2 2 +--R + +--R %pi x 8 x 2 %pi x 6 +--R 2sin(---)sin(-) + 8cos(-) sin(---)sin(-) +--R 12 2 2 12 2 +--R + +--R x 4 %pi x 4 +--R (12cos(-) - 4)sin(---)sin(-) +--R 2 12 2 +--R + +--R x 6 x 2 %pi x 2 +--R (8cos(-) + 24cos(-) )sin(---)sin(-) +--R 2 2 12 2 +--R + +--R x 8 x 4 %pi +--R (2cos(-) - 4cos(-) + 2)sin(---) +--R 2 2 12 +--R * +--R atan +--R %pi x 8 %pi x 2 %pi x 6 +--R cos(---)sin(-) + (4cos(---)cos(-) - 2cos(---))sin(-) +--R 12 2 12 2 12 2 +--R + +--R x %pi 4+-+ x x 5 +--R (- 4cos(-)sin(---) + 4\|3 cos(-))sin(-) +--R 2 12 2 2 +--R + +--R %pi x 4 %pi x 2 x 4 +--R (6cos(---)cos(-) - 2cos(---)cos(-) )sin(-) +--R 12 2 12 2 2 +--R + +--R x 3 x %pi 4+-+ x 3 x 3 +--R ((- 8cos(-) + 8cos(-))sin(---) + 8\|3 cos(-) )sin(-) +--R 2 2 12 2 2 +--R + +--R %pi x 6 %pi x 4 %pi x 2 +--R (4cos(---)cos(-) + 2cos(---)cos(-) + 2cos(---))sin(-) +--R 12 2 12 2 12 2 +--R + +--R x 5 x 3 x %pi 4+-+ x 5 +--R (- 4cos(-) - 8cos(-) - 4cos(-))sin(---) + 4\|3 cos(-) +--R 2 2 2 12 2 +--R + +--R 4+-+ x +--R - 4\|3 cos(-) +--R 2 +--R * +--R x +--R sin(-) +--R 2 +--R + +--R %pi x 8 %pi x 6 %pi x 2 %pi +--R cos(---)cos(-) + 2cos(---)cos(-) - 2cos(---)cos(-) - cos(---) +--R 12 2 12 2 12 2 12 +--R / +--R %pi 4+-+ x 8 +--R (sin(---) - \|3 )sin(-) +--R 12 2 +--R + +--R x 2 %pi 4+-+ x 2 4+-+ x 6 +--R ((4cos(-) - 2)sin(---) - 4\|3 cos(-) + 2\|3 )sin(-) +--R 2 12 2 2 +--R + +--R %pi x x 5 +--R 4cos(---)cos(-)sin(-) +--R 12 2 2 +--R + +--R x 4 x 2 %pi 4+-+ x 4 4+-+ x 2 +--R (6cos(-) - 2cos(-) )sin(---) - 6\|3 cos(-) + 2\|3 cos(-) +--R 2 2 12 2 2 +--R + +--R 4+-+ +--R - 2\|3 +--R * +--R x 4 +--R sin(-) +--R 2 +--R + +--R %pi x 3 %pi x x 3 +--R (8cos(---)cos(-) - 8cos(---)cos(-))sin(-) +--R 12 2 12 2 2 +--R + +--R x 6 x 4 %pi 4+-+ x 6 +--R (4cos(-) + 2cos(-) + 2)sin(---) - 4\|3 cos(-) +--R 2 2 12 2 +--R + +--R 4+-+ x 4 4+-+ x 2 4+-+ +--R - 2\|3 cos(-) + 12\|3 cos(-) + 2\|3 +--R 2 2 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R %pi x 5 %pi x 3 %pi x x +--R (4cos(---)cos(-) + 8cos(---)cos(-) + 4cos(---)cos(-))sin(-) +--R 12 2 12 2 12 2 2 +--R + +--R x 8 x 6 x 2 %pi 4+-+ x 8 +--R (cos(-) + 2cos(-) - 2cos(-) - 1)sin(---) - \|3 cos(-) +--R 2 2 2 12 2 +--R + +--R 4+-+ x 6 4+-+ x 4 4+-+ x 2 4+-+ +--R - 2\|3 cos(-) - 2\|3 cos(-) - 2\|3 cos(-) - \|3 +--R 2 2 2 +--R + +--R %pi x 8 x 2 %pi x 6 +--R 2sin(---)sin(-) + 8cos(-) sin(---)sin(-) +--R 12 2 2 12 2 +--R + +--R x 4 %pi x 4 +--R (12cos(-) - 4)sin(---)sin(-) +--R 2 12 2 +--R + +--R x 6 x 2 %pi x 2 +--R (8cos(-) + 24cos(-) )sin(---)sin(-) +--R 2 2 12 2 +--R + +--R x 8 x 4 %pi +--R (2cos(-) - 4cos(-) + 2)sin(---) +--R 2 2 12 +--R * +--R atan +--R %pi x 8 %pi x 2 %pi x 6 +--R cos(---)sin(-) + (4cos(---)cos(-) - 2cos(---))sin(-) +--R 12 2 12 2 12 2 +--R + +--R x %pi 4+-+ x x 5 +--R (4cos(-)sin(---) + 4\|3 cos(-))sin(-) +--R 2 12 2 2 +--R + +--R %pi x 4 %pi x 2 x 4 +--R (6cos(---)cos(-) - 2cos(---)cos(-) )sin(-) +--R 12 2 12 2 2 +--R + +--R x 3 x %pi 4+-+ x 3 x 3 +--R ((8cos(-) - 8cos(-))sin(---) + 8\|3 cos(-) )sin(-) +--R 2 2 12 2 2 +--R + +--R %pi x 6 %pi x 4 %pi x 2 +--R (4cos(---)cos(-) + 2cos(---)cos(-) + 2cos(---))sin(-) +--R 12 2 12 2 12 2 +--R + +--R x 5 x 3 x %pi 4+-+ x 5 +--R (4cos(-) + 8cos(-) + 4cos(-))sin(---) + 4\|3 cos(-) +--R 2 2 2 12 2 +--R + +--R 4+-+ x +--R - 4\|3 cos(-) +--R 2 +--R * +--R x +--R sin(-) +--R 2 +--R + +--R %pi x 8 %pi x 6 %pi x 2 %pi +--R cos(---)cos(-) + 2cos(---)cos(-) - 2cos(---)cos(-) - cos(---) +--R 12 2 12 2 12 2 12 +--R / +--R %pi 4+-+ x 8 +--R (sin(---) + \|3 )sin(-) +--R 12 2 +--R + +--R x 2 %pi 4+-+ x 2 4+-+ x 6 +--R ((4cos(-) - 2)sin(---) + 4\|3 cos(-) - 2\|3 )sin(-) +--R 2 12 2 2 +--R + +--R %pi x x 5 +--R - 4cos(---)cos(-)sin(-) +--R 12 2 2 +--R + +--R x 4 x 2 %pi 4+-+ x 4 4+-+ x 2 +--R (6cos(-) - 2cos(-) )sin(---) + 6\|3 cos(-) - 2\|3 cos(-) +--R 2 2 12 2 2 +--R + +--R 4+-+ +--R 2\|3 +--R * +--R x 4 +--R sin(-) +--R 2 +--R + +--R %pi x 3 %pi x x 3 +--R (- 8cos(---)cos(-) + 8cos(---)cos(-))sin(-) +--R 12 2 12 2 2 +--R + +--R x 6 x 4 %pi 4+-+ x 6 +--R (4cos(-) + 2cos(-) + 2)sin(---) + 4\|3 cos(-) +--R 2 2 12 2 +--R + +--R 4+-+ x 4 4+-+ x 2 4+-+ +--R 2\|3 cos(-) - 12\|3 cos(-) - 2\|3 +--R 2 2 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R %pi x 5 %pi x 3 %pi x x +--R (- 4cos(---)cos(-) - 8cos(---)cos(-) - 4cos(---)cos(-))sin(-) +--R 12 2 12 2 12 2 2 +--R + +--R x 8 x 6 x 2 %pi 4+-+ x 8 +--R (cos(-) + 2cos(-) - 2cos(-) - 1)sin(---) + \|3 cos(-) +--R 2 2 2 12 2 +--R + +--R 4+-+ x 6 4+-+ x 4 4+-+ x 2 4+-+ +--R 2\|3 cos(-) + 2\|3 cos(-) + 2\|3 cos(-) + \|3 +--R 2 2 2 +--R + +--R %pi x 8 x 2 %pi x 6 +--R - 2sin(---)sin(-) - 8cos(-) sin(---)sin(-) +--R 12 2 2 12 2 +--R + +--R x 4 %pi x 4 +--R (- 12cos(-) + 4)sin(---)sin(-) +--R 2 12 2 +--R + +--R x 6 x 2 %pi x 2 +--R (- 8cos(-) - 24cos(-) )sin(---)sin(-) +--R 2 2 12 2 +--R + +--R x 8 x 4 %pi +--R (- 2cos(-) + 4cos(-) - 2)sin(---) +--R 2 2 12 +--R * +--R atan +--R %pi x 8 %pi x 2 %pi x 6 +--R cos(---)sin(-) + (4cos(---)cos(-) - 2cos(---))sin(-) +--R 12 2 12 2 12 2 +--R + +--R x %pi 4+-+ x x 5 +--R (- 4cos(-)sin(---) - 4\|3 cos(-))sin(-) +--R 2 12 2 2 +--R + +--R %pi x 4 %pi x 2 x 4 +--R (6cos(---)cos(-) - 2cos(---)cos(-) )sin(-) +--R 12 2 12 2 2 +--R + +--R x 3 x %pi 4+-+ x 3 x 3 +--R ((- 8cos(-) + 8cos(-))sin(---) - 8\|3 cos(-) )sin(-) +--R 2 2 12 2 2 +--R + +--R %pi x 6 %pi x 4 %pi x 2 +--R (4cos(---)cos(-) + 2cos(---)cos(-) + 2cos(---))sin(-) +--R 12 2 12 2 12 2 +--R + +--R x 5 x 3 x %pi 4+-+ x 5 +--R (- 4cos(-) - 8cos(-) - 4cos(-))sin(---) - 4\|3 cos(-) +--R 2 2 2 12 2 +--R + +--R 4+-+ x +--R 4\|3 cos(-) +--R 2 +--R * +--R x +--R sin(-) +--R 2 +--R + +--R %pi x 8 %pi x 6 %pi x 2 %pi +--R cos(---)cos(-) + 2cos(---)cos(-) - 2cos(---)cos(-) - cos(---) +--R 12 2 12 2 12 2 12 +--R / +--R %pi 4+-+ x 8 +--R (sin(---) + \|3 )sin(-) +--R 12 2 +--R + +--R x 2 %pi 4+-+ x 2 4+-+ x 6 +--R ((4cos(-) - 2)sin(---) + 4\|3 cos(-) - 2\|3 )sin(-) +--R 2 12 2 2 +--R + +--R %pi x x 5 +--R 4cos(---)cos(-)sin(-) +--R 12 2 2 +--R + +--R x 4 x 2 %pi 4+-+ x 4 4+-+ x 2 +--R (6cos(-) - 2cos(-) )sin(---) + 6\|3 cos(-) - 2\|3 cos(-) +--R 2 2 12 2 2 +--R + +--R 4+-+ +--R 2\|3 +--R * +--R x 4 +--R sin(-) +--R 2 +--R + +--R %pi x 3 %pi x x 3 +--R (8cos(---)cos(-) - 8cos(---)cos(-))sin(-) +--R 12 2 12 2 2 +--R + +--R x 6 x 4 %pi 4+-+ x 6 +--R (4cos(-) + 2cos(-) + 2)sin(---) + 4\|3 cos(-) +--R 2 2 12 2 +--R + +--R 4+-+ x 4 4+-+ x 2 4+-+ +--R 2\|3 cos(-) - 12\|3 cos(-) - 2\|3 +--R 2 2 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R %pi x 5 %pi x 3 %pi x x +--R (4cos(---)cos(-) + 8cos(---)cos(-) + 4cos(---)cos(-))sin(-) +--R 12 2 12 2 12 2 2 +--R + +--R x 8 x 6 x 2 %pi 4+-+ x 8 +--R (cos(-) + 2cos(-) - 2cos(-) - 1)sin(---) + \|3 cos(-) +--R 2 2 2 12 2 +--R + +--R 4+-+ x 6 4+-+ x 4 4+-+ x 2 4+-+ +--R 2\|3 cos(-) + 2\|3 cos(-) + 2\|3 cos(-) + \|3 +--R 2 2 2 +--R + +--R 4+-+ x x 3 4+-+ x 3 x +--R 32\|3 cos(-)sin(-) - 32\|3 cos(-) sin(-) +--R 2 2 2 2 +--R / +--R 4+-+ x 8 4+-+ x 2 x 6 4+-+ x 4 4+-+ x 4 +--R 12\|3 sin(-) + 48\|3 cos(-) sin(-) + (72\|3 cos(-) - 24\|3 )sin(-) +--R 2 2 2 2 2 +--R + +--R 4+-+ x 6 4+-+ x 2 x 2 4+-+ x 8 4+-+ x 4 +--R (48\|3 cos(-) + 144\|3 cos(-) )sin(-) + 12\|3 cos(-) - 24\|3 cos(-) +--R 2 2 2 2 2 +--R + +--R 4+-+ +--R 12\|3 +--R Type: Union(Expression Integer,...) +--R +--R +--R +--E 381 + +--S 382 of 504 +--Rt0175:= 1/(1-cos(x)^8) +--R +--R +--R 1 +--R (334) - ----------- +--R 8 +--R cos(x) - 1 +--R Type: Expression Integer +--R +--E 382 + +--S 383 of 504 +--Rr0175:= 1/4*atan(tan(x)/(1-%i)^(1/2))/(1-%i)^(1/2)+1/4*atan(tan(x)/(1+%i)^(1/2))/(1+%i)^(1/2)+1/8*atan(1/2*2^(1/2)*tan(x))*2^(1/2)-1/4*cot(x) +--R +--R +--R (335) +--R +-+ +--R +------+ +------+ +-+ \|2 tan(x) +------+ tan(x) +--R \|1 - %i \|1 + %i \|2 atan(----------) + 2\|1 + %i atan(---------) +--R 2 +------+ +--R \|1 - %i +--R + +--R +------+ tan(x) +------+ +------+ +--R 2\|1 - %i atan(---------) - 2\|1 - %i \|1 + %i cot(x) +--R +------+ +--R \|1 + %i +--R / +--R +------+ +------+ +--R 8\|1 - %i \|1 + %i +--R Type: Expression Complex Integer +--R +--E 383 + +--S 384 of 504 +--Ra0175:= integrate(t0175,x) +--R +--R +--R (336) +--R +-+4+-+ %pi x 8 +-+4+-+ %pi x 2 x 6 +--R \|2 \|2 cos(---)sin(-) + 4\|2 \|2 cos(---)cos(-) sin(-) +--R 8 2 8 2 2 +--R + +--R +-+4+-+ %pi x 4 +-+4+-+ %pi x 4 +--R (6\|2 \|2 cos(---)cos(-) - 2\|2 \|2 cos(---))sin(-) +--R 8 2 8 2 +--R + +--R +-+4+-+ %pi x 6 +-+4+-+ %pi x 2 x 2 +--R (4\|2 \|2 cos(---)cos(-) + 12\|2 \|2 cos(---)cos(-) )sin(-) +--R 8 2 8 2 2 +--R + +--R +-+4+-+ %pi x 8 +-+4+-+ %pi x 4 +-+4+-+ %pi +--R \|2 \|2 cos(---)cos(-) - 2\|2 \|2 cos(---)cos(-) + \|2 \|2 cos(---) +--R 8 2 8 2 8 +--R * +--R log +--R x 4 +-+4+-+ %pi x x 3 +--R sin(-) + 2\|2 \|2 cos(---)cos(-)sin(-) +--R 2 8 2 2 +--R + +--R 4+-+2 x 2 %pi 2 4+-+2 %pi 2 x 2 x 2 +--R (2\|2 cos(-) sin(---) + (2\|2 cos(---) - 2)cos(-) )sin(-) +--R 2 8 8 2 2 +--R + +--R +-+4+-+ %pi x 3 x x 4 +--R - 2\|2 \|2 cos(---)cos(-) sin(-) + cos(-) +--R 8 2 2 2 +--R / +--R x 4 x 2 x 2 x 4 x 2 +--R sin(-) + (- 2cos(-) - 2)sin(-) + cos(-) + 2cos(-) + 1 +--R 2 2 2 2 2 +--R + +--R +-+4+-+ %pi x 8 +-+4+-+ %pi x 2 x 6 +--R - \|2 \|2 cos(---)sin(-) - 4\|2 \|2 cos(---)cos(-) sin(-) +--R 8 2 8 2 2 +--R + +--R +-+4+-+ %pi x 4 +-+4+-+ %pi x 4 +--R (- 6\|2 \|2 cos(---)cos(-) + 2\|2 \|2 cos(---))sin(-) +--R 8 2 8 2 +--R + +--R +-+4+-+ %pi x 6 +-+4+-+ %pi x 2 x 2 +--R (- 4\|2 \|2 cos(---)cos(-) - 12\|2 \|2 cos(---)cos(-) )sin(-) +--R 8 2 8 2 2 +--R + +--R +-+4+-+ %pi x 8 +-+4+-+ %pi x 4 +-+4+-+ %pi +--R - \|2 \|2 cos(---)cos(-) + 2\|2 \|2 cos(---)cos(-) - \|2 \|2 cos(---) +--R 8 2 8 2 8 +--R * +--R log +--R x 4 +-+4+-+ %pi x x 3 +--R sin(-) - 2\|2 \|2 cos(---)cos(-)sin(-) +--R 2 8 2 2 +--R + +--R 4+-+2 x 2 %pi 2 4+-+2 %pi 2 x 2 x 2 +--R (2\|2 cos(-) sin(---) + (2\|2 cos(---) - 2)cos(-) )sin(-) +--R 2 8 8 2 2 +--R + +--R +-+4+-+ %pi x 3 x x 4 +--R 2\|2 \|2 cos(---)cos(-) sin(-) + cos(-) +--R 8 2 2 2 +--R / +--R x 4 x 2 x 2 x 4 x 2 +--R sin(-) + (- 2cos(-) - 2)sin(-) + cos(-) + 2cos(-) + 1 +--R 2 2 2 2 2 +--R + +--R +-+4+-+ %pi x 8 +-+4+-+ x 2 %pi x 6 +--R - 2\|2 \|2 sin(---)sin(-) - 8\|2 \|2 cos(-) sin(---)sin(-) +--R 8 2 2 8 2 +--R + +--R +-+4+-+ x 4 +-+4+-+ %pi x 4 +--R (- 12\|2 \|2 cos(-) + 4\|2 \|2 )sin(---)sin(-) +--R 2 8 2 +--R + +--R +-+4+-+ x 6 +-+4+-+ x 2 %pi x 2 +--R (- 8\|2 \|2 cos(-) - 24\|2 \|2 cos(-) )sin(---)sin(-) +--R 2 2 8 2 +--R + +--R +-+4+-+ x 8 +-+4+-+ x 4 +-+4+-+ %pi +--R (- 2\|2 \|2 cos(-) + 4\|2 \|2 cos(-) - 2\|2 \|2 )sin(---) +--R 2 2 8 +--R * +--R 4+-+ x %pi x +--R 2\|2 cos(-)sin(---)sin(-) +--R 2 8 2 +--R atan(-----------------------------------------------------) +--R +-+ x 2 4+-+ %pi x x +-+ x 2 +--R \|2 sin(-) - 2\|2 cos(---)cos(-)sin(-) - \|2 cos(-) +--R 2 8 2 2 2 +--R + +--R +-+4+-+ %pi x 8 +-+4+-+ x 2 %pi x 6 +--R - 2\|2 \|2 sin(---)sin(-) - 8\|2 \|2 cos(-) sin(---)sin(-) +--R 8 2 2 8 2 +--R + +--R +-+4+-+ x 4 +-+4+-+ %pi x 4 +--R (- 12\|2 \|2 cos(-) + 4\|2 \|2 )sin(---)sin(-) +--R 2 8 2 +--R + +--R +-+4+-+ x 6 +-+4+-+ x 2 %pi x 2 +--R (- 8\|2 \|2 cos(-) - 24\|2 \|2 cos(-) )sin(---)sin(-) +--R 2 2 8 2 +--R + +--R +-+4+-+ x 8 +-+4+-+ x 4 +-+4+-+ %pi +--R (- 2\|2 \|2 cos(-) + 4\|2 \|2 cos(-) - 2\|2 \|2 )sin(---) +--R 2 2 8 +--R * +--R 4+-+ x %pi x +--R 2\|2 cos(-)sin(---)sin(-) +--R 2 8 2 +--R atan(-----------------------------------------------------) +--R +-+ x 2 4+-+ %pi x x +-+ x 2 +--R \|2 sin(-) + 2\|2 cos(---)cos(-)sin(-) - \|2 cos(-) +--R 2 8 2 2 2 +--R + +--R +-+ x 8 +-+ x 2 x 6 +-+ x 4 +-+ x 4 +--R - \|2 sin(-) - 4\|2 cos(-) sin(-) + (- 6\|2 cos(-) + 2\|2 )sin(-) +--R 2 2 2 2 2 +--R + +--R +-+ x 6 +-+ x 2 x 2 +-+ x 8 +-+ x 4 +--R (- 4\|2 cos(-) - 12\|2 cos(-) )sin(-) - \|2 cos(-) + 2\|2 cos(-) +--R 2 2 2 2 2 +--R + +--R +-+ +--R - \|2 +--R * +--R +-+ x x +--R 2\|2 cos(-)sin(-) +--R 2 2 +--R atan(------------------) +--R x 2 x 2 +--R sin(-) - 2cos(-) +--R 2 2 +--R + +--R +-+ x 8 +-+ x 2 x 6 +-+ x 4 +-+ x 4 +--R - \|2 sin(-) - 4\|2 cos(-) sin(-) + (- 6\|2 cos(-) + 2\|2 )sin(-) +--R 2 2 2 2 2 +--R + +--R +-+ x 6 +-+ x 2 x 2 +-+ x 8 +-+ x 4 +--R (- 4\|2 cos(-) - 12\|2 cos(-) )sin(-) - \|2 cos(-) + 2\|2 cos(-) +--R 2 2 2 2 2 +--R + +--R +-+ +--R - \|2 +--R * +--R atan +--R +-+ x x 3 +-+ x 3 +-+ x x +--R 12\|2 cos(-)sin(-) + (- 4\|2 cos(-) - 12\|2 cos(-))sin(-) +--R 2 2 2 2 2 +--R / +--R x 2 x 4 x 4 x 2 x 2 x 6 +--R 9cos(-) sin(-) + (- 6cos(-) - 18cos(-) - 8)sin(-) + cos(-) +--R 2 2 2 2 2 2 +--R + +--R x 4 x 2 +--R 6cos(-) + 9cos(-) +--R 2 2 +--R + +--R x x 3 x 3 x +--R 32cos(-)sin(-) - 32cos(-) sin(-) +--R 2 2 2 2 +--R / +--R x 8 x 2 x 6 x 4 x 4 +--R 16sin(-) + 64cos(-) sin(-) + (96cos(-) - 32)sin(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 2 x 2 x 8 x 4 +--R (64cos(-) + 192cos(-) )sin(-) + 16cos(-) - 32cos(-) + 16 +--R 2 2 2 2 2 +--R Type: Union(Expression Integer,...) +--R +--R +--R +--E 384 + +--S 385 of 504 +--Rt0176:= cos(a+b*x+c*x^2)/x^2+b*sin(a+b*x+c*x^2)/x +--R +--R +--R 2 2 +--R b x sin(c x + b x + a) + cos(c x + b x + a) +--R (337) --------------------------------------------- +--R 2 +--R x +--R Type: Expression Integer +--R +--E 385 + +--S 386 of 504 +--Rr0176:= -cos(a+b*x+c*x^2)/x-c^(1/2)*2^(1/2)*%pi^(1/2)*cos(1/4*(b^2-4*a*c)/c)*FresnelS(1/2*(b+2*c*x)/c^(1/2)*2^(1/2)/%pi^(1/2))+c^(1/2)*2^(1/2)*%pi^(1/2)*FresnelC(1/2*(b+2*c*x)/c^(1/2)*2^(1/2)/%pi^(1/2))*sin(1/4*(b^2-4*a*c)/c) +--R +--R There are no library operations named FresnelS +--R Use HyperDoc Browse or issue +--R )what op FresnelS +--R to learn if there is any operation containing " FresnelS " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R FresnelS with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--R +--E 386 + +--S 387 of 504 +--Ra0176:= integrate(t0176,x) +--R +--R +--R x 2 2 +--R ++ %H b sin(%H c + %H b + a) + cos(%H c + %H b + a) +--R (338) | ------------------------------------------------ d%H +--R ++ 2 +--R %H +--R Type: Union(Expression Integer,...) +--R +--E 387 + +--S 388 of 504 +--Rm0176:= a0176-r0176 +--R +--R +--R x 2 2 +--R ++ %H b sin(%H c + %H b + a) + cos(%H c + %H b + a) +--R (339) | ------------------------------------------------ d%H - r0176 +--R ++ 2 +--R %H +--R Type: Expression Integer +--R +--E 388 + +--S 389 of 504 +--Rd0176:= D(m0176,x) +--R +--R +--R 2 2 +--R b x sin(c x + b x + a) + cos(c x + b x + a) +--R (340) --------------------------------------------- +--R 2 +--R x +--R Type: Expression Integer +--R +--E 389 + +--S 390 of 504 +--Rt0177:= cos(a+b*x-c*x^2)/x^2+b*sin(a+b*x-c*x^2)/x +--R +--R +--R 2 2 +--R - b x sin(c x - b x - a) + cos(c x - b x - a) +--R (341) ----------------------------------------------- +--R 2 +--R x +--R Type: Expression Integer +--R +--E 390 + +--S 391 of 504 +--Rr0177:= -cos(a+b*x-c*x^2)/x+c^(1/2)*2^(1/2)*%pi^(1/2)*cos(1/4*(b^2+4*a*c)/c)*FresnelS(1/2*(b-2*c*x)/c^(1/2)*2^(1/2)/%pi^(1/2))-c^(1/2)*2^(1/2)*%pi^(1/2)*FresnelC(1/2*(b-2*c*x)/c^(1/2)*2^(1/2)/%pi^(1/2))*sin(1/4*(b^2+4*a*c)/c) +--R +--R There are no library operations named FresnelS +--R Use HyperDoc Browse or issue +--R )what op FresnelS +--R to learn if there is any operation containing " FresnelS " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R FresnelS with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--R +--E 391 + +--S 392 of 504 +--Ra0177:= integrate(t0177,x) +--R +--R +--R x 2 2 +--R ++ - %H b sin(%H c - %H b - a) + cos(%H c - %H b - a) +--R (342) | -------------------------------------------------- d%H +--R ++ 2 +--R %H +--R Type: Union(Expression Integer,...) +--R +--E 392 + +--S 393 of 504 +--Rm0177:= a0177-r0177 +--R +--R +--R x 2 2 +--R ++ - %H b sin(%H c - %H b - a) + cos(%H c - %H b - a) +--R (343) | -------------------------------------------------- d%H - r0177 +--R ++ 2 +--R %H +--R Type: Expression Integer +--R +--E 393 + +--S 394 of 504 +--Rd0177:= D(m0177,x) +--R +--R +--R 2 2 +--R - b x sin(c x - b x - a) + cos(c x - b x - a) +--R (344) ----------------------------------------------- +--R 2 +--R x +--R Type: Expression Integer +--R +--E 394 + +--S 395 of 504 +--Rt0178:= (d+e*x)^2*cos(a+b*x+c*x^2) +--R +--R +--R 2 2 2 2 +--R (345) (e x + 2d e x + d )cos(c x + b x + a) +--R Type: Expression Integer +--R +--E 395 + +--S 396 of 504 +--Rr0178:= 1/8*2^(1/2)*%pi^(1/2)*FresnelC(1/2*(b+2*c*x)/c^(1/2)*2^(1/2)/%pi^(1/2))*((2*c*d-b*e)^2*cos(a-1/4*b^2/c)-2*c*e^2*sin(a-1/4*b^2/c))/c^(5/2)-1/8*2^(1/2)*%pi^(1/2)*FresnelS(1/2*(b+2*c*x)/c^(1/2)*2^(1/2)/%pi^(1/2))*(2*c*e^2*cos(a-1/4*b^2/c)+(2*c*d-b*e)^2*sin(a-1/4*b^2/c))/c^(5/2)+1/4*e*(4*c*d-b*e)*sin(a+b*x+c*x^2)/c^2+1/2*e^2*x*sin(a+b*x+c*x^2)/c +--R +--R There are no library operations named FresnelC +--R Use HyperDoc Browse or issue +--R )what op FresnelC +--R to learn if there is any operation containing " FresnelC " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R FresnelC with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--R +--E 396 + +--S 397 of 504 +--Ra0178:= integrate(t0178,x) +--R +--R +--R x +--R ++ 2 2 2 2 +--R (346) | (%H e + 2%H d e + d )cos(%H c + %H b + a)d%H +--R ++ +--R Type: Union(Expression Integer,...) +--R +--E 397 + +--S 398 of 504 +--Rm0178:= a0178-r0178 +--R +--R +--R x +--R ++ 2 2 2 2 +--R (347) | (%H e + 2%H d e + d )cos(%H c + %H b + a)d%H - r0178 +--R ++ +--R Type: Expression Integer +--R +--E 398 + +--S 399 of 504 +--Rd0178:= D(m0178,x) +--R +--R +--R 2 2 2 2 +--R (348) (e x + 2d e x + d )cos(c x + b x + a) +--R Type: Expression Integer +--R +--E 399 + +--S 400 of 504 +--Rt0179:= cos((a+b*x)/(c+d*x))^2 +--R +--R +--R b x + a 2 +--R (349) cos(-------) +--R d x + c +--R Type: Expression Integer +--R +--E 400 + +--S 401 of 504 +--Rr0179:= 1/2*x+1/2*(c+d*x)*cos(2*(a+b*x)/(c+d*x))/d-(b*c-a*d)*Ci(-2*(b*c-a*d)/d/(c+d*x))*sin(2*b/d)/d^2-(b*c-a*d)*cos(2*b/d)*Si(2*a/(c+d*x)-2*b*c/d/(c+d*x))/d^2 +--R +--R +--R (350) +--R 2a d - 2b c 2b 2 2b x + 2a +--R (2a d - 2b c)Ci(-----------)sin(--) + (d x + c d)cos(---------) +--R 2 d d x + c +--R d x + c d +--R + +--R 2a d - 2b c 2b 2 +--R (2a d - 2b c)Si(-----------)cos(--) + d x +--R 2 d +--R d x + c d +--R / +--R 2 +--R 2d +--R Type: Expression Integer +--R +--E 401 + +--S 402 of 504 +--Ra0179:= integrate(t0179,x) +--R +--R +--R x +--R ++ %H b + a 2 +--R (351) | cos(--------) d%H +--R ++ %H d + c +--R Type: Union(Expression Integer,...) +--R +--E 402 + +--S 403 of 504 +--Rm0179:= a0179-r0179 +--R +--R +--R (352) +--R x +--R 2 ++ %H b + a 2 2a d - 2b c 2b +--R 2d | cos(--------) d%H + (- 2a d + 2b c)Ci(-----------)sin(--) +--R ++ %H d + c 2 d +--R d x + c d +--R + +--R 2 2b x + 2a 2a d - 2b c 2b 2 +--R (- d x - c d)cos(---------) + (- 2a d + 2b c)Si(-----------)cos(--) - d x +--R d x + c 2 d +--R d x + c d +--R / +--R 2 +--R 2d +--R Type: Expression Integer +--R +--E 403 + +--S 404 of 504 +--Rd0179:= D(m0179,x) +--R +--R +--R (353) +--R 2b x + 2a 2a d - 2b c 2b +--R (- 2a d + 2b c)sin(---------) + (2a d - 2b c)cos(-----------)sin(--) +--R d x + c 2 d +--R d x + c d +--R + +--R 2b 2a d - 2b c 2 2b x + 2a +--R (2a d - 2b c)cos(--)sin(-----------) + (- d x - c d)cos(---------) +--R d 2 d x + c +--R d x + c d +--R + +--R 2 b x + a 2 2 +--R (2d x + 2c d)cos(-------) - d x - c d +--R d x + c +--R / +--R 2 +--R 2d x + 2c d +--R Type: Expression Integer +--R +--E 404 + +--S 405 of 504 +--Rt0180:= cos(a+b*x^2)^2/x^3 +--R +--R +--R 2 2 +--R cos(b x + a) +--R (354) -------------- +--R 3 +--R x +--R Type: Expression Integer +--R +--E 405 + +--S 406 of 504 +--Rr0180:= -1/4*(1+cos(2*a+2*b*x^2)+2*b*Ci(2*b*x^2)*sin(2*a)*x^2+2*b*cos(2*a)*Si(2*b*x^2)*x^2)/x^2 +--R +--R +--R (355) +--R 2 2 2 2 2 +--R - 2b x Ci(2b x )sin(2a) - cos(2b x + 2a) - 2b x Si(2b x )cos(2a) - 1 +--R --------------------------------------------------------------------- +--R 2 +--R 4x +--R Type: Expression Integer +--R +--E 406 + +--S 407 of 504 +--Ra0180:= integrate(t0180,x) +--R +--R +--R x 2 2 +--R ++ cos(%H b + a) +--R (356) | -------------- d%H +--R ++ 3 +--R %H +--R Type: Union(Expression Integer,...) +--R +--E 407 + +--S 408 of 504 +--Rm0180:= a0180-r0180 +--R +--R +--R (357) +--R x 2 2 +--R 2 ++ cos(%H b + a) 2 2 2 +--R 4x | -------------- d%H + 2b x Ci(2b x )sin(2a) + cos(2b x + 2a) +--R ++ 3 +--R %H +--R + +--R 2 2 +--R 2b x Si(2b x )cos(2a) + 1 +--R / +--R 2 +--R 4x +--R Type: Expression Integer +--R +--E 408 + +--S 409 of 504 +--Rd0180:= D(m0180,x) +--R +--R +--R (358) +--R 2 2 2 2 2 2 +--R - 2b x sin(2b x + 2a) + 2b x cos(2a)sin(2b x ) + 2b x cos(2b x )sin(2a) +--R + +--R 2 2 2 +--R - cos(2b x + 2a) + 2cos(b x + a) - 1 +--R / +--R 3 +--R 2x +--R Type: Expression Integer +--R +--E 409 + +--S 410 of 504 +--Rt0181:= cos(a+b*x^2)^3/x +--R +--R +--R 2 3 +--R cos(b x + a) +--R (359) -------------- +--R x +--R Type: Expression Integer +--R +--E 410 + +--S 411 of 504 +--Rr0181:= 3/8*cos(a)*Ci(b*x^2)+1/8*cos(3*a)*Ci(3*b*x^2)-3/8*sin(a)*Si(b*x^2)-1/8*sin(3*a)*Si(3*b*x^2) +--R +--R +--R (360) +--R 2 2 2 2 +--R - Si(3b x )sin(3a) - 3Si(b x )sin(a) + Ci(3b x )cos(3a) + 3Ci(b x )cos(a) +--R ------------------------------------------------------------------------- +--R 8 +--R Type: Expression Integer +--R +--E 411 + +--S 412 of 504 +--Ra0181:= integrate(t0181,x) +--R +--R +--R x 2 3 +--R ++ cos(%H b + a) +--R (361) | -------------- d%H +--R ++ %H +--R Type: Union(Expression Integer,...) +--R +--E 412 + +--S 413 of 504 +--Rm0181:= a0181-r0181 +--R +--R +--R (362) +--R x 2 3 +--R ++ cos(%H b + a) 2 2 +--R 8 | -------------- d%H + Si(3b x )sin(3a) + 3Si(b x )sin(a) +--R ++ %H +--R + +--R 2 2 +--R - Ci(3b x )cos(3a) - 3Ci(b x )cos(a) +--R / +--R 8 +--R Type: Expression Integer +--R +--E 413 + +--S 414 of 504 +--Rd0181:= D(m0181,x) +--R +--R +--R (363) +--R 2 2 2 +--R sin(3a)sin(3b x ) + 3sin(a)sin(b x ) - cos(3a)cos(3b x ) +--R + +--R 2 3 2 +--R 4cos(b x + a) - 3cos(a)cos(b x ) +--R / +--R 4x +--R Type: Expression Integer +--R +--E 414 + +--S 415 of 504 +--Rt0182:= cos(a+b*x^2)^3/x^3 +--R +--R +--R 2 3 +--R cos(b x + a) +--R (364) -------------- +--R 3 +--R x +--R Type: Expression Integer +--R +--E 415 + +--S 416 of 504 +--Rr0182:= -1/8*(3*cos(a+b*x^2)+cos(3*a+3*b*x^2)+3*b*Ci(b*x^2)*sin(a)*x^2+3*b*Ci(3*b*x^2)*sin(3*a)*x^2+3*b*cos(a)*Si(b*x^2)*x^2+3*b*cos(3*a)*Si(3*b*x^2)*x^2)/x^2 +--R +--R +--R (365) +--R 2 2 2 2 2 +--R - 3b x Ci(3b x )sin(3a) - 3b x Ci(b x )sin(a) - cos(3b x + 3a) +--R + +--R 2 2 2 2 2 +--R - 3cos(b x + a) - 3b x Si(3b x )cos(3a) - 3b x Si(b x )cos(a) +--R / +--R 2 +--R 8x +--R Type: Expression Integer +--R +--E 416 + +--S 417 of 504 +--Ra0182:= integrate(t0182,x) +--R +--R +--R x 2 3 +--R ++ cos(%H b + a) +--R (366) | -------------- d%H +--R ++ 3 +--R %H +--R Type: Union(Expression Integer,...) +--R +--E 417 + +--S 418 of 504 +--Rm0182:= a0182-r0182 +--R +--R +--R (367) +--R x 2 3 +--R 2 ++ cos(%H b + a) 2 2 2 2 +--R 8x | -------------- d%H + 3b x Ci(3b x )sin(3a) + 3b x Ci(b x )sin(a) +--R ++ 3 +--R %H +--R + +--R 2 2 2 2 +--R cos(3b x + 3a) + 3cos(b x + a) + 3b x Si(3b x )cos(3a) +--R + +--R 2 2 +--R 3b x Si(b x )cos(a) +--R / +--R 2 +--R 8x +--R Type: Expression Integer +--R +--E 418 + +--S 419 of 504 +--Rd0182:= D(m0182,x) +--R +--R +--R (368) +--R 2 2 2 2 2 2 +--R - 3b x sin(3b x + 3a) + 3b x cos(3a)sin(3b x ) - 3b x sin(b x + a) +--R + +--R 2 2 2 2 2 2 +--R 3b x cos(a)sin(b x ) + 3b x cos(3b x )sin(3a) + 3b x cos(b x )sin(a) +--R + +--R 2 2 3 2 +--R - cos(3b x + 3a) + 4cos(b x + a) - 3cos(b x + a) +--R / +--R 3 +--R 4x +--R Type: Expression Integer +--R +--E 419 + +--S 420 of 504 +--Rt0183:= cos(a+b*x^n) +--R +--R +--R n +--R (369) cos(b x + a) +--R Type: Expression Integer +--R +--E 420 + +--S 421 of 504 +--Rr0183:= -1/2*x/n*(exp(%i*a)*(-%i*b*x^n)^(-1/n)*Gamma(1/n,-%i*b*x^n)+(%i*b*x^n)^(-1/n)*exp(-%i*a)*Gamma(1/n,%i*b*x^n)) +--R +--R +--R (370) +--R 1 1 +--R - - - - +--R - %i a n n _ 1 n %i a n n _ 1 n +--R - x %e (%i b x ) | (-,%i b x ) - x %e (- %i b x ) | (-,- %i b x ) +--R n n +--R ----------------------------------------------------------------------------- +--R 2n +--R Type: Expression Complex Integer +--R +--E 421 + +--S 422 of 504 +--Ra0183:= integrate(t0183,x) +--R +--R +--R x +--R ++ n +--R (371) | cos(b %H + a)d%H +--R ++ +--R Type: Union(Expression Integer,...) +--R +--E 422 + +--S 423 of 504 +--Rm0183:= a0183-r0183 +--R +--R +--R (372) +--R 1 +--R x - - +--R ++ n - %i a n n _ 1 n +--R 2n | cos(b %H + a)d%H + x %e (%i b x ) | (-,%i b x ) +--R ++ n +--R + +--R 1 +--R - - +--R %i a n n _ 1 n +--R x %e (- %i b x ) | (-,- %i b x ) +--R n +--R / +--R 2n +--R Type: Expression Complex Integer +--R +--E 423 + +--S 424 of 504 +--Rd0183:= D(m0183,x) +--R +--R +--R (373) +--R 1 - n - 1 +--R - - ------- +--R - %i a n n - %i a n - 1 n n +--R (%e (%i b x ) - %i b x %e x (%i b x ) ) +--R * +--R _ 1 n +--R | (-,%i b x ) +--R n +--R + +--R 1 - n - 1 +--R - - ------- +--R %i a n n %i a n - 1 n n +--R (%e (- %i b x ) + %i b x %e x (- %i b x ) ) +--R * +--R _ 1 n +--R | (-,- %i b x ) +--R n +--R + +--R - n + 1 1 +--R n ------- - - +--R - %i a n - 1 - %i b x n n n n +--R - %i b n x %e x %e (%i b x ) (%i b x ) +--R + +--R - n + 1 1 +--R n ------- - - +--R %i a n - 1 %i b x n n n n +--R %i b n x %e x %e (- %i b x ) (- %i b x ) +--R + +--R n +--R 2n cos(b x + a) +--R / +--R 2n +--R Type: Expression Complex Integer +--R +--E 424 + +--S 425 of 504 +--Rt0184:= cos(a+b*x^n)^2 +--R +--R +--R n 2 +--R (374) cos(b x + a) +--R Type: Expression Integer +--R +--E 425 + +--S 426 of 504 +--Rr0184:= -1/2*x/n*(2^(-(1+n)/n)*exp(2*%i*a)*(-%i*b*x^n)^(-1/n)*Gamma(1/n,-2*%i*b*x^n)+2^(-(1+n)/n)*exp(-2*%i*a)*(%i*b*x^n)^(-1/n)*Gamma(1/n,2*%i*b*x^n)-n) +--R +--R +--R (375) +--R - n - 1 1 +--R ------- - - +--R - 2%i a n n n _ 1 n +--R - x %e 2 (%i b x ) | (-,2%i b x ) +--R n +--R + +--R - n - 1 1 +--R ------- - - +--R 2%i a n n n _ 1 n +--R - x %e 2 (- %i b x ) | (-,- 2%i b x ) + n x +--R n +--R / +--R 2n +--R Type: Expression Complex Integer +--R +--E 426 + +--S 427 of 504 +--Ra0184:= integrate(t0184,x) +--R +--R +--R x +--R ++ n 2 +--R (376) | cos(b %H + a) d%H +--R ++ +--R Type: Union(Expression Integer,...) +--R +--E 427 + +--S 428 of 504 +--Rm0184:= a0184-r0184 +--R +--R +--R (377) +--R x +--R ++ n 2 +--R 2n | cos(b %H + a) d%H +--R ++ +--R + +--R - n - 1 1 +--R ------- - - +--R - 2%i a n n n _ 1 n +--R x %e 2 (%i b x ) | (-,2%i b x ) +--R n +--R + +--R - n - 1 1 +--R ------- - - +--R 2%i a n n n _ 1 n +--R x %e 2 (- %i b x ) | (-,- 2%i b x ) - n x +--R n +--R / +--R 2n +--R Type: Expression Complex Integer +--R +--E 428 + +--S 429 of 504 +--Rd0184:= D(m0184,x) +--R +--R +--R (378) +--R - n - 1 1 +--R ------- - - +--R - 2%i a n n n +--R %e 2 (%i b x ) +--R + +--R - n - 1 - n - 1 +--R ------- ------- +--R - 2%i a n n - 1 n n +--R - %i b x %e 2 x (%i b x ) +--R * +--R _ 1 n +--R | (-,2%i b x ) +--R n +--R + +--R - n - 1 1 +--R ------- - - +--R 2%i a n n n +--R %e 2 (- %i b x ) +--R + +--R - n - 1 - n - 1 +--R ------- ------- +--R 2%i a n n - 1 n n +--R %i b x %e 2 x (- %i b x ) +--R * +--R _ 1 n +--R | (-,- 2%i b x ) +--R n +--R + +--R - +--R - n - 1 1 +--R ------- n - - +--R - 2%i a n n - 1 - 2%i b x n n +--R 2%i b n x %e 2 x %e (%i b x ) +--R * +--R - n + 1 +--R ------- +--R n n +--R (2%i b x ) +--R + +--R - n - 1 - n + 1 +--R ------- n ------- +--R 2%i a n n - 1 2%i b x n n +--R 2%i b n x %e 2 x %e (- 2%i b x ) +--R * +--R 1 +--R - - +--R n n +--R (- %i b x ) +--R + +--R n 2 +--R 2n cos(b x + a) - n +--R / +--R 2n +--R Type: Expression Complex Integer +--R +--E 429 + +--S 430 of 504 +--Rt0185:= cos(a+b*x^n)^3 +--R +--R +--R n 3 +--R (379) cos(b x + a) +--R Type: Expression Integer +--R +--E 430 + +--S 431 of 504 +--Rr0185:= -1/8*x/n*(3*exp(%i*a)*(-%i*b*x^n)^(-1/n)*Gamma(1/n,-%i*b*x^n)+3*(%i*b*x^n)^(-1/n)*exp(-%i*a)*Gamma(1/n,%i*b*x^n)+exp(3*%i*a)*(-%i*b*x^n)^(-1/n)*3^(-1/n)*Gamma(1/n,-3*%i*b*x^n)+(%i*b*x^n)^(-1/n)*3^(-1/n)*exp(-3*%i*a)*Gamma(1/n,3*%i*b*x^n)) +--R +--R +--R (380) +--R 1 1 +--R - - - - +--R - 3%i a n n n _ 1 n +--R - x %e 3 (%i b x ) | (-,3%i b x ) +--R n +--R + +--R 1 +--R - - +--R - %i a n n _ 1 n +--R - 3x %e (%i b x ) | (-,%i b x ) +--R n +--R + +--R 1 +--R - - +--R %i a n n _ 1 n +--R - 3x %e (- %i b x ) | (-,- %i b x ) +--R n +--R + +--R 1 1 +--R - - - - +--R 3%i a n n n _ 1 n +--R - x %e 3 (- %i b x ) | (-,- 3%i b x ) +--R n +--R / +--R 8n +--R Type: Expression Complex Integer +--R +--E 431 + +--S 432 of 504 +--Ra0185:= integrate(t0185,x) +--R +--R +--R x +--R ++ n 3 +--R (381) | cos(b %H + a) d%H +--R ++ +--R Type: Union(Expression Integer,...) +--R +--E 432 + +--S 433 of 504 +--Rm0185:= a0185-r0185 +--R +--R +--R (382) +--R 1 1 +--R x - - - - +--R ++ n 3 - 3%i a n n n _ 1 n +--R 8n | cos(b %H + a) d%H + x %e 3 (%i b x ) | (-,3%i b x ) +--R ++ n +--R + +--R 1 +--R - - +--R - %i a n n _ 1 n +--R 3x %e (%i b x ) | (-,%i b x ) +--R n +--R + +--R 1 +--R - - +--R %i a n n _ 1 n +--R 3x %e (- %i b x ) | (-,- %i b x ) +--R n +--R + +--R 1 1 +--R - - - - +--R 3%i a n n n _ 1 n +--R x %e 3 (- %i b x ) | (-,- 3%i b x ) +--R n +--R / +--R 8n +--R Type: Expression Complex Integer +--R +--E 433 + +--S 434 of 504 +--Rd0185:= D(m0185,x) +--R +--R +--R (383) +--R 1 1 +--R - - - - +--R - 3%i a n n n +--R %e 3 (%i b x ) +--R + +--R 1 - n - 1 +--R - - ------- +--R - 3%i a n n - 1 n n +--R - %i b x %e 3 x (%i b x ) +--R * +--R _ 1 n +--R | (-,3%i b x ) +--R n +--R + +--R 1 - n - 1 +--R - - ------- +--R - %i a n n - %i a n - 1 n n +--R (3%e (%i b x ) - 3%i b x %e x (%i b x ) ) +--R * +--R _ 1 n +--R | (-,%i b x ) +--R n +--R + +--R 1 - n - 1 +--R - - ------- +--R %i a n n %i a n - 1 n n +--R (3%e (- %i b x ) + 3%i b x %e x (- %i b x ) ) +--R * +--R _ 1 n +--R | (-,- %i b x ) +--R n +--R + +--R 1 1 +--R - - - - +--R 3%i a n n n +--R %e 3 (- %i b x ) +--R + +--R 1 - n - 1 +--R - - ------- +--R 3%i a n n - 1 n n +--R %i b x %e 3 x (- %i b x ) +--R * +--R _ 1 n +--R | (-,- 3%i b x ) +--R n +--R + +--R 1 1 - n + 1 +--R - - n - - ------- +--R - 3%i a n n - 1 - 3%i b x n n n n +--R - 3%i b n x %e 3 x %e (%i b x ) (3%i b x ) +--R + +--R - n + 1 1 +--R n ------- - - +--R - %i a n - 1 - %i b x n n n n +--R - 3%i b n x %e x %e (%i b x ) (%i b x ) +--R + +--R - n + 1 +--R n ------- +--R %i a n - 1 %i b x n n +--R 3%i b n x %e x %e (- %i b x ) +--R + +--R 1 - n + 1 +--R - - n ------- +--R 3%i a n n - 1 3%i b x n n +--R 3%i b n x %e 3 x %e (- 3%i b x ) +--R * +--R 1 +--R - - +--R n n +--R (- %i b x ) +--R + +--R n 3 +--R 8n cos(b x + a) +--R / +--R 8n +--R Type: Expression Complex Integer +--R +--E 434 + +--S 435 of 504 +--Rt0186:= x^m*cos(a+b*x^n) +--R +--R +--R m n +--R (384) x cos(b x + a) +--R Type: Expression Integer +--R +--E 435 + +--S 436 of 504 +--Rr0186:= -1/2*x*x^m*((-%i*b*x^n)^(-(1+m)/n)*Gamma((1+m)/n,-%i*b*x^n)*exp(%i*a)+exp(-%i*a)*(%i*b*x^n)^(-(1+m)/n)*Gamma((1+m)/n,%i*b*x^n))/n +--R +--R +--R (385) +--R - m - 1 +--R ------- +--R - %i a m n n _ m + 1 n +--R - x %e x (%i b x ) | (-----,%i b x ) +--R n +--R + +--R - m - 1 +--R ------- +--R %i a m n n _ m + 1 n +--R - x %e x (- %i b x ) | (-----,- %i b x ) +--R n +--R / +--R 2n +--R Type: Expression Complex Integer +--R +--E 436 + +--S 437 of 504 +--Ra0186:= integrate(t0186,x) +--R +--R +--R x +--R ++ m n +--R (386) | %H cos(b %H + a)d%H +--R ++ +--R Type: Union(Expression Integer,...) +--R +--E 437 + +--S 438 of 504 +--Rm0186:= a0186-r0186 +--R +--R +--R (387) +--R x +--R ++ m n +--R 2n | %H cos(b %H + a)d%H +--R ++ +--R + +--R - m - 1 +--R ------- +--R - %i a m n n _ m + 1 n +--R x %e x (%i b x ) | (-----,%i b x ) +--R n +--R + +--R - m - 1 +--R ------- +--R %i a m n n _ m + 1 n +--R x %e x (- %i b x ) | (-----,- %i b x ) +--R n +--R / +--R 2n +--R Type: Expression Complex Integer +--R +--E 438 + +--S 439 of 504 +--Rd0186:= D(m0186,x) +--R +--R +--R (388) +--R - m - 1 +--R ------- +--R - %i a m - %i a m - 1 n n +--R (%e x + m x %e x )(%i b x ) +--R + +--R - n - m - 1 +--R ----------- +--R - %i a m n - 1 n n +--R (- %i b m - %i b)x %e x x (%i b x ) +--R * +--R _ m + 1 n +--R | (-----,%i b x ) +--R n +--R + +--R - m - 1 +--R ------- +--R %i a m %i a m - 1 n n +--R (%e x + m x %e x )(- %i b x ) +--R + +--R - n - m - 1 +--R ----------- +--R %i a m n - 1 n n +--R (%i b m + %i b)x %e x x (- %i b x ) +--R * +--R _ m + 1 n +--R | (-----,- %i b x ) +--R n +--R + +--R - +--R - n + m + 1 +--R n ----------- +--R - %i a m n - 1 - %i b x n n +--R %i b n x %e x x %e (%i b x ) +--R * +--R - m - 1 +--R ------- +--R n n +--R (%i b x ) +--R + +--R - n + m + 1 - m - 1 +--R n ----------- ------- +--R %i a m n - 1 %i b x n n n n +--R %i b n x %e x x %e (- %i b x ) (- %i b x ) +--R + +--R m n +--R 2n x cos(b x + a) +--R / +--R 2n +--R Type: Expression Complex Integer +--R +--E 439 + +--S 440 of 504 +--Rt0187:= x^m*cos(a+b*x^n)^2 +--R +--R +--R m n 2 +--R (389) x cos(b x + a) +--R Type: Expression Integer +--R +--E 440 + +--S 441 of 504 +--Rr0187:= x^(1+m)/(2+2*m)-2^(-2-(1+m)/n)*exp(1)^(2*%i*a)*x^(1+m)*Gamma((1+m)/n,-2*%i*b*x^n)/((-%i*b*x^n)^((1+m)/n))/n-2^(-2-(1+m)/n)*x^(1+m)*Gamma((1+m)/n,2*%i*b*x^n)/(exp(1)^(2*%i*a))/((%i*b*x^n)^((1+m)/n))/n +--R +--R +--R (390) +--R - 2n - m - 1 m + 1 +--R ------------ ----- +--R n m + 1 n n _ m + 1 n +--R (- 2m - 2)2 x (- %i b x ) | (-----,2%i b x ) +--R n +--R + +--R - 2n - m - 1 m + 1 +--R ------------ ----- +--R 2%i a 2 n m + 1 n n _ m + 1 n +--R (- 2m - 2)(%e ) 2 x (%i b x ) | (-----,- 2%i b x ) +--R n +--R + +--R m + 1 m + 1 +--R ----- ----- +--R 2%i a m + 1 n n n n +--R n %e x (- %i b x ) (%i b x ) +--R / +--R m + 1 m + 1 +--R ----- ----- +--R 2%i a n n n n +--R (2m + 2)n %e (- %i b x ) (%i b x ) +--R Type: Expression Complex Integer +--R +--E 441 + +--S 442 of 504 +--Ra0187:= integrate(t0187,x) +--R +--R +--R x +--R ++ m n 2 +--R (391) | %H cos(b %H + a) d%H +--R ++ +--R Type: Union(Expression Integer,...) +--R +--E 442 + +--S 443 of 504 +--Rm0187:= a0187-r0187 +--R +--R +--R (392) +--R m + 1 m + 1 +--R ----- ----- +--R 2%i a n n n n +--R (2m + 2)n %e (- %i b x ) (%i b x ) +--R * +--R x +--R ++ m n 2 +--R | %H cos(b %H + a) d%H +--R ++ +--R + +--R - 2n - m - 1 m + 1 +--R ------------ ----- +--R n m + 1 n n _ m + 1 n +--R (2m + 2)2 x (- %i b x ) | (-----,2%i b x ) +--R n +--R + +--R - 2n - m - 1 m + 1 +--R ------------ ----- +--R 2%i a 2 n m + 1 n n _ m + 1 n +--R (2m + 2)(%e ) 2 x (%i b x ) | (-----,- 2%i b x ) +--R n +--R + +--R m + 1 m + 1 +--R ----- ----- +--R 2%i a m + 1 n n n n +--R - n %e x (- %i b x ) (%i b x ) +--R / +--R m + 1 m + 1 +--R ----- ----- +--R 2%i a n n n n +--R (2m + 2)n %e (- %i b x ) (%i b x ) +--R Type: Expression Complex Integer +--R +--E 443 + +--S 444 of 504 +--Rd0187:= D(m0187,x) +--R +--R +--R (393) +--R - 2n - m - 1 m + 1 2 m + 1 +--R ------------ ----- ----- +--R n m n n n n +--R (2m + 2)2 x ((- %i b x ) ) (%i b x ) +--R + +--R - 2n - m - 1 m + 1 2 +--R ------------ ----- +--R n m + 1 n - 1 n n +--R (- 2%i b m - 2%i b)2 x x ((- %i b x ) ) +--R * +--R - n + m + 1 +--R ----------- +--R n n +--R (%i b x ) +--R * +--R _ m + 1 n +--R | (-----,2%i b x ) +--R n +--R + +--R - 2n - m - 1 m + 1 +--R ------------ ----- +--R 2%i a 2 n m n n +--R (2m + 2)(%e ) 2 x (- %i b x ) +--R + +--R - 2n - m - 1 +--R ------------ +--R 2%i a 2 n m + 1 n - 1 +--R (2%i b m + 2%i b)(%e ) 2 x x +--R * +--R - n + m + 1 +--R ----------- +--R n n +--R (- %i b x ) +--R * +--R m + 1 2 +--R ----- +--R n n _ m + 1 n +--R ((%i b x ) ) | (-----,- 2%i b x ) +--R n +--R + +--R - +--R - 2n - m - 1 m + 1 2 +--R ------------ n ----- +--R n m + 1 n - 1 - 2%i b x n n +--R 4%i b n 2 x x %e ((- %i b x ) ) +--R * +--R m + 1 - n + m + 1 +--R ----- ----------- +--R n n n n +--R (%i b x ) (2%i b x ) +--R + +--R m + 1 2 +--R ----- +--R 2%i a m n 2 2%i a m n n +--R (2n %e x cos(b x + a) - n %e x )((- %i b x ) ) +--R + +--R - 2n - m - 1 +--R ------------ n +--R 2%i a 2 n m + 1 n - 1 2%i b x +--R 4%i b n (%e ) 2 x x %e +--R * +--R - n + m + 1 m + 1 +--R ----------- ----- +--R n n n n +--R (- 2%i b x ) (- %i b x ) +--R * +--R m + 1 2 +--R ----- +--R n n +--R ((%i b x ) ) +--R / +--R m + 1 2 m + 1 2 +--R ----- ----- +--R 2%i a n n n n +--R 2n %e ((- %i b x ) ) ((%i b x ) ) +--R Type: Expression Complex Integer +--R +--E 444 + +--S 445 of 504 +--Rt0188:= x^m*cos(a+b*x^n)^3 +--R +--R +--R m n 3 +--R (394) x cos(b x + a) +--R Type: Expression Integer +--R +--E 445 + +--S 446 of 504 +--Rr0188:= -1/8*x*x^m*((-%i*b*x^n)^(-(1+m)/n)*3^(-(1+m)/n)*Gamma((1+m)/n,-3*%i*b*x^n)*exp(3*%i*a)+3*(-%i*b*x^n)^(-(1+m)/n)*Gamma((1+m)/n,-%i*b*x^n)*exp(%i*a)+3*exp(-%i*a)*(%i*b*x^n)^(-(1+m)/n)*Gamma((1+m)/n,%i*b*x^n)+(%i*b*x^n)^(-(1+m)/n)*3^(-(1+m)/n)*Gamma((1+m)/n,3*%i*b*x^n)*exp(-3*%i*a))/n +--R +--R +--R (395) +--R - m - 1 - m - 1 +--R ------- ------- +--R - 3%i a n m n n _ m + 1 n +--R - x %e 3 x (%i b x ) | (-----,3%i b x ) +--R n +--R + +--R - m - 1 +--R ------- +--R - %i a m n n _ m + 1 n +--R - 3x %e x (%i b x ) | (-----,%i b x ) +--R n +--R + +--R - m - 1 +--R ------- +--R %i a m n n _ m + 1 n +--R - 3x %e x (- %i b x ) | (-----,- %i b x ) +--R n +--R + +--R - m - 1 - m - 1 +--R ------- ------- +--R 3%i a n m n n _ m + 1 n +--R - x %e 3 x (- %i b x ) | (-----,- 3%i b x ) +--R n +--R / +--R 8n +--R Type: Expression Complex Integer +--R +--E 446 + +--S 447 of 504 +--Ra0188:= integrate(t0188,x) +--R +--R +--R x +--R ++ m n 3 +--R (396) | %H cos(b %H + a) d%H +--R ++ +--R Type: Union(Expression Integer,...) +--R +--E 447 + +--S 448 of 504 +--Rm0188:= a0188-r0188 +--R +--R +--R (397) +--R x +--R ++ m n 3 +--R 8n | %H cos(b %H + a) d%H +--R ++ +--R + +--R - m - 1 - m - 1 +--R ------- ------- +--R - 3%i a n m n n _ m + 1 n +--R x %e 3 x (%i b x ) | (-----,3%i b x ) +--R n +--R + +--R - m - 1 +--R ------- +--R - %i a m n n _ m + 1 n +--R 3x %e x (%i b x ) | (-----,%i b x ) +--R n +--R + +--R - m - 1 +--R ------- +--R %i a m n n _ m + 1 n +--R 3x %e x (- %i b x ) | (-----,- %i b x ) +--R n +--R + +--R - m - 1 - m - 1 +--R ------- ------- +--R 3%i a n m n n _ m + 1 n +--R x %e 3 x (- %i b x ) | (-----,- 3%i b x ) +--R n +--R / +--R 8n +--R Type: Expression Complex Integer +--R +--E 448 + +--S 449 of 504 +--Rd0188:= D(m0188,x) +--R +--R +--R (398) +--R - m - 1 - m - 1 - m - 1 +--R ------- ------- ------- +--R - 3%i a n m - 3%i a n m - 1 n n +--R (%e 3 x + m x %e 3 x )(%i b x ) +--R + +--R - m - 1 - n - m - 1 +--R ------- ----------- +--R - 3%i a n m n - 1 n n +--R (- %i b m - %i b)x %e 3 x x (%i b x ) +--R * +--R _ m + 1 n +--R | (-----,3%i b x ) +--R n +--R + +--R - m - 1 +--R ------- +--R - %i a m - %i a m - 1 n n +--R (3%e x + 3m x %e x )(%i b x ) +--R + +--R - n - m - 1 +--R ----------- +--R - %i a m n - 1 n n +--R (- 3%i b m - 3%i b)x %e x x (%i b x ) +--R * +--R _ m + 1 n +--R | (-----,%i b x ) +--R n +--R + +--R - m - 1 +--R ------- +--R %i a m %i a m - 1 n n +--R (3%e x + 3m x %e x )(- %i b x ) +--R + +--R - n - m - 1 +--R ----------- +--R %i a m n - 1 n n +--R (3%i b m + 3%i b)x %e x x (- %i b x ) +--R * +--R _ m + 1 n +--R | (-----,- %i b x ) +--R n +--R + +--R - m - 1 - m - 1 - m - 1 +--R ------- ------- ------- +--R 3%i a n m 3%i a n m - 1 n n +--R (%e 3 x + m x %e 3 x )(- %i b x ) +--R + +--R - m - 1 - n - m - 1 +--R ------- ----------- +--R 3%i a n m n - 1 n n +--R (%i b m + %i b)x %e 3 x x (- %i b x ) +--R * +--R _ m + 1 n +--R | (-----,- 3%i b x ) +--R n +--R + +--R - +--R - m - 1 - m - 1 +--R ------- n ------- +--R - 3%i a n m n - 1 - 3%i b x n n +--R 3%i b n x %e 3 x x %e (%i b x ) +--R * +--R - n + m + 1 +--R ----------- +--R n n +--R (3%i b x ) +--R + +--R - +--R - n + m + 1 +--R n ----------- +--R - %i a m n - 1 - %i b x n n +--R 3%i b n x %e x x %e (%i b x ) +--R * +--R - m - 1 +--R ------- +--R n n +--R (%i b x ) +--R + +--R - n + m + 1 +--R n ----------- +--R %i a m n - 1 %i b x n n +--R 3%i b n x %e x x %e (- %i b x ) +--R + +--R - m - 1 - n + m + 1 +--R ------- n ----------- +--R 3%i a n m n - 1 3%i b x n n +--R 3%i b n x %e 3 x x %e (- 3%i b x ) +--R * +--R - m - 1 +--R ------- +--R n n +--R (- %i b x ) +--R + +--R m n 3 +--R 8n x cos(b x + a) +--R / +--R 8n +--R Type: Expression Complex Integer +--R +--E 449 + +--S 450 of 504 +--Rt0189:= x/cos(x)^(3/2)+x*cos(x)^(1/2) +--R +--R +--R 2 +--R x cos(x) + x +--R (399) --------------- +--R +------+ +--R cos(x)\|cos(x) +--R Type: Expression Integer +--R +--E 450 + +--S 451 of 504 +--Rr0189:= 2*(2*cos(x)+x*sin(x))/cos(x)^(1/2) +--R +--R +--R 2x sin(x) + 4cos(x) +--R (400) ------------------- +--R +------+ +--R \|cos(x) +--R Type: Expression Integer +--R +--E 451 + +--S 452 of 504 +--Ra0189:= integrate(t0189,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--R +--E 452 + +--S 453 of 504 +--Rm0189:= a0189-r0189 +--R +--R +--R +------+ +--R a0189\|cos(x) - 2x sin(x) - 4cos(x) +--R (401) ------------------------------------ +--R +------+ +--R \|cos(x) +--R Type: Expression Integer +--R +--E 453 + +--S 454 of 504 +--Rd0189:= D(m0189,x) +--R +--R +--R 2 2 +--R - x sin(x) - 2x cos(x) +--R (402) ------------------------ +--R +------+ +--R cos(x)\|cos(x) +--R Type: Expression Integer +--R +--E 454 + +--S 455 of 504 +--Rt0190:= x/cos(x)^(5/2)-1/3*x/cos(x)^(1/2) +--R +--R +--R 2 +--R - x cos(x) + 3x +--R (403) ----------------- +--R 2 +------+ +--R 3cos(x) \|cos(x) +--R Type: Expression Integer +--R +--E 455 + +--S 456 of 504 +--Rr0190:= -2/3*(2*cos(x)-x*sin(x))/cos(x)^(3/2) +--R +--R +--R 2x sin(x) - 4cos(x) +--R (404) ------------------- +--R +------+ +--R 3cos(x)\|cos(x) +--R Type: Expression Integer +--R +--E 456 + +--S 457 of 504 +--Ra0190:= integrate(t0190,x) +--R +--R +--R +------+ +--R (2x sin(x) - 4cos(x))\|cos(x) +--R (405) ------------------------------ +--R 2 +--R 3cos(x) +--R Type: Union(Expression Integer,...) +--R +--E 457 + +--S 458 of 504 +--Rm0190:= a0190-r0190 +--R +--R +--R (406) 0 +--R Type: Expression Integer +--R +--E 458 + +--S 459 of 504 +--Rd0190:= D(m0190,x) +--R +--R +--R (407) 0 +--R Type: Expression Integer +--R +--E 459 + +--S 460 of 504 +--Rt0191:= x/cos(x)^(7/2)+3/5*x*cos(x)^(1/2) +--R +--R +--R 4 +--R 3x cos(x) + 5x +--R (408) ----------------- +--R 3 +------+ +--R 5cos(x) \|cos(x) +--R Type: Expression Integer +--R +--E 460 + +--S 461 of 504 +--Rr0191:= 2/15*(-2*cos(x)+18*cos(x)^3+3*x*sin(x)+9*x*sin(x)*cos(x)^2)/cos(x)^(5/2) +--R +--R +--R 2 3 +--R (18x cos(x) + 6x)sin(x) + 36cos(x) - 4cos(x) +--R (409) ---------------------------------------------- +--R 2 +------+ +--R 15cos(x) \|cos(x) +--R Type: Expression Integer +--R +--E 461 + +--S 462 of 504 +--Ra0191:= integrate(t0191,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--R +--E 462 + +--S 463 of 504 +--Rm0191:= a0191-r0191 +--R +--R +--R (410) +--R 2 +------+ 2 3 +--R 15a0191 cos(x) \|cos(x) + (- 18x cos(x) - 6x)sin(x) - 36cos(x) + 4cos(x) +--R --------------------------------------------------------------------------- +--R 2 +------+ +--R 15cos(x) \|cos(x) +--R Type: Expression Integer +--R +--E 463 + +--S 464 of 504 +--Rd0191:= D(m0191,x) +--R +--R +--R 2 2 4 2 +--R (- 3x cos(x) - 5x)sin(x) - 6x cos(x) - 2x cos(x) +--R (411) ---------------------------------------------------- +--R 3 +------+ +--R 5cos(x) \|cos(x) +--R Type: Expression Integer +--R +--E 464 + +--S 465 of 504 +--Rt0192:= x^2/cos(x)^(3/2)+x^2*cos(x)^(1/2) +--R +--R +--R 2 2 2 +--R x cos(x) + x +--R (412) --------------- +--R +------+ +--R cos(x)\|cos(x) +--R Type: Expression Integer +--R +--E 465 + +--S 466 of 504 +--Rr0192:= 8*x*cos(x)^(1/2)-16*EllipticE(1/2*x,2)+2*x^2*sin(x)/cos(x)^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Polynomial Fraction Integer +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--R +--E 466 + +--S 467 of 504 +--Ra0192:= integrate(t0192,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--R +--E 467 + +--S 468 of 504 +--Rm0192:= a0192-r0192 +--R +--R +--R (413) - r0192 + a0192 +--R Type: Polynomial Integer +--R +--E 468 + +--S 469 of 504 +--Rd0192:= D(m0192,x) +--R +--R +--R (414) 0 +--R Type: Polynomial Integer +--R +--E 469 + +--S 470 of 504 +--Rt0193:= cos(a+b*log(c*x^n)) +--R +--R +--R n +--R (415) cos(b log(c x ) + a) +--R Type: Expression Integer +--R +--E 470 + +--S 471 of 504 +--Rr0193:= x*(cos(a+b*log(c*x^n))+b*n*sin(a+b*log(c*x^n)))/(1+b^2*n^2) +--R +--R +--R n n +--R b n x sin(b log(c x ) + a) + x cos(b log(c x ) + a) +--R (416) --------------------------------------------------- +--R 2 2 +--R b n + 1 +--R Type: Expression Integer +--R +--E 471 + +--S 472 of 504 +--Ra0193:= integrate(t0193,x) +--R +--R +--R (417) +--R b n x sin(b n log(x) + b log(c) + a) + x cos(b n log(x) + b log(c) + a) +--R ----------------------------------------------------------------------- +--R 2 2 +--R b n + 1 +--R Type: Union(Expression Integer,...) +--R +--E 472 + +--S 473 of 504 +--Rm0193:= a0193-r0193 +--R +--R +--R (418) +--R n n +--R - b n x sin(b log(c x ) + a) - x cos(b log(c x ) + a) +--R + +--R b n x sin(b n log(x) + b log(c) + a) + x cos(b n log(x) + b log(c) + a) +--R / +--R 2 2 +--R b n + 1 +--R Type: Expression Integer +--R +--E 473 + +--S 474 of 504 +--Rd0193:= D(m0193,x) +--R +--R +--R (419) +--R n n - 1 n +--R (- b n x + b n x x )sin(b log(c x ) + a) +--R + +--R n 2 2 n - 1 n +--R (- x - b n x x )cos(b log(c x ) + a) +--R + +--R 2 2 n +--R (b n + 1)x cos(b n log(x) + b log(c) + a) +--R / +--R 2 2 n +--R (b n + 1)x +--R Type: Expression Integer +--R +--E 474 + +--S 475 of 504 +--Rt0194:= x*cos(a+b*log(c*x^n)) +--R +--R +--R n +--R (420) x cos(b log(c x ) + a) +--R Type: Expression Integer +--R +--E 475 + +--S 476 of 504 +--Rr0194:= x^2*(2*cos(a+b*log(c*x^n))+b*n*sin(a+b*log(c*x^n)))/(4+b^2*n^2) +--R +--R +--R 2 n 2 n +--R b n x sin(b log(c x ) + a) + 2x cos(b log(c x ) + a) +--R (421) ---------------------------------------------------- +--R 2 2 +--R b n + 4 +--R Type: Expression Integer +--R +--E 476 + +--S 477 of 504 +--Ra0194:= integrate(t0194,x) +--R +--R +--R (422) +--R 2 2 +--R b n x sin(b n log(x) + b log(c) + a) + 2x cos(b n log(x) + b log(c) + a) +--R ------------------------------------------------------------------------ +--R 2 2 +--R b n + 4 +--R Type: Union(Expression Integer,...) +--R +--E 477 + +--S 478 of 504 +--Rm0194:= a0194-r0194 +--R +--R +--R (423) +--R 2 n 2 n +--R - b n x sin(b log(c x ) + a) - 2x cos(b log(c x ) + a) +--R + +--R 2 2 +--R b n x sin(b n log(x) + b log(c) + a) + 2x cos(b n log(x) + b log(c) + a) +--R / +--R 2 2 +--R b n + 4 +--R Type: Expression Integer +--R +--E 478 + +--S 479 of 504 +--Rd0194:= D(m0194,x) +--R +--R +--R (424) +--R n 2 n - 1 n +--R (- 2b n x x + 2b n x x )sin(b log(c x ) + a) +--R + +--R n 2 2 2 n - 1 n +--R (- 4x x - b n x x )cos(b log(c x ) + a) +--R + +--R 2 2 n +--R (b n + 4)x x cos(b n log(x) + b log(c) + a) +--R / +--R 2 2 n +--R (b n + 4)x +--R Type: Expression Integer +--R +--E 479 + +--S 480 of 504 +--Rt0195:= x^2*cos(a+b*log(c*x^n)) +--R +--R +--R 2 n +--R (425) x cos(b log(c x ) + a) +--R Type: Expression Integer +--R +--E 480 + +--S 481 of 504 +--Rr0195:= x^3*(3*cos(a+b*log(c*x^n))+b*n*sin(a+b*log(c*x^n)))/(9+b^2*n^2) +--R +--R +--R 3 n 3 n +--R b n x sin(b log(c x ) + a) + 3x cos(b log(c x ) + a) +--R (426) ---------------------------------------------------- +--R 2 2 +--R b n + 9 +--R Type: Expression Integer +--R +--E 481 + +--S 482 of 504 +--Ra0195:= integrate(t0195,x) +--R +--R +--R (427) +--R 3 3 +--R b n x sin(b n log(x) + b log(c) + a) + 3x cos(b n log(x) + b log(c) + a) +--R ------------------------------------------------------------------------ +--R 2 2 +--R b n + 9 +--R Type: Union(Expression Integer,...) +--R +--E 482 + +--S 483 of 504 +--Rm0195:= a0195-r0195 +--R +--R +--R (428) +--R 3 n 3 n +--R - b n x sin(b log(c x ) + a) - 3x cos(b log(c x ) + a) +--R + +--R 3 3 +--R b n x sin(b n log(x) + b log(c) + a) + 3x cos(b n log(x) + b log(c) + a) +--R / +--R 2 2 +--R b n + 9 +--R Type: Expression Integer +--R +--E 483 + +--S 484 of 504 +--Rd0195:= D(m0195,x) +--R +--R +--R (429) +--R 2 n 3 n - 1 n +--R (- 3b n x x + 3b n x x )sin(b log(c x ) + a) +--R + +--R 2 n 2 2 3 n - 1 n +--R (- 9x x - b n x x )cos(b log(c x ) + a) +--R + +--R 2 2 2 n +--R (b n + 9)x x cos(b n log(x) + b log(c) + a) +--R / +--R 2 2 n +--R (b n + 9)x +--R Type: Expression Integer +--R +--E 484 + +--S 485 of 504 +--Rt0196:= cos(a+b*log(c*x^n))/x^2 +--R +--R +--R n +--R cos(b log(c x ) + a) +--R (430) -------------------- +--R 2 +--R x +--R Type: Expression Integer +--R +--E 485 + +--S 486 of 504 +--Rr0196:= -1/(1+b^2*n^2)/x*(cos(a+b*log(c*x^n))-b*n*sin(a+b*log(c*x^n))) +--R +--R +--R n n +--R b n sin(b log(c x ) + a) - cos(b log(c x ) + a) +--R (431) ----------------------------------------------- +--R 2 2 +--R (b n + 1)x +--R Type: Expression Integer +--R +--E 486 + +--S 487 of 504 +--Ra0196:= integrate(t0196,x) +--R +--R +--R b n sin(b n log(x) + b log(c) + a) - cos(b n log(x) + b log(c) + a) +--R (432) ------------------------------------------------------------------- +--R 2 2 +--R (b n + 1)x +--R Type: Union(Expression Integer,...) +--R +--E 487 + +--S 488 of 504 +--Rm0196:= a0196-r0196 +--R +--R +--R (433) +--R n n +--R - b n sin(b log(c x ) + a) + cos(b log(c x ) + a) +--R + +--R b n sin(b n log(x) + b log(c) + a) - cos(b n log(x) + b log(c) + a) +--R / +--R 2 2 +--R (b n + 1)x +--R Type: Expression Integer +--R +--E 488 + +--S 489 of 504 +--Rd0196:= D(m0196,x) +--R +--R +--R (434) +--R n n - 1 n +--R (b n x - b n x x )sin(b log(c x ) + a) +--R + +--R n 2 2 n - 1 n +--R (- x - b n x x )cos(b log(c x ) + a) +--R + +--R 2 2 n +--R (b n + 1)x cos(b n log(x) + b log(c) + a) +--R / +--R 2 2 2 n +--R (b n + 1)x x +--R Type: Expression Integer +--R +--E 489 + +--S 490 of 504 +--Rt0197:= x^m*cos(a+b*log(c*x^n)) +--R +--R +--R m n +--R (435) x cos(b log(c x ) + a) +--R Type: Expression Integer +--R +--E 490 + +--S 491 of 504 +--Rr0197:= (1+m)*x^(1+m)*cos(a+b*log(c*x^n))/((1+m)^2+b^2*n^2)+b*n*x^(1+m)*sin(a+b*log(c*x^n))/((1+m)^2+b^2*n^2) +--R +--R +--R m + 1 n m + 1 n +--R b n x sin(b log(c x ) + a) + (m + 1)x cos(b log(c x ) + a) +--R (436) ------------------------------------------------------------------ +--R 2 2 2 +--R b n + m + 2m + 1 +--R Type: Expression Integer +--R +--E 491 + +--S 492 of 504 +--Ra0197:= integrate(t0197,x) +--R +--R +--R (437) +--R m log(x) +--R b n x %e sin(b n log(x) + b log(c) + a) +--R + +--R m log(x) +--R (m + 1)x cos(b n log(x) + b log(c) + a)%e +--R / +--R 2 2 2 +--R b n + m + 2m + 1 +--R Type: Union(Expression Integer,...) +--R +--E 492 + +--S 493 of 504 +--Rm0197:= a0197-r0197 +--R +--R +--R (438) +--R m + 1 n m + 1 n +--R - b n x sin(b log(c x ) + a) + (- m - 1)x cos(b log(c x ) + a) +--R + +--R m log(x) +--R b n x %e sin(b n log(x) + b log(c) + a) +--R + +--R m log(x) +--R (m + 1)x cos(b n log(x) + b log(c) + a)%e +--R / +--R 2 2 2 +--R b n + m + 2m + 1 +--R Type: Expression Integer +--R +--E 493 + +--S 494 of 504 +--Rd0197:= D(m0197,x) +--R +--R +--R (439) +--R m n m + 1 n - 1 n +--R ((- b m - b)n x x + (b m + b)n x x )sin(b log(c x ) + a) +--R + +--R 2 m n 2 2 m + 1 n - 1 n +--R ((- m - 2m - 1)x x - b n x x )cos(b log(c x ) + a) +--R + +--R 2 2 2 n m log(x) +--R (b n + m + 2m + 1)x cos(b n log(x) + b log(c) + a)%e +--R / +--R 2 2 2 n +--R (b n + m + 2m + 1)x +--R Type: Expression Integer +--R +--E 494 + +--S 495 of 504 +--Rt0198:= cos(a+b*log(c*x^n))^2 +--R +--R +--R n 2 +--R (440) cos(b log(c x ) + a) +--R Type: Expression Integer +--R +--E 495 + +--S 496 of 504 +--Rr0198:= x*(2*b^2*n^2+cos(a+b*log(c*x^n))^2+2*b*n*cos(a+b*log(c*x^n))*sin(a+b*log(c*x^n)))/(1+4*b^2*n^2) +--R +--R +--R (441) +--R n n n 2 +--R 2b n x cos(b log(c x ) + a)sin(b log(c x ) + a) + x cos(b log(c x ) + a) +--R + +--R 2 2 +--R 2b n x +--R / +--R 2 2 +--R 4b n + 1 +--R Type: Expression Integer +--R +--E 496 + +--S 497 of 504 +--Ra0198:= integrate(t0198,x) +--R +--R +--R (442) +--R 2b n x cos(b n log(x) + b log(c) + a)sin(b n log(x) + b log(c) + a) +--R + +--R 2 2 2 +--R x cos(b n log(x) + b log(c) + a) + 2b n x +--R / +--R 2 2 +--R 4b n + 1 +--R Type: Union(Expression Integer,...) +--R +--E 497 + +--S 498 of 504 +--Rm0198:= a0198-r0198 +--R +--R +--R (443) +--R n n +--R - 2b n x cos(b log(c x ) + a)sin(b log(c x ) + a) +--R + +--R n 2 +--R - x cos(b log(c x ) + a) +--R + +--R 2b n x cos(b n log(x) + b log(c) + a)sin(b n log(x) + b log(c) + a) +--R + +--R 2 +--R x cos(b n log(x) + b log(c) + a) +--R / +--R 2 2 +--R 4b n + 1 +--R Type: Expression Integer +--R +--E 498 + +--S 499 of 504 +--Rd0198:= D(m0198,x) +--R +--R +--R (444) +--R 2 2 n - 1 n 2 +--R 2b n x x sin(b log(c x ) + a) +--R + +--R n n - 1 n n +--R (- 2b n x + 2b n x x )cos(b log(c x ) + a)sin(b log(c x ) + a) +--R + +--R n 2 2 n - 1 n 2 +--R (- x - 2b n x x )cos(b log(c x ) + a) +--R + +--R 2 2 n 2 +--R - 2b n x sin(b n log(x) + b log(c) + a) +--R + +--R 2 2 n 2 +--R (2b n + 1)x cos(b n log(x) + b log(c) + a) +--R / +--R 2 2 n +--R (4b n + 1)x +--R Type: Expression Integer +--R +--E 499 + +--S 500 of 504 +--Rt0199:= x*cos(a+b*log(c*x^n))^2 +--R +--R +--R n 2 +--R (445) x cos(b log(c x ) + a) +--R Type: Expression Integer +--R +--E 500 + +--S 501 of 504 +--Rr0199:= 1/4/(1+b^2*n^2)*x^2*(b^2*n^2+2*cos(a+b*log(c*x^n))^2+2*b*n*cos(a+b*log(c*x^n))*sin(a+b*log(c*x^n))) +--R +--R +--R (446) +--R 2 n n +--R 2b n x cos(b log(c x ) + a)sin(b log(c x ) + a) +--R + +--R 2 n 2 2 2 2 +--R 2x cos(b log(c x ) + a) + b n x +--R / +--R 2 2 +--R 4b n + 4 +--R Type: Expression Integer +--R +--E 501 + +--S 502 of 504 +--Ra0199:= integrate(t0199,x) +--R +--R +--R (447) +--R 2 +--R 2b n x cos(b n log(x) + b log(c) + a)sin(b n log(x) + b log(c) + a) +--R + +--R 2 2 2 2 2 +--R 2x cos(b n log(x) + b log(c) + a) + b n x +--R / +--R 2 2 +--R 4b n + 4 +--R Type: Union(Expression Integer,...) +--R +--E 502 + +--S 503 of 504 +--Rm0199:= a0199-r0199 +--R +--R +--R (448) +--R 2 n n +--R - b n x cos(b log(c x ) + a)sin(b log(c x ) + a) +--R + +--R 2 n 2 +--R - x cos(b log(c x ) + a) +--R + +--R 2 +--R b n x cos(b n log(x) + b log(c) + a)sin(b n log(x) + b log(c) + a) +--R + +--R 2 2 +--R x cos(b n log(x) + b log(c) + a) +--R / +--R 2 2 +--R 2b n + 2 +--R Type: Expression Integer +--R +--E 503 + +--S 504 of 504 +--Rd0199:= D(m0199,x) +--R +--R +--R (449) +--R 2 2 2 n - 1 n 2 +--R b n x x sin(b log(c x ) + a) +--R + +--R n 2 n - 1 n n +--R (- 2b n x x + 2b n x x )cos(b log(c x ) + a)sin(b log(c x ) + a) +--R + +--R n 2 2 2 n - 1 n 2 +--R (- 2x x - b n x x )cos(b log(c x ) + a) +--R + +--R 2 2 n 2 +--R - b n x x sin(b n log(x) + b log(c) + a) +--R + +--R 2 2 n 2 +--R (b n + 2)x x cos(b n log(x) + b log(c) + a) +--R / +--R 2 2 n +--R (2b n + 2)x +--R Type: Expression Integer +--E 504 +)spool + +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} Albert D. Rich ``Rule-based Mathematics'' +\verb|www.apmaths.uwo.ca/~arich| +\end{thebibliography} +\end{document}