diff --git a/changelog b/changelog index 8c13d02..355b823 100644 --- a/changelog +++ b/changelog @@ -1,3 +1,6 @@ +20100605 tpd src/axiom-website/patches.html 20100605.02.tpd.patch +20100605 tpd src/input/Makefile rule-based algebraic integration +20100605 tpd src/input/richalgebraic200-299.input rule-based algebraic int. 20100605 tpd src/axiom-website/patches.html 20100605.01.myb.patch 20100605 myb books/bookvol8 add 3D graphic file format table 20100605 tpd books/bookvolbib cite Martin Baker website diff --git a/src/axiom-website/patches.html b/src/axiom-website/patches.html index b0223b3..f82b035 100644 --- a/src/axiom-website/patches.html +++ b/src/axiom-website/patches.html @@ -2852,5 +2852,8 @@ books/bookvol10.5 use simple-array, not simple-vector type
books/bookvol10.4 add GnuDraw package
20100605.01.myb.patch books/bookvol8 add 3D graphic file format table
+20100605.02.tpd.patch +src/input/richalgebraic200-299.input rule-based algebraic integration.
+ diff --git a/src/input/Makefile.pamphlet b/src/input/Makefile.pamphlet index 9b4d525..29c3a26 100644 --- a/src/input/Makefile.pamphlet +++ b/src/input/Makefile.pamphlet @@ -371,6 +371,7 @@ REGRES= ackermann.regress \ repa6.regress \ richalgebraic000-099.regress \ richalgebraic100-199.regress \ + richalgebraic200-299.regress \ richrational.regress robidoux.regress \ roman.regress roots.regress ruleset.regress rules.regress \ rubey.regress sae.regress spline.regress \ @@ -685,6 +686,7 @@ FILES= ${OUT}/ackermann.input \ ${OUT}/reclos.input ${OUT}/reclos2.input ${OUT}/regset.input \ ${OUT}/richalgebraic000-099.input \ ${OUT}/richalgebraic100-199.input \ + ${OUT}/richalgebraic200-299.input \ ${OUT}/richrational.input \ ${OUT}/robidoux.input ${OUT}/roman.input ${OUT}/roots.input \ ${OUT}/ruleset.input ${OUT}/rules.input ${OUT}/rubey.input \ @@ -1029,6 +1031,7 @@ DOCFILES= \ ${DOC}/ribbonsnew.input.dvi \ ${DOC}/richalgebraic000-099.input.dvi \ ${DOC}/richalgebraic100-199.input.dvi \ + ${DOC}/richalgebraic200-299.input.dvi \ ${DOC}/richrational.input.dvi \ ${DOC}/rk4draw.input.dvi \ ${DOC}/robidoux.input.dvi ${DOC}/roman.input.dvi \ diff --git a/src/input/richalgebraic200-299.input.pamphlet b/src/input/richalgebraic200-299.input.pamphlet new file mode 100644 index 0000000..ad9d5f0 --- /dev/null +++ b/src/input/richalgebraic200-299.input.pamphlet @@ -0,0 +1,10313 @@ +\documentclass{article} +\usepackage{axiom} +\begin{document} +\title{\$SPAD/src/input richalgebraic200-299.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f richalgebraic200-299.output +)spool richalgebraic200-299.output +)set message test on +)set message auto off +)clear all + +--S 1 of 554 +t0200:= x^2/(1-a^2-2*a*b*x-b^2*x^2)^(1/2) +--R +--R +--R 2 +--R x +--R (1) --------------------------- +--R +------------------------+ +--R | 2 2 2 +--R \|- b x - 2a b x - a + 1 +--R Type: Expression Integer +--E 1 + +--S 2 of 554 +r0200:= 1/2*(3*a*(1-a^2-2*a*b*x-b^2*x^2)^(1/2)-_ + x*(1-a^2-2*a*b*x-b^2*x^2)^(1/2)*b+asin(a+b*x)+2*a^2*asin(a+b*x))/b^3 +--R +--R +--R +------------------------+ +--R | 2 2 2 2 +--R (- b x + 3a)\|- b x - 2a b x - a + 1 + (2a + 1)asin(b x + a) +--R (2) ---------------------------------------------------------------- +--R 3 +--R 2b +--R Type: Expression Integer +--E 2 + +--S 3 of 554 +a0200:= integrate(t0200,x) +--R +--R +--R (3) +--R +------------------------+ +--------+ +--R 3 4 2 | 2 2 2 | 2 +--R ((8a + 4a)b x + 8a - 4a - 4)\|- b x - 2a b x - a + 1 \|- a + 1 +--R + +--R 4 2 2 5 3 6 4 +--R (8a - 2)b x + (16a - 8a - 8a)b x + 8a - 12a + 4 +--R * +--R +--------+ +------------------------+ +--R | 2 | 2 2 2 +--R \|- a + 1 - \|- b x - 2a b x - a + 1 +--R atan(-----------------------------------------) +--R b x +--R + +--R +--------+ +--R 4 4 3 3 3 2 2 4 2 | 2 +--R (2a b x - 2b x + (- 6a - 3a)b x + (- 4a + 2a + 2)b x)\|- a + 1 +--R + +--R 2 3 3 3 2 2 4 2 +--R ((- 2a + 1)b x + (2a + a)b x + (4a - 2a - 2)b x) +--R * +--R +------------------------+ +--R | 2 2 2 +--R \|- b x - 2a b x - a + 1 +--R / +--R +------------------------+ +--------+ +--R 4 2 3 | 2 2 2 | 2 +--R (4a b x + (4a - 4)b )\|- b x - 2a b x - a + 1 \|- a + 1 +--R + +--R 2 5 2 3 4 4 2 3 +--R (4a - 2)b x + (8a - 8a)b x + (4a - 8a + 4)b +--R Type: Union(Expression Integer,...) +--E 3 + +--S 4 of 554 +m0200:= a0200-r0200 +--R +--R +--R (4) +--R +------------------------+ +--------+ +--R 3 4 2 | 2 2 2 | 2 +--R ((8a + 4a)b x + 8a - 4a - 4)\|- b x - 2a b x - a + 1 \|- a + 1 +--R + +--R 4 2 2 5 3 6 4 +--R (8a - 2)b x + (16a - 8a - 8a)b x + 8a - 12a + 4 +--R * +--R +--------+ +------------------------+ +--R | 2 | 2 2 2 +--R \|- a + 1 - \|- b x - 2a b x - a + 1 +--R atan(-----------------------------------------) +--R b x +--R + +--R 3 4 2 +--R ((- 4a - 2a)b x - 4a + 2a + 2)asin(b x + a) +--R * +--R +------------------------+ +--R | 2 2 2 +--R \|- b x - 2a b x - a + 1 +--R + +--R 3 2 2 4 2 5 3 +--R (6a - 3a)b x + (12a - 12a )b x + 6a - 12a + 6a +--R * +--R +--------+ +--R | 2 +--R \|- a + 1 +--R + +--R +------------------------+ +--R 4 2 5 3 | 2 2 2 +--R ((- 6a + 6a )b x - 6a + 12a - 6a)\|- b x - 2a b x - a + 1 +--R + +--R 4 2 2 5 3 6 4 +--R ((- 4a + 1)b x + (- 8a + 4a + 4a)b x - 4a + 6a - 2)asin(b x + a) +--R / +--R +------------------------+ +--------+ +--R 4 2 3 | 2 2 2 | 2 +--R (4a b x + (4a - 4)b )\|- b x - 2a b x - a + 1 \|- a + 1 +--R + +--R 2 5 2 3 4 4 2 3 +--R (4a - 2)b x + (8a - 8a)b x + (4a - 8a + 4)b +--R Type: Expression Integer +--E 4 + +--S 5 of 554 +d0200:= D(m0200,x) +--R +--R +--R (5) 0 +--R Type: Expression Integer +--E 5 + +--S 6 of 554 +t0201:= x^2/(1+a^2+2*a*b*x+b^2*x^2)^(1/2) +--R +--R +--R 2 +--R x +--R (6) ------------------------- +--R +----------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a + 1 +--R Type: Expression Integer +--E 6 + +--S 7 of 554 +r0201:= -1/2*(3*a*(1+a^2+2*a*b*x+b^2*x^2)^(1/2)-_ + x*(1+a^2+2*a*b*x+b^2*x^2)^(1/2)*b+asinh(a+b*x)-2*a^2*asinh(a+b*x))/b^3 +--R +--R +--R +----------------------+ +--R | 2 2 2 2 +--R (b x - 3a)\|b x + 2a b x + a + 1 + (2a - 1)asinh(b x + a) +--R (7) ------------------------------------------------------------- +--R 3 +--R 2b +--R Type: Expression Integer +--E 7 + +--S 8 of 554 +a0201:= integrate(t0201,x) +--R +--R +--R (8) +--R +----------------------+ +--R 2 3 | 2 2 2 +--R ((- 16a + 8)b x - 16a + 8a)\|b x + 2a b x + a + 1 +--R + +--R 2 2 2 3 4 +--R (16a - 8)b x + (32a - 16a)b x + 16a - 4 +--R * +--R +----------------------+ +--R | 2 2 2 +--R log(\|b x + 2a b x + a + 1 - b x - a) +--R + +--R +----------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (- 8b x + 8a b x + (26a - 4)b x + 10a + 12a)\|b x + 2a b x + a + 1 +--R + +--R 4 4 2 2 2 3 4 2 +--R 8b x + (- 34a + 8)b x + (- 36a - 16a)b x - 10a - 17a +--R / +--R +----------------------+ +--R 4 3 | 2 2 2 5 2 4 +--R (16b x + 16a b )\|b x + 2a b x + a + 1 - 16b x - 32a b x +--R + +--R 2 3 +--R (- 16a - 8)b +--R Type: Union(Expression Integer,...) +--E 8 + +--S 9 of 554 +m0201:= a0201-r0201 +--R +--R +--R (9) +--R +----------------------+ +--R 2 | 2 2 2 +--R (- 8a + 4)log(\|b x + 2a b x + a + 1 - b x - a) +--R + +--R 2 2 +--R (- 8a + 4)asinh(b x + a) - 7a +--R / +--R 3 +--R 8b +--R Type: Expression Integer +--E 9 + +--S 10 of 554 +d0201:= D(m0201,x) +--R +--R +--R (10) 0 +--R Type: Expression Integer +--E 10 + +--S 11 of 554 +t0202:= 1/(x-(1-x^2)^(1/2)) +--R +--R +--R 1 +--R (11) - --------------- +--R +--------+ +--R | 2 +--R \|- x + 1 - x +--R Type: Expression Integer +--E 11 + +--S 12 of 554 +r0202:= -1/2*asin(x)-1/2*atanh(x/(1-x^2)^(1/2))+1/4*log(1-2*x^2) +--R +--R +--R x 2 +--R - 2atanh(-----------) + log(- 2x + 1) - 2asin(x) +--R +--------+ +--R | 2 +--R \|- x + 1 +--R (12) ------------------------------------------------- +--R 4 +--R Type: Expression Integer +--E 12 + +--S 13 of 554 +a0202:= integrate(t0202,x) +--R +--R +--R (13) +--R +--------+ +--R | 2 2 +--R (x - 1)\|- x + 1 - x - x + 1 +--R - log(-------------------------------) +--R 2 +--R x +--R + +--R +--------+ +--------+ +--R | 2 2 | 2 +--R (- x - 1)\|- x + 1 - x + x + 1 \|- x + 1 - 1 +--R log(---------------------------------) + 4atan(---------------) +--R 2 x +--R x +--R + +--R 2 +--R log(2x - 1) +--R / +--R 4 +--R Type: Union(Expression Integer,...) +--E 13 + +--S 14 of 554 +m0202:= a0202-r0202 +--R +--R +--R (14) +--R +--------+ +--R | 2 2 +--R (x - 1)\|- x + 1 - x - x + 1 +--R - log(-------------------------------) +--R 2 +--R x +--R + +--R +--------+ +--R | 2 2 +--R (- x - 1)\|- x + 1 - x + x + 1 x +--R log(---------------------------------) + 2atanh(-----------) +--R 2 +--------+ +--R x | 2 +--R \|- x + 1 +--R + +--R +--------+ +--R | 2 +--R \|- x + 1 - 1 2 2 +--R 4atan(---------------) + log(2x - 1) - log(- 2x + 1) + 2asin(x) +--R x +--R / +--R 4 +--R Type: Expression Integer +--E 14 + +--S 15 of 554 +d0202:= D(m0202,x) +--R +--R +--R (15) 0 +--R Type: Expression Integer +--E 15 + +--S 16 of 554 +t0203:= x/(x-(1-x^2)^(1/2)) +--R +--R +--R x +--R (16) - --------------- +--R +--------+ +--R | 2 +--R \|- x + 1 - x +--R Type: Expression Integer +--E 16 + +--S 17 of 554 +r0203:= 1/2*x+1/2*(1-x^2)^(1/2)-1/4*atanh(x*2^(1/2))*2^(1/2)-_ + 1/4*atanh(2^(1/2)*(1-x^2)^(1/2))*2^(1/2) +--R +--R +--R +--------+ +--------+ +--R +-+ +-+ | 2 | 2 +-+ +-+ +--R - \|2 atanh(\|2 \|- x + 1 ) + 2\|- x + 1 - \|2 atanh(x\|2 ) + 2x +--R (17) ------------------------------------------------------------------- +--R 4 +--R Type: Expression Integer +--E 17 + +--S 18 of 554 +a0203:= integrate(t0203,x) +--R +--R +--R (18) +--R +--------+ +--R | 2 +--R (\|- x + 1 - 1) +--R * +--R +--------+ +--R 2 +-+ 2 | 2 4 2 +-+ 4 2 +--R ((4x - 2)\|2 - 4x )\|- x + 1 + (6x - 5x + 2)\|2 - 8x + 4x +--R log(------------------------------------------------------------------) +--R +--------+ +--R 2 | 2 4 2 +--R (4x - 2)\|- x + 1 + 2x - 5x + 2 +--R + +--R 2 +-+ +--------+ 2 +-+ +--R (2x + 1)\|2 - 4x +-+ | 2 (2x + 1)\|2 - 4x +--R (log(------------------) + 2x\|2 )\|- x + 1 - log(------------------) +--R 2 2 +--R 2x - 1 2x - 1 +--R + +--R 2 +-+ +--R (- 2x - 2x)\|2 +--R / +--R +--------+ +--R +-+ | 2 +-+ +--R 4\|2 \|- x + 1 - 4\|2 +--R Type: Union(Expression Integer,...) +--E 18 + +--S 19 of 554 +m0203:= a0203-r0203 +--R +--R +--R (19) +--R +--------+ +--R 2 +-+ 2 | 2 4 2 +-+ 4 2 +--R ((4x - 2)\|2 - 4x )\|- x + 1 + (6x - 5x + 2)\|2 - 8x + 4x +--R log(------------------------------------------------------------------) +--R +--------+ +--R 2 | 2 4 2 +--R (4x - 2)\|- x + 1 + 2x - 5x + 2 +--R + +--R +--------+ 2 +-+ +--R +-+ | 2 (2x + 1)\|2 - 4x +-+ +-+ +--R 2atanh(\|2 \|- x + 1 ) + log(------------------) + 2atanh(x\|2 ) + 2\|2 +--R 2 +--R 2x - 1 +--R / +--R +-+ +--R 4\|2 +--R Type: Expression Integer +--E 19 + +--S 20 of 554 +d0203:= D(m0203,x) +--R +--R +--R (20) 0 +--R Type: Expression Integer +--E 20 + +--S 21 of 554 +t0204:= 1/(2+b*x^2)^(1/2)/(3+d*x^2)^(1/2) +--R +--R +--R 1 +--R (21) ---------------------- +--R +--------+ +--------+ +--R | 2 | 2 +--R \|b x + 2 \|d x + 3 +--R Type: Expression Integer +--E 21 + +--S 22 of 554 +r0204:= 1/2*EllipticF(asin(1/3*(-d)^(1/2)*x*3^(1/2)),3/2*b/d)*_ + 2^(1/2)/(-d)^(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 +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression Integer +--R Fraction Polynomial 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. +--E 22 + +--S 23 of 554 +a0204:= integrate(t0204,x) +--R +--R +--R x +--R ++ 1 +--R (22) | ---------------------- d%T +--R ++ +--------+ +--------+ +--R | 2 | 2 +--R \|%T b + 2 \|%T d + 3 +--R Type: Union(Expression Integer,...) +--E 23 + +--S 24 of 554 +m0204:= a0204-r0204 +--R +--R +--R x +--R ++ 1 +--R (23) | ---------------------- d%T - r0204 +--R ++ +--------+ +--------+ +--R | 2 | 2 +--R \|%T b + 2 \|%T d + 3 +--R Type: Expression Integer +--E 24 + +--S 25 of 554 +d0204:= D(m0204,x) +--R +--R +--R 1 +--R (24) ---------------------- +--R +--------+ +--------+ +--R | 2 | 2 +--R \|b x + 2 \|d x + 3 +--R Type: Expression Integer +--E 25 + +--S 26 of 554 +t0205:= x/(2+b*x^2)^(1/2)/(3+d*x^2)^(1/2) +--R +--R +--R x +--R (25) ---------------------- +--R +--------+ +--------+ +--R | 2 | 2 +--R \|b x + 2 \|d x + 3 +--R Type: Expression Integer +--E 26 + +--S 27 of 554 +r0205:= atanh(d^(1/2)*(2+b*x^2)^(1/2)/b^(1/2)/(3+d*x^2)^(1/2))/b^(1/2)/d^(1/2) +--R +--R +--R +--------+ +--R +-+ | 2 +--R \|d \|b x + 2 +--R atanh(---------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|d x + 3 +--R (26) ---------------------- +--R +-+ +-+ +--R \|b \|d +--R Type: Expression Integer +--E 27 + +--S 28 of 554 +--a0205:= integrate(t0205,x) +--E 28 + +--S 29 of 554 +--m0205:= a0205-r0205 +--E 29 + +--S 30 of 554 +--d0205:= D(m0205,x) +--E 30 + +--S 31 of 554 +t0206:= x^2/(2+b*x^2)^(1/2)/(3+d*x^2)^(1/2) +--R +--R +--R 2 +--R x +--R (27) ---------------------- +--R +--------+ +--------+ +--R | 2 | 2 +--R \|b x + 2 \|d x + 3 +--R Type: Expression Integer +--E 31 + +--S 32 of 554 +r0206:= 2^(1/2)*(EllipticE(asin(1/3*(-d)^(1/2)*x*3^(1/2)),3/2*b/d)-_ + EllipticF(asin(1/3*(-d)^(1/2)*x*3^(1/2)),3/2*b/d))/b/(-d)^(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 +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression Integer +--R Fraction Polynomial 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. +--E 32 + +--S 33 of 554 +a0206:= integrate(t0206,x) +--R +--R +--R x 2 +--R ++ %T +--R (28) | ---------------------- d%T +--R ++ +--------+ +--------+ +--R | 2 | 2 +--R \|%T b + 2 \|%T d + 3 +--R Type: Union(Expression Integer,...) +--E 33 + +--S 34 of 554 +m0206:= a0206-r0206 +--R +--R +--R x 2 +--R ++ %T +--R (29) | ---------------------- d%T - r0206 +--R ++ +--------+ +--------+ +--R | 2 | 2 +--R \|%T b + 2 \|%T d + 3 +--R Type: Expression Integer +--E 34 + +--S 35 of 554 +d0206:= D(m0206,x) +--R +--R +--R 2 +--R x +--R (30) ---------------------- +--R +--------+ +--------+ +--R | 2 | 2 +--R \|b x + 2 \|d x + 3 +--R Type: Expression Integer +--E 35 + +--S 36 of 554 +t0207:= x/(a+b*x^2)^(1/2)/(c+d*x^2)^(1/2) +--R +--R +--R x +--R (31) ---------------------- +--R +--------+ +--------+ +--R | 2 | 2 +--R \|b x + a \|d x + c +--R Type: Expression Integer +--E 36 + +--S 37 of 554 +r0207:= atanh(d^(1/2)*(a+b*x^2)^(1/2)/b^(1/2)/(c+d*x^2)^(1/2))/b^(1/2)/d^(1/2) +--R +--R +--R +--------+ +--R +-+ | 2 +--R \|d \|b x + a +--R atanh(---------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|d x + c +--R (32) ---------------------- +--R +-+ +-+ +--R \|b \|d +--R Type: Expression Integer +--E 37 + +--S 38 of 554 +--a0207:= integrate(t0207,x) +--E 38 + +--S 39 of 554 +--m0207:= a0207-r0207 +--E 39 + +--S 40 of 554 +--d0207:= D(m0207,x) +--E 40 + +--S 41 of 554 +t0208:= 1/(1-x^2)^(1/2)/(2+3*x^2)^(1/2) +--R +--R +--R 1 +--R (33) --------------------- +--R +--------+ +-------+ +--R | 2 | 2 +--R \|- x + 1 \|3x + 2 +--R Type: Expression Integer +--E 41 + +--S 42 of 554 +r0208:= 1/2*EllipticF(asin(x),3/2)*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 +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression Integer +--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. +--E 42 + +--S 43 of 554 +a0208:= integrate(t0208,x) +--R +--R +--R x +--R ++ 1 +--R (34) | ----------------------- d%T +--R ++ +---------+ +--------+ +--R | 2 | 2 +--R \|- %T + 1 \|3%T + 2 +--R Type: Union(Expression Integer,...) +--E 43 + +--S 44 of 554 +m0208:= a0208-r0208 +--R +--R +--R x +--R ++ 1 +--R (35) | ----------------------- d%T - r0208 +--R ++ +---------+ +--------+ +--R | 2 | 2 +--R \|- %T + 1 \|3%T + 2 +--R Type: Expression Integer +--E 44 + +--S 45 of 554 +d0208:= D(m0208,x) +--R +--R +--R 1 +--R (36) --------------------- +--R +--------+ +-------+ +--R | 2 | 2 +--R \|- x + 1 \|3x + 2 +--R Type: Expression Integer +--E 45 + +--S 46 of 554 +t0209:= 1/(1-x^2)^(1/2)/(2-3*x^2)^(1/2) +--R +--R +--R 1 +--R (37) ----------------------- +--R +---------+ +--------+ +--R | 2 | 2 +--R \|- 3x + 2 \|- x + 1 +--R Type: Expression Integer +--E 46 + +--S 47 of 554 +r0209:= 1/2*EllipticF(asin(x),3/2)*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 +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression Integer +--R Fraction Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 47 + +--S 48 of 554 +a0209:= integrate(t0209,x) +--R +--R +--R x +--R ++ 1 +--R (38) | ------------------------- d%T +--R ++ +----------+ +---------+ +--R | 2 | 2 +--R \|- 3%T + 2 \|- %T + 1 +--R Type: Union(Expression Integer,...) +--E 48 + +--S 49 of 554 +m0209:= a0209-r0209 +--R +--R +--R x +--R ++ 1 +--R (39) | ------------------------- d%T - r0209 +--R ++ +----------+ +---------+ +--R | 2 | 2 +--R \|- 3%T + 2 \|- %T + 1 +--R Type: Expression Integer +--E 49 + +--S 50 of 554 +d0209:= D(m0209,x) +--R +--R +--R 1 +--R (40) ----------------------- +--R +---------+ +--------+ +--R | 2 | 2 +--R \|- 3x + 2 \|- x + 1 +--R Type: Expression Integer +--E 50 + +--S 51 of 554 +t0210:= 1/(4-x^2)^(1/2)/(2+3*x^2)^(1/2) +--R +--R +--R 1 +--R (41) --------------------- +--R +--------+ +-------+ +--R | 2 | 2 +--R \|- x + 4 \|3x + 2 +--R Type: Expression Integer +--E 51 + +--S 52 of 554 +r0210:= 1/2*EllipticF(asin(1/2*x),6)*2^(1/2) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression Integer +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 52 + +--S 53 of 554 +a0210:= integrate(t0210,x) +--R +--R +--R x +--R ++ 1 +--R (42) | ----------------------- d%T +--R ++ +---------+ +--------+ +--R | 2 | 2 +--R \|- %T + 4 \|3%T + 2 +--R Type: Union(Expression Integer,...) +--E 53 + +--S 54 of 554 +m0210:= a0210-r0210 +--R +--R +--R x +--R ++ 1 +--R (43) | ----------------------- d%T - r0210 +--R ++ +---------+ +--------+ +--R | 2 | 2 +--R \|- %T + 4 \|3%T + 2 +--R Type: Expression Integer +--E 54 + +--S 55 of 554 +d0210:= D(m0210,x) +--R +--R +--R 1 +--R (44) --------------------- +--R +--------+ +-------+ +--R | 2 | 2 +--R \|- x + 4 \|3x + 2 +--R Type: Expression Integer +--E 55 + +--S 56 of 554 +t0211:= 1/(4-x^2)^(1/2)/(2-3*x^2)^(1/2) +--R +--R +--R 1 +--R (45) ----------------------- +--R +---------+ +--------+ +--R | 2 | 2 +--R \|- 3x + 2 \|- x + 4 +--R Type: Expression Integer +--E 56 + +--S 57 of 554 +r0211:= 1/2*EllipticF(asin(1/2*x),6)*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 +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression Integer +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 57 + +--S 58 of 554 +a0211:= integrate(t0211,x) +--R +--R +--R x +--R ++ 1 +--R (46) | ------------------------- d%T +--R ++ +----------+ +---------+ +--R | 2 | 2 +--R \|- 3%T + 2 \|- %T + 4 +--R Type: Union(Expression Integer,...) +--E 58 + +--S 59 of 554 +m0211:= a0211-r0211 +--R +--R +--R x +--R ++ 1 +--R (47) | ------------------------- d%T - r0211 +--R ++ +----------+ +---------+ +--R | 2 | 2 +--R \|- 3%T + 2 \|- %T + 4 +--R Type: Expression Integer +--E 59 + +--S 60 of 554 +d0211:= D(m0211,x) +--R +--R +--R 1 +--R (48) ----------------------- +--R +---------+ +--------+ +--R | 2 | 2 +--R \|- 3x + 2 \|- x + 4 +--R Type: Expression Integer +--E 60 + +--S 61 of 554 +t0212:= 1/(1-4*x^2)^(1/2)/(2+3*x^2)^(1/2) +--R +--R +--R 1 +--R (49) ---------------------- +--R +---------+ +-------+ +--R | 2 | 2 +--R \|- 4x + 1 \|3x + 2 +--R Type: Expression Integer +--E 61 + +--S 62 of 554 +r0212:= 1/4*EllipticF(asin(2*x),3/8)*2^(1/2) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression Integer +--R Fraction Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 62 + +--S 63 of 554 +a0212:= integrate(t0212,x) +--R +--R +--R x +--R ++ 1 +--R (50) | ------------------------ d%T +--R ++ +----------+ +--------+ +--R | 2 | 2 +--R \|- 4%T + 1 \|3%T + 2 +--R Type: Union(Expression Integer,...) +--E 63 + +--S 64 of 554 +m0212:= a0212-r0212 +--R +--R +--R x +--R ++ 1 +--R (51) | ------------------------ d%T - r0212 +--R ++ +----------+ +--------+ +--R | 2 | 2 +--R \|- 4%T + 1 \|3%T + 2 +--R Type: Expression Integer +--E 64 + +--S 65 of 554 +d0212:= D(m0212,x) +--R +--R +--R 1 +--R (52) ---------------------- +--R +---------+ +-------+ +--R | 2 | 2 +--R \|- 4x + 1 \|3x + 2 +--R Type: Expression Integer +--E 65 + +--S 66 of 554 +t0213:= 1/(1-4*x^2)^(1/2)/(2-3*x^2)^(1/2) +--R +--R +--R 1 +--R (53) ------------------------ +--R +---------+ +---------+ +--R | 2 | 2 +--R \|- 4x + 1 \|- 3x + 2 +--R Type: Expression Integer +--E 66 + +--S 67 of 554 +r0213:= 1/4*EllipticF(asin(2*x),3/8)*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 +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression Integer +--R Fraction Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 67 + +--S 68 of 554 +a0213:= integrate(t0213,x) +--R +--R +--R x +--R ++ 1 +--R (54) | -------------------------- d%T +--R ++ +----------+ +----------+ +--R | 2 | 2 +--R \|- 4%T + 1 \|- 3%T + 2 +--R Type: Union(Expression Integer,...) +--E 68 + +--S 69 of 554 +m0213:= a0213-r0213 +--R +--R +--R x +--R ++ 1 +--R (55) | -------------------------- d%T - r0213 +--R ++ +----------+ +----------+ +--R | 2 | 2 +--R \|- 4%T + 1 \|- 3%T + 2 +--R Type: Expression Integer +--E 69 + +--S 70 of 554 +d0213:= D(m0213,x) +--R +--R +--R 1 +--R (56) ------------------------ +--R +---------+ +---------+ +--R | 2 | 2 +--R \|- 4x + 1 \|- 3x + 2 +--R Type: Expression Integer +--E 70 + +--S 71 of 554 +t0214:= 1/(1+x^2)^(1/2)/(2+3*x^2)^(1/2) +--R +--R +--R 1 +--R (57) ------------------- +--R +------+ +-------+ +--R | 2 | 2 +--R \|x + 1 \|3x + 2 +--R Type: Expression Integer +--E 71 + +--S 72 of 554 +r0214:= -1/2*%i*EllipticF(%i*asinh(x),3/2)*2^(1/2) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression Complex Integer +--R Fraction Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 72 + +--S 73 of 554 +a0214:= integrate(t0214,x) +--R +--R +--R x +--R ++ 1 +--R (58) | --------------------- d%T +--R ++ +-------+ +--------+ +--R | 2 | 2 +--R \|%T + 1 \|3%T + 2 +--R Type: Union(Expression Integer,...) +--E 73 + +--S 74 of 554 +m0214:= a0214-r0214 +--R +--R +--R x +--R ++ 1 +--R (59) | --------------------- d%T - r0214 +--R ++ +-------+ +--------+ +--R | 2 | 2 +--R \|%T + 1 \|3%T + 2 +--R Type: Expression Integer +--E 74 + +--S 75 of 554 +d0214:= D(m0214,x) +--R +--R +--R 1 +--R (60) ------------------- +--R +------+ +-------+ +--R | 2 | 2 +--R \|x + 1 \|3x + 2 +--R Type: Expression Integer +--E 75 + +--S 76 of 554 +t0215:= 1/(1+x^2)^(1/2)/(2-3*x^2)^(1/2) +--R +--R +--R 1 +--R (61) --------------------- +--R +---------+ +------+ +--R | 2 | 2 +--R \|- 3x + 2 \|x + 1 +--R Type: Expression Integer +--E 76 + +--S 77 of 554 +r0215:= 1/3*EllipticF(asin(1/2*6^(1/2)*x),2/3)*3^(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 +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression Integer +--R Fraction Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 77 + +--S 78 of 554 +a0215:= integrate(t0215,x) +--R +--R +--R x +--R ++ 1 +--R (62) | ----------------------- d%T +--R ++ +----------+ +-------+ +--R | 2 | 2 +--R \|- 3%T + 2 \|%T + 1 +--R Type: Union(Expression Integer,...) +--E 78 + +--S 79 of 554 +m0215:= a0215-r0215 +--R +--R +--R x +--R ++ 1 +--R (63) | ----------------------- d%T - r0215 +--R ++ +----------+ +-------+ +--R | 2 | 2 +--R \|- 3%T + 2 \|%T + 1 +--R Type: Expression Integer +--E 79 + +--S 80 of 554 +d0215:= D(m0215,x) +--R +--R +--R 1 +--R (64) --------------------- +--R +---------+ +------+ +--R | 2 | 2 +--R \|- 3x + 2 \|x + 1 +--R Type: Expression Integer +--E 80 + +--S 81 of 554 +t0216:= 1/(4+x^2)^(1/2)/(2-3*x^2)^(1/2) +--R +--R +--R 1 +--R (65) --------------------- +--R +---------+ +------+ +--R | 2 | 2 +--R \|- 3x + 2 \|x + 4 +--R Type: Expression Integer +--E 81 + +--S 82 of 554 +r0216:= 1/6*EllipticF(asin(1/2*6^(1/2)*x),1/6)*3^(1/2) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression Integer +--R Fraction Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 82 + +--S 83 of 554 +a0216:= integrate(t0216,x) +--R +--R +--R x +--R ++ 1 +--R (66) | ----------------------- d%T +--R ++ +----------+ +-------+ +--R | 2 | 2 +--R \|- 3%T + 2 \|%T + 4 +--R Type: Union(Expression Integer,...) +--E 83 + +--S 84 of 554 +m0216:= a0216-r0216 +--R +--R +--R x +--R ++ 1 +--R (67) | ----------------------- d%T - r0216 +--R ++ +----------+ +-------+ +--R | 2 | 2 +--R \|- 3%T + 2 \|%T + 4 +--R Type: Expression Integer +--E 84 + +--S 85 of 554 +d0216:= D(m0216,x) +--R +--R +--R 1 +--R (68) --------------------- +--R +---------+ +------+ +--R | 2 | 2 +--R \|- 3x + 2 \|x + 4 +--R Type: Expression Integer +--E 85 + +--S 86 of 554 +t0217:= 1/(1+4*x^2)^(1/2)/(2+3*x^2)^(1/2) +--R +--R +--R 1 +--R (69) -------------------- +--R +-------+ +-------+ +--R | 2 | 2 +--R \|3x + 2 \|4x + 1 +--R Type: Expression Integer +--E 86 + +--S 87 of 554 +r0217:= -1/4*%i*EllipticF(%i*asinh(2*x),3/8)*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 +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression Complex Integer +--R Fraction Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 87 + +--S 88 of 554 +a0217:= integrate(t0217,x) +--R +--R +--R x +--R ++ 1 +--R (70) | ---------------------- d%T +--R ++ +--------+ +--------+ +--R | 2 | 2 +--R \|3%T + 2 \|4%T + 1 +--R Type: Union(Expression Integer,...) +--E 88 + +--S 89 of 554 +m0217:= a0217-r0217 +--R +--R +--R x +--R ++ 1 +--R (71) | ---------------------- d%T - r0217 +--R ++ +--------+ +--------+ +--R | 2 | 2 +--R \|3%T + 2 \|4%T + 1 +--R Type: Expression Integer +--E 89 + +--S 90 of 554 +d0217:= D(m0217,x) +--R +--R +--R 1 +--R (72) -------------------- +--R +-------+ +-------+ +--R | 2 | 2 +--R \|3x + 2 \|4x + 1 +--R Type: Expression Integer +--E 90 + +--S 91 of 554 +t0218:= 1/(1+4*x^2)^(1/2)/(2-3*x^2)^(1/2) +--R +--R +--R 1 +--R (73) ---------------------- +--R +---------+ +-------+ +--R | 2 | 2 +--R \|- 3x + 2 \|4x + 1 +--R Type: Expression Integer +--E 91 + +--S 92 of 554 +r0218:= 1/3*EllipticF(asin(1/2*6^(1/2)*x),8/3)*3^(1/2) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression Integer +--R Fraction Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 92 + +--S 93 of 554 +a0218:= integrate(t0218,x) +--R +--R +--R x +--R ++ 1 +--R (74) | ------------------------ d%T +--R ++ +----------+ +--------+ +--R | 2 | 2 +--R \|- 3%T + 2 \|4%T + 1 +--R Type: Union(Expression Integer,...) +--E 93 + +--S 94 of 554 +m0218:= a0218-r0218 +--R +--R +--R x +--R ++ 1 +--R (75) | ------------------------ d%T - r0218 +--R ++ +----------+ +--------+ +--R | 2 | 2 +--R \|- 3%T + 2 \|4%T + 1 +--R Type: Expression Integer +--E 94 + +--S 95 of 554 +d0218:= D(m0218,x) +--R +--R +--R 1 +--R (76) ---------------------- +--R +---------+ +-------+ +--R | 2 | 2 +--R \|- 3x + 2 \|4x + 1 +--R Type: Expression Integer +--E 95 + +--S 96 of 554 +t0219:= 1/(1-x^2)^(1/2)/(-1+2*x^2)^(1/2) +--R +--R +--R 1 +--R (77) --------------------- +--R +--------+ +-------+ +--R | 2 | 2 +--R \|- x + 1 \|2x - 1 +--R Type: Expression Integer +--E 96 + +--S 97 of 554 +r0219:= -EllipticF(acos(x),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 +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression Integer +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 97 + +--S 98 of 554 +a0219:= integrate(t0219,x) +--R +--R +--R x +--R ++ 1 +--R (78) | ----------------------- d%T +--R ++ +---------+ +--------+ +--R | 2 | 2 +--R \|- %T + 1 \|2%T - 1 +--R Type: Union(Expression Integer,...) +--E 98 + +--S 99 of 554 +m0219:= a0219-r0219 +--R +--R +--R x +--R ++ 1 +--R (79) | ----------------------- d%T - r0219 +--R ++ +---------+ +--------+ +--R | 2 | 2 +--R \|- %T + 1 \|2%T - 1 +--R Type: Expression Integer +--E 99 + +--S 100 of 554 +d0219:= D(m0219,x) +--R +--R +--R 1 +--R (80) --------------------- +--R +--------+ +-------+ +--R | 2 | 2 +--R \|- x + 1 \|2x - 1 +--R Type: Expression Integer +--E 100 + +--S 101 of 554 +t0220:= 1/(-1+x)^(1/2)/(1+x)^(1/2)/(-1+2*x^2)^(1/2) +--R +--R +--R 1 +--R (81) -------------------------- +--R +-------+ +--R +-----+ +-----+ | 2 +--R \|x - 1 \|x + 1 \|2x - 1 +--R Type: Expression Integer +--E 101 + +--S 102 of 554 +r0220:= -%i*EllipticF(%i*acosh(x),2) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression Complex Integer +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 102 + +--S 103 of 554 +a0220:= integrate(t0220,x) +--R +--R +--R x +--R ++ 1 +--R (82) | ----------------------------- d%T +--R ++ +--------+ +--R +------+ +------+ | 2 +--R \|%T - 1 \|%T + 1 \|2%T - 1 +--R Type: Union(Expression Integer,...) +--E 103 + +--S 104 of 554 +m0220:= a0220-r0220 +--R +--R +--R x +--R ++ 1 +--R (83) | ----------------------------- d%T - r0220 +--R ++ +--------+ +--R +------+ +------+ | 2 +--R \|%T - 1 \|%T + 1 \|2%T - 1 +--R Type: Expression Integer +--E 104 + +--S 105 of 554 +d0220:= D(m0220,x) +--R +--R +--R 1 +--R (84) -------------------------- +--R +-------+ +--R +-----+ +-----+ | 2 +--R \|x - 1 \|x + 1 \|2x - 1 +--R Type: Expression Integer +--E 105 + +--S 106 of 554 +t0221:= (2+b*x^2)^(1/2)/(3+d*x^2)^(1/2) +--R +--R +--R +--------+ +--R | 2 +--R \|b x + 2 +--R (85) ----------- +--R +--------+ +--R | 2 +--R \|d x + 3 +--R Type: Expression Integer +--E 106 + +--S 107 of 554 +r0221:= 2^(1/2)*EllipticE(asin(1/3*(-d)^(1/2)*x*3^(1/2)),3/2*b/d)/(-d)^(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 +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression Integer +--R Fraction Polynomial 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. +--E 107 + +--S 108 of 554 +a0221:= integrate(t0221,x) +--R +--R +--R +--------+ +--R x | 2 +--R ++ \|%T b + 2 +--R (86) | ----------- d%T +--R ++ +--------+ +--R | 2 +--R \|%T d + 3 +--R Type: Union(Expression Integer,...) +--E 108 + +--S 109 of 554 +m0221:= a0221-r0221 +--R +--R +--R +--------+ +--R x | 2 +--R ++ \|%T b + 2 +--R (87) | ----------- d%T - r0221 +--R ++ +--------+ +--R | 2 +--R \|%T d + 3 +--R Type: Expression Integer +--E 109 + +--S 110 of 554 +d0221:= D(m0221,x) +--R +--R +--R +--------+ +--R | 2 +--R \|b x + 2 +--R (88) ----------- +--R +--------+ +--R | 2 +--R \|d x + 3 +--R Type: Expression Integer +--E 110 + +--S 111 of 554 +t0222:= x*(2+b*x^2)^(1/2)/(3+d*x^2)^(1/2) +--R +--R +--R +--------+ +--R | 2 +--R x\|b x + 2 +--R (89) ------------ +--R +--------+ +--R | 2 +--R \|d x + 3 +--R Type: Expression Integer +--E 111 + +--S 112 of 554 +r0222:= 1/2*(2+b*x^2)^(1/2)*(3+d*x^2)^(1/2)/d-1/2*(3*b-2*d)*_ + atanh(d^(1/2)*(2+b*x^2)^(1/2)/b^(1/2)/(3+d*x^2)^(1/2))/b^(1/2)/d^(3/2) +--R +--R +--R +--------+ +--R +-+ | 2 +--------+ +--------+ +--R \|d \|b x + 2 +-+ +-+ | 2 | 2 +--R (2d - 3b)atanh(---------------) + \|b \|d \|b x + 2 \|d x + 3 +--R +--------+ +--R +-+ | 2 +--R \|b \|d x + 3 +--R (90) ---------------------------------------------------------------- +--R +-+ +-+ +--R 2d\|b \|d +--R Type: Expression Integer +--E 112 + +--S 113 of 554 +--a0222:= integrate(t0222,x) +--E 113 + +--S 114 of 554 +--m0222:= a0222-r0222 +--E 114 + +--S 115 of 554 +--d0222:= D(m0222,x) +--E 115 + +--S 116 of 554 +t0223:= x^2*(2+b*x^2)^(1/2)/(3+d*x^2)^(1/2) +--R +--R +--R +--------+ +--R 2 | 2 +--R x \|b x + 2 +--R (91) ------------- +--R +--------+ +--R | 2 +--R \|d x + 3 +--R Type: Expression Integer +--E 116 + +--S 117 of 554 +r0223:= 1/3*x*(2+b*x^2)^(1/2)*(3+d*x^2)^(1/2)/d-_ + 2/3*(3*b-d)*EllipticE(asin(1/2*(-b)^(1/2)*x*2^(1/2)),2/3*d/b)*_ + 3^(1/2)/(-b)^(1/2)/d^2+2^(1/2)*(3*b-2*d)*_ + EllipticF(asin(1/3*(-d)^(1/2)*x*3^(1/2)),3/2*b/d)/(-d)^(5/2) +--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 +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression Integer +--R Fraction Polynomial 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. +--E 117 + +--S 118 of 554 +a0223:= integrate(t0223,x) +--R +--R +--R +--------+ +--R x 2 | 2 +--R ++ %T \|%T b + 2 +--R (92) | -------------- d%T +--R ++ +--------+ +--R | 2 +--R \|%T d + 3 +--R Type: Union(Expression Integer,...) +--E 118 + +--S 119 of 554 +m0223:= a0223-r0223 +--R +--R +--R +--------+ +--R x 2 | 2 +--R ++ %T \|%T b + 2 +--R (93) | -------------- d%T - r0223 +--R ++ +--------+ +--R | 2 +--R \|%T d + 3 +--R Type: Expression Integer +--E 119 + +--S 120 of 554 +d0223:= D(m0223,x) +--R +--R +--R +--------+ +--R 2 | 2 +--R x \|b x + 2 +--R (94) ------------- +--R +--------+ +--R | 2 +--R \|d x + 3 +--R Type: Expression Integer +--E 120 + +--S 121 of 554 +t0224:= (a+b*x^2)^(1/2)/(c+d*x^2)^(1/2) +--R +--R +--R +--------+ +--R | 2 +--R \|b x + a +--R (95) ----------- +--R +--------+ +--R | 2 +--R \|d x + c +--R Type: Expression Integer +--E 121 + +--S 122 of 554 +r0224:= c^(1/2)*(a+b*x^2)^(1/2)*((c+d*x^2)/c)^(1/2)*_ + EllipticE(asin((-d)^(1/2)*x/c^(1/2)),b*c/a/d)/(-d)^(1/2)/_ + ((a+b*x^2)/a)^(1/2)/(c+d*x^2)^(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 +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression 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. +--E 122 + +--S 123 of 554 +a0224:= integrate(t0224,x) +--R +--R +--R +--------+ +--R x | 2 +--R ++ \|%T b + a +--R (96) | ----------- d%T +--R ++ +--------+ +--R | 2 +--R \|%T d + c +--R Type: Union(Expression Integer,...) +--E 123 + +--S 124 of 554 +m0224:= a0224-r0224 +--R +--R +--R +--------+ +--R x | 2 +--R ++ \|%T b + a +--R (97) | ----------- d%T - r0224 +--R ++ +--------+ +--R | 2 +--R \|%T d + c +--R Type: Expression Integer +--E 124 + +--S 125 of 554 +d0224:= D(m0224,x) +--R +--R +--R +--------+ +--R | 2 +--R \|b x + a +--R (98) ----------- +--R +--------+ +--R | 2 +--R \|d x + c +--R Type: Expression Integer +--E 125 + +--S 126 of 554 +t0225:= x*(a+b*x^2)^(1/2)/(c+d*x^2)^(1/2) +--R +--R +--R +--------+ +--R | 2 +--R x\|b x + a +--R (99) ------------ +--R +--------+ +--R | 2 +--R \|d x + c +--R Type: Expression Integer +--E 126 + +--S 127 of 554 +r0225:= 1/2*(a+b*x^2)^(1/2)*(c+d*x^2)^(1/2)/d-1/2*(b*c-a*d)*_ + atanh(d^(1/2)*(a+b*x^2)^(1/2)/b^(1/2)/(c+d*x^2)^(1/2))/b^(1/2)/d^(3/2) +--R +--R +--R +--------+ +--R +-+ | 2 +--------+ +--------+ +--R \|d \|b x + a +-+ +-+ | 2 | 2 +--R (a d - b c)atanh(---------------) + \|b \|d \|b x + a \|d x + c +--R +--------+ +--R +-+ | 2 +--R \|b \|d x + c +--R (100) ------------------------------------------------------------------ +--R +-+ +-+ +--R 2d\|b \|d +--R Type: Expression Integer +--E 127 + +--S 128 of 554 +--a0225:= integrate(t0225,x) +--E 128 + +--S 129 of 554 +--m0225:= a0225-r0225 +--E 129 + +--S 130 of 554 +--d0225:= D(m0225,x) +--E 130 + +--S 131 of 554 +t0226:= x^2*(a+b*x^2)^(1/2)/(c+d*x^2)^(1/2) +--R +--R +--R +--------+ +--R 2 | 2 +--R x \|b x + a +--R (101) ------------- +--R +--------+ +--R | 2 +--R \|d x + c +--R Type: Expression Integer +--E 131 + +--S 132 of 554 +r0226:= 1/3*x*(a+b*x^2)^(1/2)*(c+d*x^2)^(1/2)/d+1/3*%i*c*(2*b*c-a*d)*_ + (1+b*x^2/a)^(1/2)*(1+d*x^2/c)^(1/2)*_ + EllipticE(%i*asinh((b/a)^(1/2)*x),a*d/b/c)/(b/a)^(1/2)/d^2/_ + (a+b*x^2)^(1/2)/(c+d*x^2)^(1/2)-2/3*%i*c*(b*c-a*d)*_ + (1+b*x^2/a)^(1/2)*(1+d*x^2/c)^(1/2)*_ + EllipticF(%i*asinh((b/a)^(1/2)*x),a*d/b/c)/(b/a)^(1/2)/_ + d^2/(a+b*x^2)^(1/2)/(c+d*x^2)^(1/2) +--R +--R There are 35 exposed and 23 unexposed library operations named * +--R having 2 argument(s) but none was determined to be applicable. +--R Use HyperDoc Browse, or issue +--R )display op * +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named * +--R with argument type(s) +--R Polynomial Complex Fraction Integer +--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. +--E 132 + +--S 133 of 554 +a0226:= integrate(t0226,x) +--R +--R +--R +--------+ +--R x 2 | 2 +--R ++ %T \|%T b + a +--R (102) | -------------- d%T +--R ++ +--------+ +--R | 2 +--R \|%T d + c +--R Type: Union(Expression Integer,...) +--E 133 + +--S 134 of 554 +m0226:= a0226-r0226 +--R +--R +--R +--------+ +--R x 2 | 2 +--R ++ %T \|%T b + a +--R (103) | -------------- d%T - r0226 +--R ++ +--------+ +--R | 2 +--R \|%T d + c +--R Type: Expression Integer +--E 134 + +--S 135 of 554 +d0226:= D(m0226,x) +--R +--R +--R +--------+ +--R 2 | 2 +--R x \|b x + a +--R (104) ------------- +--R +--------+ +--R | 2 +--R \|d x + c +--R Type: Expression Integer +--E 135 + +--S 136 of 554 +t0227:= (x-(-4+x^2)^(1/2))^(1/2) +--R +--R +--R +---------------+ +--R | +------+ +--R | | 2 +--R (105) \|- \|x - 4 + x +--R Type: Expression Integer +--E 136 + +--S 137 of 554 +r0227:= 2/3*(x-(-4+x^2)^(1/2))^(1/2)*(2*x+(-4+x^2)^(1/2)) +--R +--R +--R +---------------+ +--R +------+ | +------+ +--R | 2 | | 2 +--R (2\|x - 4 + 4x)\|- \|x - 4 + x +--R (106) ----------------------------------- +--R 3 +--R Type: Expression Integer +--E 137 + +--S 138 of 554 +a0227:= integrate(t0227,x) +--R +--R +--R +------+ +--R | 2 2 +--R - 2x\|x - 4 + 2x + 8 +--R (107) ----------------------- +--R +---------------+ +--R | +------+ +--R | | 2 +--R 3\|- \|x - 4 + x +--R Type: Union(Expression Integer,...) +--E 138 + +--S 139 of 554 +m0227:= a0227-r0227 +--R +--R +--R (108) 0 +--R Type: Expression Integer +--E 139 + +--S 140 of 554 +d0227:= D(m0227,x) +--R +--R +--R (109) 0 +--R Type: Expression Integer +--E 140 + +--S 141 of 554 +t0228:= (1+(1-x^2)^(1/2))^(1/2) +--R +--R +--R +---------------+ +--R | +--------+ +--R | | 2 +--R (110) \|\|- x + 1 + 1 +--R Type: Expression Integer +--E 141 + +--S 142 of 554 +r0228:= 2/3*(1+x^2-(1-x^2)^(1/2))*(1+(1-x^2)^(1/2))^(1/2)/x +--R +--R +--R +---------------+ +--R +--------+ | +--------+ +--R | 2 2 | | 2 +--R (- 2\|- x + 1 + 2x + 2)\|\|- x + 1 + 1 +--R (111) -------------------------------------------- +--R 3x +--R Type: Expression Integer +--E 142 + +--S 143 of 554 +a0228:= integrate(t0228,x) +--R +--R +--R +---------------+ +--R +--------+ | +--------+ +--R | 2 2 | | 2 +--R (- 2\|- x + 1 + 2x + 2)\|\|- x + 1 + 1 +--R (112) -------------------------------------------- +--R 3x +--R Type: Union(Expression Integer,...) +--E 143 + +--S 144 of 554 +m0228:= a0228-r0228 +--R +--R +--R (113) 0 +--R Type: Expression Integer +--E 144 + +--S 145 of 554 +d0228:= D(m0228,x) +--R +--R +--R (114) 0 +--R Type: Expression Integer +--E 145 + +--S 146 of 554 +t0229:= (-1+4*x^2)^(1/2)/(x+(-1+4*x^2)^(1/2)) +--R +--R +--R +-------+ +--R | 2 +--R \|4x - 1 +--R (115) -------------- +--R +-------+ +--R | 2 +--R \|4x - 1 + x +--R Type: Expression Integer +--E 146 + +--S 147 of 554 +r0229:= 4/3*x-1/3*(-1+4*x^2)^(1/2)-1/9*atanh(3^(1/2)*x)*3^(1/2)+_ + 1/9*atanh(3^(1/2)*(-1+4*x^2)^(1/2))*3^(1/2) +--R +--R +--R +-------+ +-------+ +--R +-+ +-+ | 2 | 2 +-+ +-+ +--R \|3 atanh(\|3 \|4x - 1 ) - 3\|4x - 1 - \|3 atanh(x\|3 ) + 12x +--R (116) ---------------------------------------------------------------- +--R 9 +--R Type: Expression Integer +--E 147 + +--S 148 of 554 +a0229:= integrate(t0229,x) +--R +--R +--R (117) +--R +-------+ +--R | 2 +--R (\|4x - 1 - 2x) +--R * +--R log +--R +-------+ +--R 3 +-+ 2 | 2 4 2 +-+ +--R ((24x - 4x)\|3 - 24x + 3)\|4x - 1 + (- 48x + 14x - 1)\|3 +--R + +--R 3 +--R 48x - 12x +--R / +--R +-------+ +--R 3 | 2 4 2 +--R (12x - 4x)\|4x - 1 - 24x + 11x - 1 +--R + +--R 2 +-+ +-------+ +--R (3x + 1)\|3 - 6x +-+ | 2 +--R (log(------------------) + 12x\|3 )\|4x - 1 +--R 2 +--R 3x - 1 +--R + +--R 2 +-+ +--R (3x + 1)\|3 - 6x 2 +-+ +--R - 2x log(------------------) + (- 24x + 2)\|3 +--R 2 +--R 3x - 1 +--R / +--R +-------+ +--R +-+ | 2 +-+ +--R 6\|3 \|4x - 1 - 12x\|3 +--R Type: Union(Expression Integer,...) +--E 148 + +--S 149 of 554 +m0229:= a0229-r0229 +--R +--R +--R (118) +--R log +--R +-------+ +--R 3 +-+ 2 | 2 4 2 +-+ +--R ((24x - 4x)\|3 - 24x + 3)\|4x - 1 + (- 48x + 14x - 1)\|3 +--R + +--R 3 +--R 48x - 12x +--R / +--R +-------+ +--R 3 | 2 4 2 +--R (12x - 4x)\|4x - 1 - 24x + 11x - 1 +--R + +--R +-------+ 2 +-+ +--R +-+ | 2 (3x + 1)\|3 - 6x +-+ +--R - 2atanh(\|3 \|4x - 1 ) + log(------------------) + 2atanh(x\|3 ) +--R 2 +--R 3x - 1 +--R / +--R +-+ +--R 6\|3 +--R Type: Expression Integer +--E 149 + +--S 150 of 554 +d0229:= D(m0229,x) +--R +--R +--R (119) 0 +--R Type: Expression Integer +--E 150 + +--S 151 of 554 +t0230:= (-1+x+x^2)/(1+(1+x^2)^(1/2)) +--R +--R +--R 2 +--R x + x - 1 +--R (120) ------------- +--R +------+ +--R | 2 +--R \|x + 1 + 1 +--R Type: Expression Integer +--E 151 + +--S 152 of 554 +r0230:= -1/x-x+(1+1/x+1/2*x)*(1+x^2)^(1/2)-1/2*asinh(x)-log(1+(1+x^2)^(1/2)) +--R +--R +--R (121) +--R +------+ +------+ +--R | 2 2 | 2 2 +--R - 2x log(\|x + 1 + 1) + (x + 2x + 2)\|x + 1 - x asinh(x) - 2x - 2 +--R ----------------------------------------------------------------------- +--R 2x +--R Type: Expression Integer +--E 152 + +--S 153 of 554 +a0230:= integrate(t0230,x) +--R +--R +--R (122) +--R +------+ +------+ +--R 3 | 2 4 2 | 2 +--R ((- 8x - 2x)\|x + 1 + 8x + 6x )log(\|x + 1 - x + 1) +--R + +--R +------+ +------+ +--R 3 | 2 4 2 | 2 +--R ((4x + x)\|x + 1 - 4x - 3x )log(\|x + 1 - x) +--R + +--R +------+ +------+ +--R 3 | 2 4 2 | 2 +--R ((8x + 2x)\|x + 1 - 8x - 6x )log(\|x + 1 - x - 1) +--R + +--R +------+ +--R 3 5 4 3 2 | 2 +--R ((- 8x - 2x)log(x) - 4x - 16x - 3x - 16x - 4x - 2)\|x + 1 +--R + +--R 4 2 6 5 4 3 2 +--R (8x + 6x )log(x) + 4x + 16x + 5x + 24x + 5x + 8x + 2 +--R / +--R +------+ +--R 3 | 2 4 2 +--R (8x + 2x)\|x + 1 - 8x - 6x +--R Type: Union(Expression Integer,...) +--E 153 + +--S 154 of 554 +m0230:= a0230-r0230 +--R +--R +--R (123) +--R +------+ +------+ +------+ +--R | 2 | 2 | 2 +--R 2log(\|x + 1 + 1) - 2log(\|x + 1 - x + 1) + log(\|x + 1 - x) +--R + +--R +------+ +--R | 2 +--R 2log(\|x + 1 - x - 1) - 2log(x) + asinh(x) + 2 +--R / +--R 2 +--R Type: Expression Integer +--E 154 + +--S 155 of 554 +d0230:= D(m0230,x) +--R +--R +--R (124) 0 +--R Type: Expression Integer +--E 155 + +--S 156 of 554 +t0231:= (-1+x+x^2)/(1+x+(1+x^2)^(1/2)) +--R +--R +--R 2 +--R x + x - 1 +--R (125) ----------------- +--R +------+ +--R | 2 +--R \|x + 1 + x + 1 +--R Type: Expression Integer +--E 156 + +--S 157 of 554 +r0231:= 1/2*x^2+1/6*x^3+1/12*(4-3*x-2*x^2)*(1+x^2)^(1/2)-_ + 1/4*asinh(x)-1/2*log(1+(1+x^2)^(1/2)) +--R +--R +--R (126) +--R +------+ +------+ +--R | 2 2 | 2 3 2 +--R - 6log(\|x + 1 + 1) + (- 2x - 3x + 4)\|x + 1 - 3asinh(x) + 2x + 6x +--R ------------------------------------------------------------------------- +--R 12 +--R Type: Expression Integer +--E 157 + +--S 158 of 554 +a0231:= integrate(t0231,x) +--R +--R +--R (127) +--R +------+ +------+ +--R 2 | 2 3 | 2 +--R ((- 24x - 6)\|x + 1 + 24x + 18x)log(\|x + 1 - x + 1) +--R + +--R +------+ +------+ +--R 2 | 2 3 | 2 +--R ((12x + 3)\|x + 1 - 12x - 9x)log(\|x + 1 - x) +--R + +--R +------+ +------+ +--R 2 | 2 3 | 2 +--R ((24x + 6)\|x + 1 - 24x - 18x)log(\|x + 1 - x - 1) +--R + +--R +------+ +--R 2 5 4 3 2 | 2 +--R ((- 24x - 6)log(x) + 16x + 36x - 8x + 15x - 12x)\|x + 1 +--R + +--R 3 6 5 3 2 +--R (24x + 18x)log(x) - 16x - 36x - 33x + 18x - 3x + 4 +--R / +--R +------+ +--R 2 | 2 3 +--R (48x + 12)\|x + 1 - 48x - 36x +--R Type: Union(Expression Integer,...) +--E 158 + +--S 159 of 554 +m0231:= a0231-r0231 +--R +--R +--R (128) +--R +------+ +------+ +------+ +--R | 2 | 2 | 2 +--R 2log(\|x + 1 + 1) - 2log(\|x + 1 - x + 1) + log(\|x + 1 - x) +--R + +--R +------+ +--R | 2 +--R 2log(\|x + 1 - x - 1) - 2log(x) + asinh(x) +--R / +--R 4 +--R Type: Expression Integer +--E 159 + +--S 160 of 554 +d0231:= D(m0231,x) +--R +--R +--R (129) 0 +--R Type: Expression Integer +--E 160 + +--S 161 of 554 +t0232:= x/(1-x^3)^(2/3) +--R +--R +--R x +--R (130) ------------ +--R +--------+2 +--R 3| 3 +--R \|- x + 1 +--R Type: Expression Integer +--E 161 + +--S 162 of 554 +r0232:= -1/3*atan(1/3*(1-2*x/(1-x^3)^(1/3))*3^(1/2))*3^(1/2)+_ + 1/6*log(1+x^2/(1-x^3)^(2/3)-x/(1-x^3)^(1/3))-1/3*log(1+x/(1-x^3)^(1/3)) +--R +--R +--R (131) +--R +--------+ +--------+2 +--------+ +--R 3| 3 3| 3 3| 3 2 +--R \|- x + 1 + x \|- x + 1 - x\|- x + 1 + x +--R - 2log(---------------) + log(--------------------------------) +--R +--------+ +--------+2 +--R 3| 3 3| 3 +--R \|- x + 1 \|- x + 1 +--R + +--R +--------+ +--R +-+3| 3 +-+ +--R +-+ \|3 \|- x + 1 - 2x\|3 +--R - 2\|3 atan(------------------------) +--R +--------+ +--R 3| 3 +--R 3\|- x + 1 +--R / +--R 6 +--R Type: Expression Integer +--E 162 + +--S 163 of 554 +a0232:= integrate(t0232,x) +--R +--R +--R (132) +--R +--------+2 +--------+ +--------+ +--R 3| 3 3| 3 2 3| 3 +--R +-+ \|- x + 1 - x\|- x + 1 + x +-+ \|- x + 1 + x +--R \|3 log(--------------------------------) - 2\|3 log(---------------) +--R 2 x +--R x +--R + +--R +--------+ +--R +-+3| 3 +-+ +--R 2\|3 \|- x + 1 - x\|3 +--R - 6atan(------------------------) +--R 3x +--R / +--R +-+ +--R 6\|3 +--R Type: Union(Expression Integer,...) +--E 163 + +--S 164 of 554 +m0232:= a0232-r0232 +--R +--R +--R (133) +--R +--------+2 +--------+ +--------+ +--R 3| 3 3| 3 2 3| 3 +--R +-+ \|- x + 1 - x\|- x + 1 + x +-+ \|- x + 1 + x +--R \|3 log(--------------------------------) - 2\|3 log(---------------) +--R 2 x +--R x +--R + +--R +--------+ +--------+2 +--------+ +--R 3| 3 3| 3 3| 3 2 +--R +-+ \|- x + 1 + x +-+ \|- x + 1 - x\|- x + 1 + x +--R 2\|3 log(---------------) - \|3 log(--------------------------------) +--R +--------+ +--------+2 +--R 3| 3 3| 3 +--R \|- x + 1 \|- x + 1 +--R + +--R +--------+ +--------+ +--R +-+3| 3 +-+ +-+3| 3 +-+ +--R 2\|3 \|- x + 1 - x\|3 \|3 \|- x + 1 - 2x\|3 +--R - 6atan(------------------------) + 6atan(------------------------) +--R 3x +--------+ +--R 3| 3 +--R 3\|- x + 1 +--R / +--R +-+ +--R 6\|3 +--R Type: Expression Integer +--E 164 + +--S 165 of 554 +d0232:= D(m0232,x) +--R +--R +--R (134) 0 +--R Type: Expression Integer +--E 165 + +--S 166 of 554 +t0233:= x*(1-x^3)^(1/3) +--R +--R +--R +--------+ +--R 3| 3 +--R (135) x\|- x + 1 +--R Type: Expression Integer +--E 166 + +--S 167 of 554 +r0233:= 1/3*x^2*(1-x^3)^(1/3)-1/9*atan(1/3*(1-2*x/(1-x^3)^(1/3))*3^(1/2))*_ + 3^(1/2)+1/18*log(1+x^2/(1-x^3)^(2/3)-x/(1-x^3)^(1/3))-_ + 1/9*log(1+x/(1-x^3)^(1/3)) +--R +--R +--R (136) +--R +--------+ +--------+2 +--------+ +--R 3| 3 3| 3 3| 3 2 +--R \|- x + 1 + x \|- x + 1 - x\|- x + 1 + x +--R - 2log(---------------) + log(--------------------------------) +--R +--------+ +--------+2 +--R 3| 3 3| 3 +--R \|- x + 1 \|- x + 1 +--R + +--R +--------+ +--R +-+3| 3 +-+ +--------+ +--R +-+ \|3 \|- x + 1 - 2x\|3 2 3| 3 +--R - 2\|3 atan(------------------------) + 6x \|- x + 1 +--R +--------+ +--R 3| 3 +--R 3\|- x + 1 +--R / +--R 18 +--R Type: Expression Integer +--E 167 + +--S 168 of 554 +a0233:= integrate(t0233,x) +--R +--R +--R (137) +--R +--------+2 +--------+ +--------+ +--R 3| 3 3| 3 2 3| 3 +--R +-+ \|- x + 1 - x\|- x + 1 + x +-+ \|- x + 1 + x +--R \|3 log(--------------------------------) - 2\|3 log(---------------) +--R 2 x +--R x +--R + +--R +--------+ +--R +-+3| 3 +-+ +--------+ +--R 2\|3 \|- x + 1 - x\|3 2 +-+3| 3 +--R - 6atan(------------------------) + 6x \|3 \|- x + 1 +--R 3x +--R / +--R +-+ +--R 18\|3 +--R Type: Union(Expression Integer,...) +--E 168 + +--S 169 of 554 +m0233:= a0233-r0233 +--R +--R +--R (138) +--R +--------+2 +--------+ +--------+ +--R 3| 3 3| 3 2 3| 3 +--R +-+ \|- x + 1 - x\|- x + 1 + x +-+ \|- x + 1 + x +--R \|3 log(--------------------------------) - 2\|3 log(---------------) +--R 2 x +--R x +--R + +--R +--------+ +--------+2 +--------+ +--R 3| 3 3| 3 3| 3 2 +--R +-+ \|- x + 1 + x +-+ \|- x + 1 - x\|- x + 1 + x +--R 2\|3 log(---------------) - \|3 log(--------------------------------) +--R +--------+ +--------+2 +--R 3| 3 3| 3 +--R \|- x + 1 \|- x + 1 +--R + +--R +--------+ +--------+ +--R +-+3| 3 +-+ +-+3| 3 +-+ +--R 2\|3 \|- x + 1 - x\|3 \|3 \|- x + 1 - 2x\|3 +--R - 6atan(------------------------) + 6atan(------------------------) +--R 3x +--------+ +--R 3| 3 +--R 3\|- x + 1 +--R / +--R +-+ +--R 18\|3 +--R Type: Expression Integer +--E 169 + +--S 170 of 554 +d0233:= D(m0233,x) +--R +--R +--R (139) 0 +--R Type: Expression Integer +--E 170 + +--S 171 of 554 +t0234:= (a+b*x^4)^(3/2) +--R +--R +--R +--------+ +--R 4 | 4 +--R (140) (b x + a)\|b x + a +--R Type: Expression Integer +--E 171 + +--S 172 of 554 +r0234:= 2/7*a*x*(a+b*x^4)^(1/2)+1/7*x*(a+b*x^4)^(3/2)+4/7*a^(9/4)*_ + ((a+b*x^4)/a)^(1/2)*atanh(asin((-b)^(1/4)*x/a^(1/4)))/_ + (-b)^(1/4)/(a+b*x^4)^(1/2) +--R +--R +--R (141) +--R +--------+ +--R | 4 4+---+ +--R 2 4+-+ |b x + a x\|- b 2 9 5 2 4+---+ +--R 4a \|a |-------- atanh(asin(-------) + (b x + 4a b x + 3a x)\|- b +--R \| a 4+-+ +--R \|a +--R ---------------------------------------------------------------------- +--R +--------+ +--R 4+---+ | 4 +--R 7\|- b \|b x + a +--R Type: Expression Integer +--E 172 + +--S 173 of 554 +a0234:= integrate(t0234,x) +--R +--R +--R x +--------+ +--R ++ 4 | 4 +--R (142) | (%T b + a)\|%T b + a d%T +--R ++ +--R Type: Union(Expression Integer,...) +--E 173 + +--S 174 of 554 +m0234:= a0234-r0234 +--R +--R +--R (143) +--R +--------+ +--R | 4 4+---+ +--R 2 4+-+ |b x + a x\|- b +--R - 4a \|a |-------- atanh(asin(-------)) +--R \| a 4+-+ +--R \|a +--R + +--R +--------+ x +--------+ +--R 4+---+ | 4 ++ 4 | 4 +--R 7\|- b \|b x + a | (%T b + a)\|%T b + a d%T +--R ++ +--R + +--R 2 9 5 2 4+---+ +--R (- b x - 4a b x - 3a x)\|- b +--R / +--R +--------+ +--R 4+---+ | 4 +--R 7\|- b \|b x + a +--R Type: Expression Integer +--E 174 + +--S 175 of 554 +d0234:= D(m0234,x) +--R +--R +--R (144) +--R +--------+ +--------+ +-----------------+ +--R | 4 4+---+ 2 | 4 |4+-+2 2 4+---+2 +--R 2 |b x + a x\|- b 2 |b x + a |\|a - x \|- b +--R (4a |-------- asin(-------) - 4a |-------- ) |----------------- +--R \| a 4+-+ \| a | 4+-+2 +--R \|a \| \|a +--R + +--R 4 2 +--R 4a b x + 4a +--R / +--R +--------+ +--------+ +--R | 4 +--------+ 4+---+ 2 | 4 +--------+ +--R |b x + a | 4 x\|- b |b x + a | 4 +--R (7 |-------- \|b x + a asin(-------) - 7 |-------- \|b x + a) +--R \| a 4+-+ \| a +--R \|a +--R * +--R +-----------------+ +--R |4+-+2 2 4+---+2 +--R |\|a - x \|- b +--R |----------------- +--R | 4+-+2 +--R \| \|a +--R Type: Expression Integer +--E 175 + +--S 176 of 554 +t0235:= (a+b*x^4)^(1/2) +--R +--R +--R +--------+ +--R | 4 +--R (145) \|b x + a +--R Type: Expression Integer +--E 176 + +--S 177 of 554 +r0235:= 1/3*x*(a+b*x^4)^(1/2)+2/3*a^(5/4)*((a+b*x^4)/a)^(1/2)*_ + atanh(asin((-b)^(1/4)*x/a^(1/4)))/(-b)^(1/4)/(a+b*x^4)^(1/2) +--R +--R +--R +--------+ +--R | 4 4+---+ +--R 4+-+ |b x + a x\|- b 5 4+---+ +--R 2a\|a |-------- atanh(asin(-------)) + (b x + a x)\|- b +--R \| a 4+-+ +--R \|a +--R (146) ---------------------------------------------------------- +--R +--------+ +--R 4+---+ | 4 +--R 3\|- b \|b x + a +--R Type: Expression Integer +--E 177 + +--S 178 of 554 +a0235:= integrate(t0235,x) +--R +--R +--R x +--------+ +--R ++ | 4 +--R (147) | \|%T b + a d%T +--R ++ +--R Type: Union(Expression Integer,...) +--E 178 + +--S 179 of 554 +m0235:= a0235-r0235 +--R +--R +--R (148) +--R +--------+ +--R | 4 4+---+ +--R 4+-+ |b x + a x\|- b +--R - 2a\|a |-------- atanh(asin(-------)) +--R \| a 4+-+ +--R \|a +--R + +--R +--------+ x +--------+ +--R 4+---+ | 4 ++ | 4 5 4+---+ +--R 3\|- b \|b x + a | \|%T b + a d%T + (- b x - a x)\|- b +--R ++ +--R / +--R +--------+ +--R 4+---+ | 4 +--R 3\|- b \|b x + a +--R Type: Expression Integer +--E 179 + +--S 180 of 554 +d0235:= D(m0235,x) +--R +--R +--R (149) +--R +--------+ +--------+ +-----------------+ +--R | 4 4+---+ 2 | 4 |4+-+2 2 4+---+2 +--R |b x + a x\|- b |b x + a |\|a - x \|- b 4 +--R (2a |-------- asin(-------) - 2a |-------- ) |----------------- + 2b x +--R \| a 4+-+ \| a | 4+-+2 +--R \|a \| \|a +--R + +--R 2a +--R / +--R +--------+ +--------+ +--R | 4 +--------+ 4+---+ 2 | 4 +--------+ +--R |b x + a | 4 x\|- b |b x + a | 4 +--R (3 |-------- \|b x + a asin(-------) - 3 |-------- \|b x + a) +--R \| a 4+-+ \| a +--R \|a +--R * +--R +-----------------+ +--R |4+-+2 2 4+---+2 +--R |\|a - x \|- b +--R |----------------- +--R | 4+-+2 +--R \| \|a +--R Type: Expression Integer +--E 180 + +--S 181 of 554 +t0236:= 1/(a+b*x^4)^(1/2) +--R +--R +--R 1 +--R (150) ----------- +--R +--------+ +--R | 4 +--R \|b x + a +--R Type: Expression Integer +--E 181 + +--S 182 of 554 +r0236:= a^(1/4)*((a+b*x^4)/a)^(1/2)*atanh(asin((-b)^(1/4)*x/a^(1/4)))/_ + (-b)^(1/4)/(a+b*x^4)^(1/2) +--R +--R +--R +--------+ +--R | 4 4+---+ +--R 4+-+ |b x + a x\|- b +--R \|a |-------- atanh(asin(-------)) +--R \| a 4+-+ +--R \|a +--R (151) ----------------------------------- +--R +--------+ +--R 4+---+ | 4 +--R \|- b \|b x + a +--R Type: Expression Integer +--E 182 + +--S 183 of 554 +a0236:= integrate(t0236,x) +--R +--R +--R x +--R ++ 1 +--R (152) | ----------- d%T +--R ++ +--------+ +--R | 4 +--R \|%T b + a +--R Type: Union(Expression Integer,...) +--E 183 + +--S 184 of 554 +m0236:= a0236-r0236 +--R +--R +--R (153) +--R +--------+ +--R | 4 4+---+ +--R 4+-+ |b x + a x\|- b +--R - \|a |-------- atanh(asin(-------)) +--R \| a 4+-+ +--R \|a +--R + +--R +--------+ x +--R 4+---+ | 4 ++ 1 +--R \|- b \|b x + a | ----------- d%T +--R ++ +--------+ +--R | 4 +--R \|%T b + a +--R / +--R +--------+ +--R 4+---+ | 4 +--R \|- b \|b x + a +--R Type: Expression Integer +--E 184 + +--S 185 of 554 +d0236:= D(m0236,x) +--R +--R +--R (154) +--R +--------+ +--------+ +-----------------+ +--R | 4 4+---+ 2 | 4 |4+-+2 2 4+---+2 +--R |b x + a x\|- b |b x + a |\|a - x \|- b 4 +--R (a |-------- asin(-------) - a |-------- ) |----------------- + b x + a +--R \| a 4+-+ \| a | 4+-+2 +--R \|a \| \|a +--R / +--R +--------+ +--------+ +--R | 4 +--------+ 4+---+ 2 | 4 +--------+ +--R |b x + a | 4 x\|- b |b x + a | 4 +--R (a |-------- \|b x + a asin(-------) - a |-------- \|b x + a ) +--R \| a 4+-+ \| a +--R \|a +--R * +--R +-----------------+ +--R |4+-+2 2 4+---+2 +--R |\|a - x \|- b +--R |----------------- +--R | 4+-+2 +--R \| \|a +--R Type: Expression Integer +--E 185 + +--S 186 of 554 +t0237:= 1/(a+b*x^4)^(3/2) +--R +--R +--R 1 +--R (155) --------------------- +--R +--------+ +--R 4 | 4 +--R (b x + a)\|b x + a +--R Type: Expression Integer +--E 186 + +--S 187 of 554 +r0237:= 1/2*(x*a^(3/4)*(-b)^(1/4)+((a+b*x^4)/a)^(1/2)*_ + atanh(asin((-b)^(1/4)*x/a^(1/4)))*a)/a^(7/4)/(a+b*x^4)^(1/2)/(-b)^(1/4) +--R +--R +--R +--------+ +--R | 4 4+---+ +--R |b x + a x\|- b 4+---+4+-+3 +--R a |-------- atanh(asin(-------)) + x\|- b \|a +--R \| a 4+-+ +--R \|a +--R (156) ----------------------------------------------- +--R +--------+ +--R 4+---+4+-+3 | 4 +--R 2a\|- b \|a \|b x + a +--R Type: Expression Integer +--E 187 + +--S 188 of 554 +a0237:= integrate(t0237,x) +--R +--R +--R x +--R ++ 1 +--R (157) | --------------------- d%T +--R ++ +--------+ +--R 4 | 4 +--R (%T b + a)\|%T b + a +--R Type: Union(Expression Integer,...) +--E 188 + +--S 189 of 554 +m0237:= a0237-r0237 +--R +--R +--R (158) +--R +--------+ +--R | 4 4+---+ +--R |b x + a x\|- b +--R - a |-------- atanh(asin(-------)) +--R \| a 4+-+ +--R \|a +--R + +--R +--------+ x +--R 4+---+4+-+3 | 4 ++ 1 4+---+4+-+3 +--R 2a\|- b \|a \|b x + a | --------------------- d%T - x\|- b \|a +--R ++ +--------+ +--R 4 | 4 +--R (%T b + a)\|%T b + a +--R / +--R +--------+ +--R 4+---+4+-+3 | 4 +--R 2a\|- b \|a \|b x + a +--R Type: Expression Integer +--E 189 + +--S 190 of 554 +d0237:= D(m0237,x) +--R +--R +--R (159) +--R +--------+ +--------+ +-----------------+ +--R | 4 4+---+ 2 | 4 |4+-+2 2 4+---+2 +--R |b x + a x\|- b |b x + a |\|a - x \|- b 4 +--R (a |-------- asin(-------) - a |-------- ) |----------------- + b x + a +--R \| a 4+-+ \| a | 4+-+2 +--R \|a \| \|a +--R / +--R +--------+ +--------+ +--R | 4 +--------+ 4+---+ 2 | 4 +--------+ +--R 2 |b x + a | 4 x\|- b 2 |b x + a | 4 +--R (2a |-------- \|b x + a asin(-------) - 2a |-------- \|b x + a ) +--R \| a 4+-+ \| a +--R \|a +--R * +--R +-----------------+ +--R |4+-+2 2 4+---+2 +--R |\|a - x \|- b +--R |----------------- +--R | 4+-+2 +--R \| \|a +--R Type: Expression Integer +--E 190 + +--S 191 of 554 +t0238:= 1/(a+b*x^4)^(5/2) +--R +--R +--R 1 +--R (160) -------------------------------- +--R +--------+ +--R 2 8 4 2 | 4 +--R (b x + 2a b x + a )\|b x + a +--R Type: Expression Integer +--E 191 + +--S 192 of 554 +r0238:= 1/6*x/a/(a+b*x^4)^(3/2)+5/12*x/a^2/(a+b*x^4)^(1/2)+_ + 5/12*((a+b*x^4)/a)^(1/2)*atanh(asin((-b)^(1/4)*x/a^(1/4)))/_ + a^(7/4)/(-b)^(1/4)/(a+b*x^4)^(1/2) +--R +--R +--R (161) +--R +--------+ +--R | 4 4+---+ +--R 4 2 |b x + a x\|- b 5 4+---+4+-+3 +--R (5a b x + 5a ) |-------- atanh(asin(-------)) + (5b x + 7a x)\|- b \|a +--R \| a 4+-+ +--R \|a +--R -------------------------------------------------------------------------- +--R +--------+ +--R 2 4 3 4+---+4+-+3 | 4 +--R (12a b x + 12a )\|- b \|a \|b x + a +--R Type: Expression Integer +--E 192 + +--S 193 of 554 +a0238:= integrate(t0238,x) +--R +--R +--R x +--R ++ 1 +--R (162) | --------------------------------- d%T +--R ++ +--------+ +--R 8 2 4 2 | 4 +--R (%T b + 2%T a b + a )\|%T b + a +--R Type: Union(Expression Integer,...) +--E 193 + +--S 194 of 554 +m0238:= a0238-r0238 +--R +--R +--R (163) +--R +--------+ +--R | 4 4+---+ +--R 4 2 |b x + a x\|- b +--R (- 5a b x - 5a ) |-------- atanh(asin(-------)) +--R \| a 4+-+ +--R \|a +--R + +--R +--------+ +--R 2 4 3 4+---+4+-+3 | 4 +--R (12a b x + 12a )\|- b \|a \|b x + a +--R * +--R x +--R ++ 1 +--R | --------------------------------- d%T +--R ++ +--------+ +--R 8 2 4 2 | 4 +--R (%T b + 2%T a b + a )\|%T b + a +--R + +--R 5 4+---+4+-+3 +--R (- 5b x - 7a x)\|- b \|a +--R / +--R +--------+ +--R 2 4 3 4+---+4+-+3 | 4 +--R (12a b x + 12a )\|- b \|a \|b x + a +--R Type: Expression Integer +--E 194 + +--S 195 of 554 +d0238:= D(m0238,x) +--R +--R +--R (164) +--R +--------+ +--------+ +-----------------+ +--R | 4 4+---+ 2 | 4 |4+-+2 2 4+---+2 +--R |b x + a x\|- b |b x + a |\|a - x \|- b 4 +--R (5a |-------- asin(-------) - 5a |-------- ) |----------------- + 5b x +--R \| a 4+-+ \| a | 4+-+2 +--R \|a \| \|a +--R + +--R 5a +--R / +--R +--------+ +--------+ +--R | 4 +--------+ 4+---+ 2 | 4 +--------+ +--R 3 |b x + a | 4 x\|- b 3 |b x + a | 4 +--R (12a |-------- \|b x + a asin(-------) - 12a |-------- \|b x + a ) +--R \| a 4+-+ \| a +--R \|a +--R * +--R +-----------------+ +--R |4+-+2 2 4+---+2 +--R |\|a - x \|- b +--R |----------------- +--R | 4+-+2 +--R \| \|a +--R Type: Expression Integer +--E 195 + +--S 196 of 554 +t0239:= (1+x^4)^(3/2) +--R +--R +--R +------+ +--R 4 | 4 +--R (165) (x + 1)\|x + 1 +--R Type: Expression Integer +--E 196 + +--S 197 of 554 +r0239:= 2/7*x*(1+x^4)^(1/2)+1/7*x*(1+x^4)^(3/2)-4/7*(-1)^(3/4)*_ + atanh(asin((-1)^(1/4)*x)) +--R +--R +--R +---+ +------+ +--R +---+ x\|- 1 + x 5 +-+ | 4 +--R (- 4\|- 1 + 4)atanh(asin(-----------)) + (x + 3x)\|2 \|x + 1 +--R +-+ +--R \|2 +--R (166) ---------------------------------------------------------------- +--R +-+ +--R 7\|2 +--R Type: Expression Integer +--E 197 + +--S 198 of 554 +a0239:= integrate(t0239,x) +--R +--R +--R x +-------+ +--R ++ 4 | 4 +--R (167) | (%T + 1)\|%T + 1 d%T +--R ++ +--R Type: Union(Expression Integer,...) +--E 198 + +--S 199 of 554 +m0239:= a0239-r0239 +--R +--R +--R (168) +--R x +-------+ +---+ +--R +-+ ++ 4 | 4 +---+ x\|- 1 + x +--R 7\|2 | (%T + 1)\|%T + 1 d%T + (4\|- 1 - 4)atanh(asin(-----------)) +--R ++ +-+ +--R \|2 +--R + +--R +------+ +--R 5 +-+ | 4 +--R (- x - 3x)\|2 \|x + 1 +--R / +--R +-+ +--R 7\|2 +--R Type: Expression Integer +--E 199 + +--S 200 of 554 +d0239:= D(m0239,x) +--R +--R +--R +------+ +---+ 2 +--------------+ +--R | 4 x\|- 1 + x | 2 +---+ +--R 4\|x + 1 + (4asin(-----------) - 4)\|- x \|- 1 + 1 +--R +-+ +--R \|2 +--R (169) ------------------------------------------------------- +--R +---+ 2 +--------------+ +------+ +--R x\|- 1 + x | 2 +---+ | 4 +--R (7asin(-----------) - 7)\|- x \|- 1 + 1 \|x + 1 +--R +-+ +--R \|2 +--R Type: Expression Integer +--E 200 + +--S 201 of 554 +t0240:= (1+x^4)^(1/2) +--R +--R +--R +------+ +--R | 4 +--R (170) \|x + 1 +--R Type: Expression Integer +--E 201 + +--S 202 of 554 +r0240:= 1/3*x*(1+x^4)^(1/2)-2/3*(-1)^(3/4)*atanh(asin((-1)^(1/4)*x)) +--R +--R +--R +---+ +------+ +--R +---+ x\|- 1 + x +-+ | 4 +--R (- 2\|- 1 + 2)atanh(asin(-----------)) + x\|2 \|x + 1 +--R +-+ +--R \|2 +--R (171) -------------------------------------------------------- +--R +-+ +--R 3\|2 +--R Type: Expression Integer +--E 202 + +--S 203 of 554 +a0240:= integrate(t0240,x) +--R +--R +--R x +-------+ +--R ++ | 4 +--R (172) | \|%T + 1 d%T +--R ++ +--R Type: Union(Expression Integer,...) +--E 203 + +--S 204 of 554 +m0240:= a0240-r0240 +--R +--R +--R (173) +--R x +-------+ +---+ +--R +-+ ++ | 4 +---+ x\|- 1 + x +--R 3\|2 | \|%T + 1 d%T + (2\|- 1 - 2)atanh(asin(-----------)) +--R ++ +-+ +--R \|2 +--R + +--R +------+ +--R +-+ | 4 +--R - x\|2 \|x + 1 +--R / +--R +-+ +--R 3\|2 +--R Type: Expression Integer +--E 204 + +--S 205 of 554 +d0240:= D(m0240,x) +--R +--R +--R +------+ +---+ 2 +--------------+ +--R | 4 x\|- 1 + x | 2 +---+ +--R 2\|x + 1 + (2asin(-----------) - 2)\|- x \|- 1 + 1 +--R +-+ +--R \|2 +--R (174) ------------------------------------------------------- +--R +---+ 2 +--------------+ +------+ +--R x\|- 1 + x | 2 +---+ | 4 +--R (3asin(-----------) - 3)\|- x \|- 1 + 1 \|x + 1 +--R +-+ +--R \|2 +--R Type: Expression Integer +--E 205 + +--S 206 of 554 +t0241:= 1/(1+x^4)^(1/2) +--R +--R +--R 1 +--R (175) --------- +--R +------+ +--R | 4 +--R \|x + 1 +--R Type: Expression Integer +--E 206 + +--S 207 of 554 +r0241:= -(-1)^(3/4)*atanh(asin((-1)^(1/4)*x)) +--R +--R +--R +---+ +--R +---+ x\|- 1 + x +--R (- \|- 1 + 1)atanh(asin(-----------)) +--R +-+ +--R \|2 +--R (176) -------------------------------------- +--R +-+ +--R \|2 +--R Type: Expression Integer +--E 207 + +--S 208 of 554 +a0241:= integrate(t0241,x) +--R +--R +--R x +--R ++ 1 +--R (177) | ---------- d%T +--R ++ +-------+ +--R | 4 +--R \|%T + 1 +--R Type: Union(Expression Integer,...) +--E 208 + +--S 209 of 554 +m0241:= a0241-r0241 +--R +--R +--R x +---+ +--R +-+ ++ 1 +---+ x\|- 1 + x +--R \|2 | ---------- d%T + (\|- 1 - 1)atanh(asin(-----------)) +--R ++ +-------+ +-+ +--R | 4 \|2 +--R \|%T + 1 +--R (178) --------------------------------------------------------------- +--R +-+ +--R \|2 +--R Type: Expression Integer +--E 209 + +--S 210 of 554 +d0241:= D(m0241,x) +--R +--R +--R +------+ +---+ 2 +--------------+ +--R | 4 x\|- 1 + x | 2 +---+ +--R \|x + 1 + (asin(-----------) - 1)\|- x \|- 1 + 1 +--R +-+ +--R \|2 +--R (179) ----------------------------------------------------- +--R +---+ 2 +--------------+ +------+ +--R x\|- 1 + x | 2 +---+ | 4 +--R (asin(-----------) - 1)\|- x \|- 1 + 1 \|x + 1 +--R +-+ +--R \|2 +--R Type: Expression Integer +--E 210 + +--S 211 of 554 +t0242:= 1/(1+x^4)^(3/2) +--R +--R +--R 1 +--R (180) ----------------- +--R +------+ +--R 4 | 4 +--R (x + 1)\|x + 1 +--R Type: Expression Integer +--E 211 + +--S 212 of 554 +r0242:= 1/2*x/(1+x^4)^(1/2)-1/2*(-1)^(3/4)*atanh(asin((-1)^(1/4)*x)) +--R +--R +--R +------+ +---+ +--R +---+ | 4 x\|- 1 + x +-+ +--R (- \|- 1 + 1)\|x + 1 atanh(asin(-----------)) + x\|2 +--R +-+ +--R \|2 +--R (181) ------------------------------------------------------- +--R +------+ +--R +-+ | 4 +--R 2\|2 \|x + 1 +--R Type: Expression Integer +--E 212 + +--S 213 of 554 +a0242:= integrate(t0242,x) +--R +--R +--R x +--R ++ 1 +--R (182) | ------------------- d%T +--R ++ +-------+ +--R 4 | 4 +--R (%T + 1)\|%T + 1 +--R Type: Union(Expression Integer,...) +--E 213 + +--S 214 of 554 +m0242:= a0242-r0242 +--R +--R +--R (183) +--R +------+ x +--R +-+ | 4 ++ 1 +--R 2\|2 \|x + 1 | ------------------- d%T +--R ++ +-------+ +--R 4 | 4 +--R (%T + 1)\|%T + 1 +--R + +--R +------+ +---+ +--R +---+ | 4 x\|- 1 + x +-+ +--R (\|- 1 - 1)\|x + 1 atanh(asin(-----------)) - x\|2 +--R +-+ +--R \|2 +--R / +--R +------+ +--R +-+ | 4 +--R 2\|2 \|x + 1 +--R Type: Expression Integer +--E 214 + +--S 215 of 554 +d0242:= D(m0242,x) +--R +--R +--R +------+ +---+ 2 +--------------+ +--R | 4 x\|- 1 + x | 2 +---+ +--R \|x + 1 + (asin(-----------) - 1)\|- x \|- 1 + 1 +--R +-+ +--R \|2 +--R (184) ----------------------------------------------------- +--R +---+ 2 +--------------+ +------+ +--R x\|- 1 + x | 2 +---+ | 4 +--R (2asin(-----------) - 2)\|- x \|- 1 + 1 \|x + 1 +--R +-+ +--R \|2 +--R Type: Expression Integer +--E 215 + +--S 216 of 554 +t0243:= 1/(1+x^4)^(5/2) +--R +--R +--R 1 +--R (185) ----------------------- +--R +------+ +--R 8 4 | 4 +--R (x + 2x + 1)\|x + 1 +--R Type: Expression Integer +--E 216 + +--S 217 of 554 +r0243:= 1/6*x/(1+x^4)^(3/2)+5/12*x/(1+x^4)^(1/2)-5/12*(-1)^(3/4)*_ + atanh(asin((-1)^(1/4)*x)) +--R +--R +--R (186) +--R +------+ +---+ +--R 4 +---+ 4 | 4 x\|- 1 + x +--R ((- 5x - 5)\|- 1 + 5x + 5)\|x + 1 atanh(asin(-----------)) +--R +-+ +--R \|2 +--R + +--R 5 +-+ +--R (5x + 7x)\|2 +--R / +--R +------+ +--R 4 +-+ | 4 +--R (12x + 12)\|2 \|x + 1 +--R Type: Expression Integer +--E 217 + +--S 218 of 554 +a0243:= integrate(t0243,x) +--R +--R +--R x +--R ++ 1 +--R (187) | -------------------------- d%T +--R ++ +-------+ +--R 8 4 | 4 +--R (%T + 2%T + 1)\|%T + 1 +--R Type: Union(Expression Integer,...) +--E 218 + +--S 219 of 554 +m0243:= a0243-r0243 +--R +--R +--R (188) +--R +------+ x +--R 4 +-+ | 4 ++ 1 +--R (12x + 12)\|2 \|x + 1 | -------------------------- d%T +--R ++ +-------+ +--R 8 4 | 4 +--R (%T + 2%T + 1)\|%T + 1 +--R + +--R +------+ +---+ +--R 4 +---+ 4 | 4 x\|- 1 + x +--R ((5x + 5)\|- 1 - 5x - 5)\|x + 1 atanh(asin(-----------)) +--R +-+ +--R \|2 +--R + +--R 5 +-+ +--R (- 5x - 7x)\|2 +--R / +--R +------+ +--R 4 +-+ | 4 +--R (12x + 12)\|2 \|x + 1 +--R Type: Expression Integer +--E 219 + +--S 220 of 554 +d0243:= D(m0243,x) +--R +--R +--R +------+ +---+ 2 +--------------+ +--R | 4 x\|- 1 + x | 2 +---+ +--R 5\|x + 1 + (5asin(-----------) - 5)\|- x \|- 1 + 1 +--R +-+ +--R \|2 +--R (189) ------------------------------------------------------- +--R +---+ 2 +--------------+ +------+ +--R x\|- 1 + x | 2 +---+ | 4 +--R (12asin(-----------) - 12)\|- x \|- 1 + 1 \|x + 1 +--R +-+ +--R \|2 +--R Type: Expression Integer +--E 220 + +--S 221 of 554 +t0244:= (1-x^4)^(1/2) +--R +--R +--R +--------+ +--R | 4 +--R (190) \|- x + 1 +--R Type: Expression Integer +--E 221 + +--S 222 of 554 +r0244:= 1/3*x*(1-x^4)^(1/2)+2/3*atanh(asin(x)) +--R +--R +--R +--------+ +--R | 4 +--R 2atanh(asin(x)) + x\|- x + 1 +--R (191) ------------------------------ +--R 3 +--R Type: Expression Integer +--E 222 + +--S 223 of 554 +a0244:= integrate(t0244,x) +--R +--R +--R x +---------+ +--R ++ | 4 +--R (192) | \|- %T + 1 d%T +--R ++ +--R Type: Union(Expression Integer,...) +--E 223 + +--S 224 of 554 +m0244:= a0244-r0244 +--R +--R +--R x +---------+ +--------+ +--R ++ | 4 | 4 +--R 3 | \|- %T + 1 d%T - 2atanh(asin(x)) - x\|- x + 1 +--R ++ +--R (193) ------------------------------------------------------- +--R 3 +--R Type: Expression Integer +--E 224 + +--S 225 of 554 +d0244:= D(m0244,x) +--R +--R +--R +--------+ +--------+ +--R 2 | 2 | 4 +--R (2asin(x) - 2)\|- x + 1 + 2\|- x + 1 +--R (194) ----------------------------------------- +--R +--------+ +--------+ +--R 2 | 4 | 2 +--R (3asin(x) - 3)\|- x + 1 \|- x + 1 +--R Type: Expression Integer +--E 225 + +--S 226 of 554 +t0245:= 1/(1-x^4)^(1/2) +--R +--R +--R 1 +--R (195) ----------- +--R +--------+ +--R | 4 +--R \|- x + 1 +--R Type: Expression Integer +--E 226 + +--S 227 of 554 +r0245:= atanh(asin(x)) +--R +--R +--R (196) atanh(asin(x)) +--R Type: Expression Integer +--E 227 + +--S 228 of 554 +a0245:= integrate(t0245,x) +--R +--R +--R x +--R ++ 1 +--R (197) | ------------ d%T +--R ++ +---------+ +--R | 4 +--R \|- %T + 1 +--R Type: Union(Expression Integer,...) +--E 228 + +--S 229 of 554 +m0245:= a0245-r0245 +--R +--R +--R x +--R ++ 1 +--R (198) | ------------ d%T - atanh(asin(x)) +--R ++ +---------+ +--R | 4 +--R \|- %T + 1 +--R Type: Expression Integer +--E 229 + +--S 230 of 554 +d0245:= D(m0245,x) +--R +--R +--R +--------+ +--------+ +--R 2 | 2 | 4 +--R (asin(x) - 1)\|- x + 1 + \|- x + 1 +--R (199) --------------------------------------- +--R +--------+ +--------+ +--R 2 | 4 | 2 +--R (asin(x) - 1)\|- x + 1 \|- x + 1 +--R Type: Expression Integer +--E 230 + +--S 231 of 554 +t0246:= 1/(1-x^4)^(3/2) +--R +--R +--R 1 +--R (200) - ------------------- +--R +--------+ +--R 4 | 4 +--R (x - 1)\|- x + 1 +--R Type: Expression Integer +--E 231 + +--S 232 of 554 +r0246:= 1/2*x/(1-x^4)^(1/2)+1/2*atanh(asin(x)) +--R +--R +--R +--------+ +--R | 4 +--R \|- x + 1 atanh(asin(x)) + x +--R (201) ----------------------------- +--R +--------+ +--R | 4 +--R 2\|- x + 1 +--R Type: Expression Integer +--E 232 + +--S 233 of 554 +a0246:= integrate(t0246,x) +--R +--R +--R x +--R ++ 1 +--R (202) | - --------------------- d%T +--R ++ +---------+ +--R 4 | 4 +--R (%T - 1)\|- %T + 1 +--R Type: Union(Expression Integer,...) +--E 233 + +--S 234 of 554 +m0246:= a0246-r0246 +--R +--R +--R (203) +--R +--------+ x +--------+ +--R | 4 ++ 1 | 4 +--R 2\|- x + 1 | - --------------------- d%T - \|- x + 1 atanh(asin(x)) - x +--R ++ +---------+ +--R 4 | 4 +--R (%T - 1)\|- %T + 1 +--R ----------------------------------------------------------------------------- +--R +--------+ +--R | 4 +--R 2\|- x + 1 +--R Type: Expression Integer +--E 234 + +--S 235 of 554 +d0246:= D(m0246,x) +--R +--R +--R +--------+ +--------+ +--R 2 | 2 | 4 +--R (asin(x) - 1)\|- x + 1 + \|- x + 1 +--R (204) --------------------------------------- +--R +--------+ +--------+ +--R 2 | 4 | 2 +--R (2asin(x) - 2)\|- x + 1 \|- x + 1 +--R Type: Expression Integer +--E 235 + +--S 236 of 554 +t0247:= 1/(1-x^4)^(5/2) +--R +--R +--R 1 +--R (205) ------------------------- +--R +--------+ +--R 8 4 | 4 +--R (x - 2x + 1)\|- x + 1 +--R Type: Expression Integer +--E 236 + +--S 237 of 554 +r0247:= 1/6*x/(1-x^4)^(3/2)+5/12*x/(1-x^4)^(1/2)+5/12*atanh(asin(x)) +--R +--R +--R +--------+ +--R 4 | 4 5 +--R (5x - 5)\|- x + 1 atanh(asin(x)) + 5x - 7x +--R (206) --------------------------------------------- +--R +--------+ +--R 4 | 4 +--R (12x - 12)\|- x + 1 +--R Type: Expression Integer +--E 237 + +--S 238 of 554 +a0247:= integrate(t0247,x) +--R +--R +--R x +--R ++ 1 +--R (207) | ---------------------------- d%T +--R ++ +---------+ +--R 8 4 | 4 +--R (%T - 2%T + 1)\|- %T + 1 +--R Type: Union(Expression Integer,...) +--E 238 + +--S 239 of 554 +m0247:= a0247-r0247 +--R +--R +--R (208) +--R +--------+ x +--R 4 | 4 ++ 1 +--R (12x - 12)\|- x + 1 | ---------------------------- d%T +--R ++ +---------+ +--R 8 4 | 4 +--R (%T - 2%T + 1)\|- %T + 1 +--R + +--R +--------+ +--R 4 | 4 5 +--R (- 5x + 5)\|- x + 1 atanh(asin(x)) - 5x + 7x +--R / +--R +--------+ +--R 4 | 4 +--R (12x - 12)\|- x + 1 +--R Type: Expression Integer +--E 239 + +--S 240 of 554 +d0247:= D(m0247,x) +--R +--R +--R +--------+ +--------+ +--R 2 | 2 | 4 +--R (5asin(x) - 5)\|- x + 1 + 5\|- x + 1 +--R (209) ----------------------------------------- +--R +--------+ +--------+ +--R 2 | 4 | 2 +--R (12asin(x) - 12)\|- x + 1 \|- x + 1 +--R Type: Expression Integer +--E 240 + +--S 241 of 554 +t0248:= 1/x/(1+x^6)^(1/2) +--R +--R +--R 1 +--R (210) ---------- +--R +------+ +--R | 6 +--R x\|x + 1 +--R Type: Expression Integer +--E 241 + +--S 242 of 554 +r0248:= -1/3*atanh((1+x^6)^(1/2)) +--R +--R +--R +------+ +--R | 6 +--R atanh(\|x + 1 ) +--R (211) - ---------------- +--R 3 +--R Type: Expression Integer +--E 242 + +--S 243 of 554 +a0248:= integrate(t0248,x) +--R +--R +--R +------+ +------+ +--R | 6 | 6 +--R - log(\|x + 1 + 1) + log(\|x + 1 - 1) +--R (212) ----------------------------------------- +--R 6 +--R Type: Union(Expression Integer,...) +--E 243 + +--S 244 of 554 +m0248:= a0248-r0248 +--R +--R +--R +------+ +------+ +------+ +--R | 6 | 6 | 6 +--R - log(\|x + 1 + 1) + log(\|x + 1 - 1) + 2atanh(\|x + 1 ) +--R (213) ------------------------------------------------------------- +--R 6 +--R Type: Expression Integer +--E 244 + +--S 245 of 554 +d0248:= D(m0248,x) +--R +--R +--R (214) 0 +--R Type: Expression Integer +--E 245 + +--S 246 of 554 +t0249:= 1/x/(-25+x^6)^(1/2) +--R +--R +--R 1 +--R (215) ----------- +--R +-------+ +--R | 6 +--R x\|x - 25 +--R Type: Expression Integer +--E 246 + +--S 247 of 554 +r0249:= 1/15*atan(1/5*(-25+x^6)^(1/2)) +--R +--R +--R +-------+ +--R | 6 +--R \|x - 25 +--R atan(----------) +--R 5 +--R (216) ---------------- +--R 15 +--R Type: Expression Integer +--E 247 + +--S 248 of 554 +a0249:= integrate(t0249,x) +--R +--R +--R +-------+ +--R | 6 +--R \|x - 25 +--R atan(----------) +--R 5 +--R (217) ---------------- +--R 15 +--R Type: Union(Expression Integer,...) +--E 248 + +--S 249 of 554 +m0249:= a0249-r0249 +--R +--R +--R (218) 0 +--R Type: Expression Integer +--E 249 + +--S 250 of 554 +d0249:= D(m0249,x) +--R +--R +--R (219) 0 +--R Type: Expression Integer +--E 250 + +--S 251 of 554 +t0250:= x^8*(-1+4*x^6)^(1/2) +--R +--R +--R +-------+ +--R 8 | 6 +--R (220) x \|4x - 1 +--R Type: Expression Integer +--E 251 + +--S 252 of 554 +r0250:= -1/96*x^3*(-1+4*x^6)^(1/2)+1/12*x^9*(-1+4*x^6)^(1/2)-_ + 1/192*atanh(1/2*(-1+4*x^6)^(1/2)/x^3) +--R +--R +--R +-------+ +--R | 6 +-------+ +--R \|4x - 1 9 3 | 6 +--R - atanh(----------) + (16x - 2x )\|4x - 1 +--R 3 +--R 2x +--R (221) -------------------------------------------- +--R 192 +--R Type: Expression Integer +--E 252 + +--S 253 of 554 +a0250:= integrate(t0250,x) +--R +--R +--R (222) +--R +-------+ +-------+ +--R 9 3 | 6 12 6 | 6 3 +--R ((64x - 8x )\|4x - 1 - 128x + 32x - 1)log(\|4x - 1 - 2x ) +--R + +--R +-------+ +--R 21 15 9 3 | 6 24 18 12 +--R (- 2048x + 768x - 80x + 2x )\|4x - 1 + 4096x - 2048x + 320x +--R + +--R 6 +--R - 16x +--R / +--R +-------+ +--R 9 3 | 6 12 6 +--R (12288x - 1536x )\|4x - 1 - 24576x + 6144x - 192 +--R Type: Union(Expression Integer,...) +--E 253 + +--S 254 of 554 +m0250:= a0250-r0250 +--R +--R +--R +-------+ +--R +-------+ | 6 +--R | 6 3 \|4x - 1 +--R log(\|4x - 1 - 2x ) + atanh(----------) +--R 3 +--R 2x +--R (223) ----------------------------------------- +--R 192 +--R Type: Expression Integer +--E 254 + +--S 255 of 554 +d0250:= D(m0250,x) +--R +--R +--R (224) 0 +--R Type: Expression Integer +--E 255 + +--S 256 of 554 +t0251:= x^2*(-2+x^6)^(1/2) +--R +--R +--R +------+ +--R 2 | 6 +--R (225) x \|x - 2 +--R Type: Expression Integer +--E 256 + +--S 257 of 554 +r0251:= 1/6*x^3*(-2+x^6)^(1/2)-1/3*atanh((-2+x^6)^(1/2)/x^3) +--R +--R +--R +------+ +--R | 6 +------+ +--R \|x - 2 3 | 6 +--R - 2atanh(---------) + x \|x - 2 +--R 3 +--R x +--R (226) --------------------------------- +--R 6 +--R Type: Expression Integer +--E 257 + +--S 258 of 554 +a0251:= integrate(t0251,x) +--R +--R +--R (227) +--R +------+ +------+ +------+ +--R 3 | 6 6 | 6 3 9 3 | 6 12 +--R (2x \|x - 2 - 2x + 2)log(\|x - 2 - x ) + (- x + x )\|x - 2 + x +--R + +--R 6 +--R - 2x +--R / +--R +------+ +--R 3 | 6 6 +--R 6x \|x - 2 - 6x + 6 +--R Type: Union(Expression Integer,...) +--E 258 + +--S 259 of 554 +m0251:= a0251-r0251 +--R +--R +--R +------+ +--R +------+ | 6 +--R | 6 3 \|x - 2 +--R log(\|x - 2 - x ) + atanh(---------) +--R 3 +--R x +--R (228) -------------------------------------- +--R 3 +--R Type: Expression Integer +--E 259 + +--S 260 of 554 +d0251:= D(m0251,x) +--R +--R +--R (229) 0 +--R Type: Expression Integer +--E 260 + +--S 261 of 554 +t0252:= 1/x/(1+x^8)^(1/2) +--R +--R +--R 1 +--R (230) ---------- +--R +------+ +--R | 8 +--R x\|x + 1 +--R Type: Expression Integer +--E 261 + +--S 262 of 554 +r0252:= -1/4*atanh((1+x^8)^(1/2)) +--R +--R +--R +------+ +--R | 8 +--R atanh(\|x + 1 ) +--R (231) - ---------------- +--R 4 +--R Type: Expression Integer +--E 262 + +--S 263 of 554 +a0252:= integrate(t0252,x) +--R +--R +--R +------+ +------+ +--R | 8 | 8 +--R - log(\|x + 1 + 1) + log(\|x + 1 - 1) +--R (232) ----------------------------------------- +--R 8 +--R Type: Union(Expression Integer,...) +--E 263 + +--S 264 of 554 +m0252:= a0252-r0252 +--R +--R +--R +------+ +------+ +------+ +--R | 8 | 8 | 8 +--R - log(\|x + 1 + 1) + log(\|x + 1 - 1) + 2atanh(\|x + 1 ) +--R (233) ------------------------------------------------------------- +--R 8 +--R Type: Expression Integer +--E 264 + +--S 265 of 554 +d0252:= D(m0252,x) +--R +--R +--R (234) 0 +--R Type: Expression Integer +--E 265 + +--S 266 of 554 +t0253:= x^3*(-2+x^8)^(1/2) +--R +--R +--R +------+ +--R 3 | 8 +--R (235) x \|x - 2 +--R Type: Expression Integer +--E 266 + +--S 267 of 554 +r0253:= 1/8*x^4*(-2+x^8)^(1/2)-1/4*atanh((-2+x^8)^(1/2)/x^4) +--R +--R +--R +------+ +--R | 8 +------+ +--R \|x - 2 4 | 8 +--R - 2atanh(---------) + x \|x - 2 +--R 4 +--R x +--R (236) --------------------------------- +--R 8 +--R Type: Expression Integer +--E 267 + +--S 268 of 554 +a0253:= integrate(t0253,x) +--R +--R +--R (237) +--R +------+ +------+ +------+ +--R 4 | 8 8 | 8 4 12 4 | 8 16 +--R (2x \|x - 2 - 2x + 2)log(\|x - 2 - x ) + (- x + x )\|x - 2 + x +--R + +--R 8 +--R - 2x +--R / +--R +------+ +--R 4 | 8 8 +--R 8x \|x - 2 - 8x + 8 +--R Type: Union(Expression Integer,...) +--E 268 + +--S 269 of 554 +m0253:= a0253-r0253 +--R +--R +--R +------+ +--R +------+ | 8 +--R | 8 4 \|x - 2 +--R log(\|x - 2 - x ) + atanh(---------) +--R 4 +--R x +--R (238) -------------------------------------- +--R 4 +--R Type: Expression Integer +--E 269 + +--S 270 of 554 +d0253:= D(m0253,x) +--R +--R +--R (239) 0 +--R Type: Expression Integer +--E 270 + +--S 271 of 554 +t0254:= (1+x^8)^(1/2)*(1+2*x^8)/(x+2*x^9+x^17) +--R +--R +--R +------+ +--R 8 | 8 +--R (2x + 1)\|x + 1 +--R (240) ------------------ +--R 17 9 +--R x + 2x + x +--R Type: Expression Integer +--E 271 + +--S 272 of 554 +r0254:= -1/4/(1+x^8)^(1/2)-1/4*atanh((1+x^8)^(1/2)) +--R +--R +--R +------+ +------+ +--R | 8 | 8 +--R - \|x + 1 atanh(\|x + 1 ) - 1 +--R (241) ------------------------------- +--R +------+ +--R | 8 +--R 4\|x + 1 +--R Type: Expression Integer +--E 272 + +--S 273 of 554 +a0254:= integrate(t0254,x) +--R +--R +--R +------+ +------+ +------+ +------+ +--R | 8 | 8 | 8 | 8 +--R - \|x + 1 log(\|x + 1 + 1) + \|x + 1 log(\|x + 1 - 1) - 2 +--R (242) --------------------------------------------------------------- +--R +------+ +--R | 8 +--R 8\|x + 1 +--R Type: Union(Expression Integer,...) +--E 273 + +--S 274 of 554 +m0254:= a0254-r0254 +--R +--R +--R +------+ +------+ +------+ +--R | 8 | 8 | 8 +--R - log(\|x + 1 + 1) + log(\|x + 1 - 1) + 2atanh(\|x + 1 ) +--R (243) ------------------------------------------------------------- +--R 8 +--R Type: Expression Integer +--E 274 + +--S 275 of 554 +d0254:= D(m0254,x) +--R +--R +--R (244) 0 +--R Type: Expression Integer +--E 275 + +--S 276 of 554 +t0255:= x^4/(-2+x^10)^(1/2) +--R +--R +--R 4 +--R x +--R (245) ---------- +--R +-------+ +--R | 10 +--R \|x - 2 +--R Type: Expression Integer +--E 276 + +--S 277 of 554 +r0255:= 1/5*atanh((-2+x^10)^(1/2)/x^5) +--R +--R +--R +-------+ +--R | 10 +--R \|x - 2 +--R atanh(----------) +--R 5 +--R x +--R (246) ----------------- +--R 5 +--R Type: Expression Integer +--E 277 + +--S 278 of 554 +a0255:= integrate(t0255,x) +--R +--R +--R +-------+ +--R | 10 5 +--R log(\|x - 2 - x ) +--R (247) - -------------------- +--R 5 +--R Type: Union(Expression Integer,...) +--E 278 + +--S 279 of 554 +m0255:= a0255-r0255 +--R +--R +--R +-------+ +--R +-------+ | 10 +--R | 10 5 \|x - 2 +--R - log(\|x - 2 - x ) - atanh(----------) +--R 5 +--R x +--R (248) ------------------------------------------ +--R 5 +--R Type: Expression Integer +--E 279 + +--S 280 of 554 +d0255:= D(m0255,x) +--R +--R +--R (249) 0 +--R Type: Expression Integer +--E 280 + +--S 281 of 554 +t0256:= x^31*(1+x^16)^(1/2)/(1-x^16) +--R +--R +--R +-------+ +--R 31 | 16 +--R x \|x + 1 +--R (250) - ------------- +--R 16 +--R x - 1 +--R Type: Expression Integer +--E 281 + +--S 282 of 554 +r0256:= -1/8*(1+x^16)^(1/2)-1/24*(1+x^16)^(3/2)+1/8*_ + atanh(1/2*(1+x^16)^(1/2)*2^(1/2))*2^(1/2) +--R +--R +--R +-------+ +--R +-+ | 16 +-------+ +--R +-+ \|2 \|x + 1 16 | 16 +--R 3\|2 atanh(--------------) + (- x - 4)\|x + 1 +--R 2 +--R (251) -------------------------------------------------- +--R 24 +--R Type: Expression Integer +--E 282 + +--S 283 of 554 +a0256:= integrate(t0256,x) +--R +--R +--R +-------+ +--R | 16 16 +-+ +-------+ +--R 4\|x + 1 + (x + 3)\|2 16 +-+ | 16 +--R 3log(---------------------------) + (- x - 4)\|2 \|x + 1 +--R 16 +--R x - 1 +--R (252) ------------------------------------------------------------- +--R +-+ +--R 24\|2 +--R Type: Union(Expression Integer,...) +--E 283 + +--S 284 of 554 +m0256:= a0256-r0256 +--R +--R +--R +-------+ +-------+ +--R | 16 16 +-+ +-+ | 16 +--R 4\|x + 1 + (x + 3)\|2 \|2 \|x + 1 +--R log(---------------------------) - 2atanh(--------------) +--R 16 2 +--R x - 1 +--R (253) --------------------------------------------------------- +--R +-+ +--R 8\|2 +--R Type: Expression Integer +--E 284 + +--S 285 of 554 +d0256:= D(m0256,x) +--R +--R +--R (254) 0 +--R Type: Expression Integer +--E 285 + +--S 286 of 554 +t0257:= x^3*(a+b/x)^(1/2) +--R +--R +--R +-------+ +--R 3 |a x + b +--R (255) x |------- +--R \| x +--R Type: Expression Integer +--E 286 + +--S 287 of 554 +r0257:= 5/64*b^3*(a+b/x)^(1/2)*x/a^3-5/96*b^2*(a+b/x)^(1/2)*x^2/a^2+_ + 1/24*b*(a+b/x)^(1/2)*x^3/a+1/4*(a+b/x)^(1/2)*x^4-_ + 5/64*b^4*atanh((a+b/x)^(1/2)/a^(1/2))/a^(7/2) +--R +--R +--R (256) +--R +-------+ +--R |a x + b +--R |------- +-------+ +--R 4 \| x 3 4 2 3 2 2 3 +-+ |a x + b +--R - 15b atanh(----------) + (48a x + 8a b x - 10a b x + 15b x)\|a |------- +--R +-+ \| x +--R \|a +--R ----------------------------------------------------------------------------- +--R 3 +-+ +--R 192a \|a +--R Type: Expression Integer +--E 287 + +--S 288 of 554 +a0257:= integrate(t0257,x) +--R +--R +--R (257) +--R [ +--R +-------+ +--R 4 |a x + b +-+ +--R 15b log(- 2a x |------- + (2a x + b)\|a ) +--R \| x +--R + +--R +-------+ +--R 3 4 2 3 2 2 3 +-+ |a x + b +--R (96a x + 16a b x - 20a b x + 30b x)\|a |------- +--R \| x +--R / +--R 3 +-+ +--R 384a \|a +--R , +--R +--R +-------+ +--R +---+ |a x + b +--R \|- a |------- +--R 4 \| x +--R - 15b atan(----------------) +--R a +--R + +--R +-------+ +--R 3 4 2 3 2 2 3 +---+ |a x + b +--R (48a x + 8a b x - 10a b x + 15b x)\|- a |------- +--R \| x +--R / +--R 3 +---+ +--R 192a \|- a +--R ] +--R Type: Union(List Expression Integer,...) +--E 288 + +--S 289 of 554 +m0257a:= a0257.1-r0257 +--R +--R +--R +-------+ +--R |a x + b +--R +-------+ |------- +--R 4 |a x + b +-+ 4 \| x +--R 5b log(- 2a x |------- + (2a x + b)\|a ) + 10b atanh(----------) +--R \| x +-+ +--R \|a +--R (258) ----------------------------------------------------------------- +--R 3 +-+ +--R 128a \|a +--R Type: Expression Integer +--E 289 + +--S 290 of 554 +d0257a:= D(m0257a,x) +--R +--R +--R (259) 0 +--R Type: Expression Integer +--E 290 + +--S 291 of 554 +m0257b:= a0257.2-r0257 +--R +--R +--R +-------+ +-------+ +--R |a x + b +---+ |a x + b +--R |------- \|- a |------- +--R 4 +---+ \| x 4 +-+ \| x +--R 5b \|- a atanh(----------) - 5b \|a atan(----------------) +--R +-+ a +--R \|a +--R (260) ---------------------------------------------------------- +--R 3 +---+ +-+ +--R 64a \|- a \|a +--R Type: Expression Integer +--E 291 + +--S 292 of 554 +d0257b:= D(m0257b,x) +--R +--R +--R (261) 0 +--R Type: Expression Integer +--E 292 + +--S 293 of 554 +t0258:= x^2*(a+b/x)^(1/2) +--R +--R +--R +-------+ +--R 2 |a x + b +--R (262) x |------- +--R \| x +--R Type: Expression Integer +--E 293 + +--S 294 of 554 +r0258:= -1/8*b^2*(a+b/x)^(1/2)*x/a^2+1/12*b*(a+b/x)^(1/2)*x^2/a+_ + 1/3*x^3*(a+b/x)^(1/2)+1/8*b^3*atanh((a+b/x)^(1/2)/a^(1/2))/a^(5/2) +--R +--R +--R +-------+ +--R |a x + b +--R |------- +-------+ +--R 3 \| x 2 3 2 2 +-+ |a x + b +--R 3b atanh(----------) + (8a x + 2a b x - 3b x)\|a |------- +--R +-+ \| x +--R \|a +--R (263) ------------------------------------------------------------- +--R 2 +-+ +--R 24a \|a +--R Type: Expression Integer +--E 294 + +--S 295 of 554 +a0258:= integrate(t0258,x) +--R +--R +--R (264) +--R [ +--R +-------+ +--R 3 |a x + b +-+ +--R 3b log(2a x |------- + (2a x + b)\|a ) +--R \| x +--R + +--R +-------+ +--R 2 3 2 2 +-+ |a x + b +--R (16a x + 4a b x - 6b x)\|a |------- +--R \| x +--R / +--R 2 +-+ +--R 48a \|a +--R , +--R +-------+ +--R +---+ |a x + b +--R \|- a |------- +-------+ +--R 3 \| x 2 3 2 2 +---+ |a x + b +--R 3b atan(----------------) + (8a x + 2a b x - 3b x)\|- a |------- +--R a \| x +--R --------------------------------------------------------------------] +--R 2 +---+ +--R 24a \|- a +--R Type: Union(List Expression Integer,...) +--E 295 + +--S 296 of 554 +m0258a:= a0258.1-r0258 +--R +--R +--R +-------+ +--R |a x + b +--R +-------+ |------- +--R 3 |a x + b +-+ 3 \| x +--R b log(2a x |------- + (2a x + b)\|a ) - 2b atanh(----------) +--R \| x +-+ +--R \|a +--R (265) ------------------------------------------------------------- +--R 2 +-+ +--R 16a \|a +--R Type: Expression Integer +--E 296 + +--S 297 of 554 +d0258a:= D(m0258a,x) +--R +--R +--R (266) 0 +--R Type: Expression Integer +--E 297 + +--S 298 of 554 +m0258b:= a0258.2-r0258 +--R +--R +--R +-------+ +-------+ +--R |a x + b +---+ |a x + b +--R |------- \|- a |------- +--R 3 +---+ \| x 3 +-+ \| x +--R - b \|- a atanh(----------) + b \|a atan(----------------) +--R +-+ a +--R \|a +--R (267) ---------------------------------------------------------- +--R 2 +---+ +-+ +--R 8a \|- a \|a +--R Type: Expression Integer +--E 298 + +--S 299 of 554 +d0258b:= D(m0258b,x) +--R +--R +--R (268) 0 +--R Type: Expression Integer +--E 299 + +--S 300 of 554 +t0259:= x*(a+b/x)^(1/2) +--R +--R +--R +-------+ +--R |a x + b +--R (269) x |------- +--R \| x +--R Type: Expression Integer +--E 300 + +--S 301 of 554 +r0259:= 1/4*b*(a+b/x)^(1/2)*x/a+1/2*x^2*(a+b/x)^(1/2)-_ + 1/4*b^2*atanh((a+b/x)^(1/2)/a^(1/2))/a^(3/2) +--R +--R +--R +-------+ +--R |a x + b +--R |------- +-------+ +--R 2 \| x 2 +-+ |a x + b +--R - b atanh(----------) + (2a x + b x)\|a |------- +--R +-+ \| x +--R \|a +--R (270) --------------------------------------------------- +--R +-+ +--R 4a\|a +--R Type: Expression Integer +--E 301 + +--S 302 of 554 +a0259:= integrate(t0259,x) +--R +--R +--R (271) +--R +-------+ +-------+ +--R 2 |a x + b +-+ 2 +-+ |a x + b +--R b log(- 2a x |------- + (2a x + b)\|a ) + (4a x + 2b x)\|a |------- +--R \| x \| x +--R [-----------------------------------------------------------------------, +--R +-+ +--R 8a\|a +--R +-------+ +--R +---+ |a x + b +--R \|- a |------- +-------+ +--R 2 \| x 2 +---+ |a x + b +--R - b atan(----------------) + (2a x + b x)\|- a |------- +--R a \| x +--R ----------------------------------------------------------] +--R +---+ +--R 4a\|- a +--R Type: Union(List Expression Integer,...) +--E 302 + +--S 303 of 554 +m0259a:= a0259.1-r0259 +--R +--R +--R +-------+ +--R |a x + b +--R +-------+ |------- +--R 2 |a x + b +-+ 2 \| x +--R b log(- 2a x |------- + (2a x + b)\|a ) + 2b atanh(----------) +--R \| x +-+ +--R \|a +--R (272) --------------------------------------------------------------- +--R +-+ +--R 8a\|a +--R Type: Expression Integer +--E 303 + +--S 304 of 554 +d0259a:= D(m0259a,x) +--R +--R +--R (273) 0 +--R Type: Expression Integer +--E 304 + +--S 305 of 554 +m0259b:= a0259.2-r0259 +--R +--R +--R +-------+ +-------+ +--R |a x + b +---+ |a x + b +--R |------- \|- a |------- +--R 2 +---+ \| x 2 +-+ \| x +--R b \|- a atanh(----------) - b \|a atan(----------------) +--R +-+ a +--R \|a +--R (274) -------------------------------------------------------- +--R +---+ +-+ +--R 4a\|- a \|a +--R Type: Expression Integer +--E 305 + +--S 306 of 554 +d0259b:= D(m0259b,x) +--R +--R +--R (275) 0 +--R Type: Expression Integer +--E 306 + +--S 307 of 554 +t0260:= (a+b/x)^(1/2) +--R +--R +--R +-------+ +--R |a x + b +--R (276) |------- +--R \| x +--R Type: Expression Integer +--E 307 + +--S 308 of 554 +r0260:= x*(a+b/x)^(1/2)+b*atanh((a+b/x)^(1/2)/a^(1/2))/a^(1/2) +--R +--R +--R +-------+ +--R |a x + b +--R |------- +-------+ +--R \| x +-+ |a x + b +--R b atanh(----------) + x\|a |------- +--R +-+ \| x +--R \|a +--R (277) ------------------------------------- +--R +-+ +--R \|a +--R Type: Expression Integer +--E 308 + +--S 309 of 554 +a0260:= integrate(t0260,x) +--R +--R +--R (278) +--R +-------+ +-------+ +--R |a x + b +-+ +-+ |a x + b +--R b log(2a x |------- + (2a x + b)\|a ) + 2x\|a |------- +--R \| x \| x +--R [---------------------------------------------------------, +--R +-+ +--R 2\|a +--R +-------+ +--R +---+ |a x + b +--R \|- a |------- +-------+ +--R \| x +---+ |a x + b +--R b atan(----------------) + x\|- a |------- +--R a \| x +--R --------------------------------------------] +--R +---+ +--R \|- a +--R Type: Union(List Expression Integer,...) +--E 309 + +--S 310 of 554 +m0260a:= a0260.1-r0260 +--R +--R +--R +-------+ +--R |a x + b +--R +-------+ |------- +--R |a x + b +-+ \| x +--R b log(2a x |------- + (2a x + b)\|a ) - 2b atanh(----------) +--R \| x +-+ +--R \|a +--R (279) ------------------------------------------------------------- +--R +-+ +--R 2\|a +--R Type: Expression Integer +--E 310 + +--S 311 of 554 +d0260a:= D(m0260a,x) +--R +--R +--R (280) 0 +--R Type: Expression Integer +--E 311 + +--S 312 of 554 +m0260b:= a0260.2-r0260 +--R +--R +--R +-------+ +-------+ +--R |a x + b +---+ |a x + b +--R |------- \|- a |------- +--R +---+ \| x +-+ \| x +--R - b\|- a atanh(----------) + b\|a atan(----------------) +--R +-+ a +--R \|a +--R (281) -------------------------------------------------------- +--R +---+ +-+ +--R \|- a \|a +--R Type: Expression Integer +--E 312 + +--S 313 of 554 +d0260b:= D(m0260b,x) +--R +--R +--R (282) 0 +--R Type: Expression Integer +--E 313 + +--S 314 of 554 +t0261:= (a+b/x)^(1/2)/x +--R +--R +--R +-------+ +--R |a x + b +--R |------- +--R \| x +--R (283) ---------- +--R x +--R Type: Expression Integer +--E 314 + +--S 315 of 554 +r0261:= -2*(a+b/x)^(1/2)+2*a^(1/2)*atanh((a+b/x)^(1/2)/a^(1/2)) +--R +--R +--R +-------+ +--R |a x + b +--R |------- +-------+ +--R +-+ \| x |a x + b +--R (284) 2\|a atanh(----------) - 2 |------- +--R +-+ \| x +--R \|a +--R Type: Expression Integer +--E 315 + +--S 316 of 554 +a0261:= integrate(t0261,x) +--R +--R +--R (285) +--R +-------+ +-------+ +--R +-+ +-+ |a x + b |a x + b +--R [\|a log(2x\|a |------- + 2a x + b) - 2 |-------, +--R \| x \| x +--R +-------+ +--R |a x + b +--R |------- +-------+ +--R +---+ \| x |a x + b +--R 2\|- a atan(----------) - 2 |-------] +--R +---+ \| x +--R \|- a +--R Type: Union(List Expression Integer,...) +--E 316 + +--S 317 of 554 +m0261a:= a0261.1-r0261 +--R +--R +--R +-------+ +--R |a x + b +--R +-------+ |------- +--R +-+ +-+ |a x + b +-+ \| x +--R (286) \|a log(2x\|a |------- + 2a x + b) - 2\|a atanh(----------) +--R \| x +-+ +--R \|a +--R Type: Expression Integer +--E 317 + +--S 318 of 554 +d0261a:= D(m0261a,x) +--R +--R +--R (287) 0 +--R Type: Expression Integer +--E 318 + +--S 319 of 554 +m0261b:= a0261.2-r0261 +--R +--R +--R +-------+ +-------+ +--R |a x + b |a x + b +--R |------- |------- +--R +-+ \| x +---+ \| x +--R (288) - 2\|a atanh(----------) + 2\|- a atan(----------) +--R +-+ +---+ +--R \|a \|- a +--R Type: Expression Integer +--E 319 + +--S 320 of 554 +d0261b:= D(m0261b,x) +--R +--R +--R (289) 0 +--R Type: Expression Integer +--E 320 + +--S 321 of 554 +t0262:= x^3*(-a+b/x)^(1/2) +--R +--R +--R +---------+ +--R 3 |- a x + b +--R (290) x |--------- +--R \| x +--R Type: Expression Integer +--E 321 + +--S 322 of 554 +r0262:= -5/64*b^3*(-a+b/x)^(1/2)*x/a^3-5/96*b^2*(-a+b/x)^(1/2)*x^2/a^2-_ + 1/24*b*(-a+b/x)^(1/2)*x^3/a+1/4*(-a+b/x)^(1/2)*x^4-_ + 5/64*b^4*atan((-a+b/x)^(1/2)/a^(1/2))/a^(7/2) +--R +--R +--R (291) +--R +---------+ +--R |- a x + b +--R |--------- +--R 4 \| x +--R - 15b atan(------------) +--R +-+ +--R \|a +--R + +--R +---------+ +--R 3 4 2 3 2 2 3 |- a x + b +-+ +--R (48a x - 8a b x - 10a b x - 15b x) |--------- \|a +--R \| x +--R / +--R 3 +-+ +--R 192a \|a +--R Type: Expression Integer +--E 322 + +--S 323 of 554 +a0262:= integrate(t0262,x) +--R +--R +--R (292) +--R [ +--R +---------+ +--R 4 |- a x + b +---+ +--R 15b log(- 2a x |--------- + (- 2a x + b)\|- a ) +--R \| x +--R + +--R +---------+ +--R 3 4 2 3 2 2 3 +---+ |- a x + b +--R (96a x - 16a b x - 20a b x - 30b x)\|- a |--------- +--R \| x +--R / +--R 3 +---+ +--R 384a \|- a +--R , +--R +--R +---------+ +--R |- a x + b +-+ +--R |--------- \|a +--R 4 \| x +--R - 15b atan(----------------) +--R a +--R + +--R +---------+ +--R 3 4 2 3 2 2 3 |- a x + b +-+ +--R (48a x - 8a b x - 10a b x - 15b x) |--------- \|a +--R \| x +--R / +--R 3 +-+ +--R 192a \|a +--R ] +--R Type: Union(List Expression Integer,...) +--E 323 + +--S 324 of 554 +m0262a:= a0262.1-r0262 +--R +--R +--R (293) +--R +---------+ +--R 4 +-+ |- a x + b +---+ +--R 5b \|a log(- 2a x |--------- + (- 2a x + b)\|- a ) +--R \| x +--R + +--R +---------+ +--R |- a x + b +--R |--------- +--R 4 +---+ \| x +--R 10b \|- a atan(------------) +--R +-+ +--R \|a +--R / +--R 3 +---+ +-+ +--R 128a \|- a \|a +--R Type: Expression Integer +--E 324 + +--S 325 of 554 +d0262a:= D(m0262a,x) +--R +--R +--R (294) 0 +--R Type: Expression Integer +--E 325 + +--S 326 of 554 +m0262b:= a0262.2-r0262 +--R +--R +--R +---------+ +---------+ +--R |- a x + b +-+ |- a x + b +--R |--------- \|a |--------- +--R 4 \| x 4 \| x +--R - 5b atan(----------------) + 5b atan(------------) +--R a +-+ +--R \|a +--R (295) --------------------------------------------------- +--R 3 +-+ +--R 64a \|a +--R Type: Expression Integer +--E 326 + +--S 327 of 554 +d0262b:= D(m0262b,x) +--R +--R +--R (296) 0 +--R Type: Expression Integer +--E 327 + +--S 328 of 554 +t0263:= x^2*(-a+b/x)^(1/2) +--R +--R +--R +---------+ +--R 2 |- a x + b +--R (297) x |--------- +--R \| x +--R Type: Expression Integer +--E 328 + +--S 329 of 554 +r0263:= -1/8*b^2*(-a+b/x)^(1/2)*x/a^2-1/12*b*(-a+b/x)^(1/2)*x^2/a+_ + 1/3*x^3*(-a+b/x)^(1/2)-1/8*b^3*atan((-a+b/x)^(1/2)/a^(1/2))/a^(5/2) +--R +--R +--R +---------+ +--R |- a x + b +--R |--------- +---------+ +--R 3 \| x 2 3 2 2 |- a x + b +-+ +--R - 3b atan(------------) + (8a x - 2a b x - 3b x) |--------- \|a +--R +-+ \| x +--R \|a +--R (298) ------------------------------------------------------------------ +--R 2 +-+ +--R 24a \|a +--R Type: Expression Integer +--E 329 + +--S 330 of 554 +a0263:= integrate(t0263,x) +--R +--R +--R (299) +--R [ +--R +---------+ +--R 3 |- a x + b +---+ +--R 3b log(- 2a x |--------- + (- 2a x + b)\|- a ) +--R \| x +--R + +--R +---------+ +--R 2 3 2 2 +---+ |- a x + b +--R (16a x - 4a b x - 6b x)\|- a |--------- +--R \| x +--R / +--R 2 +---+ +--R 48a \|- a +--R , +--R +---------+ +--R |- a x + b +-+ +--R |--------- \|a +---------+ +--R 3 \| x 2 3 2 2 |- a x + b +-+ +--R - 3b atan(----------------) + (8a x - 2a b x - 3b x) |--------- \|a +--R a \| x +--R ----------------------------------------------------------------------] +--R 2 +-+ +--R 24a \|a +--R Type: Union(List Expression Integer,...) +--E 330 + +--S 331 of 554 +m0263a:= a0263.1-r0263 +--R +--R +--R (300) +--R +---------+ +--R 3 +-+ |- a x + b +---+ +--R b \|a log(- 2a x |--------- + (- 2a x + b)\|- a ) +--R \| x +--R + +--R +---------+ +--R |- a x + b +--R |--------- +--R 3 +---+ \| x +--R 2b \|- a atan(------------) +--R +-+ +--R \|a +--R / +--R 2 +---+ +-+ +--R 16a \|- a \|a +--R Type: Expression Integer +--E 331 + +--S 332 of 554 +d0263a:= D(m0263a,x) +--R +--R +--R (301) 0 +--R Type: Expression Integer +--E 332 + +--S 333 of 554 +m0263b:= a0263.2-r0263 +--R +--R +--R +---------+ +---------+ +--R |- a x + b +-+ |- a x + b +--R |--------- \|a |--------- +--R 3 \| x 3 \| x +--R - b atan(----------------) + b atan(------------) +--R a +-+ +--R \|a +--R (302) ------------------------------------------------- +--R 2 +-+ +--R 8a \|a +--R Type: Expression Integer +--E 333 + +--S 334 of 554 +d0263b:= D(m0263b,x) +--R +--R +--R (303) 0 +--R Type: Expression Integer +--E 334 + +--S 335 of 554 +t0264:= x*(-a+b/x)^(1/2) +--R +--R +--R +---------+ +--R |- a x + b +--R (304) x |--------- +--R \| x +--R Type: Expression Integer +--E 335 + +--S 336 of 554 +r0264:= -1/4*b*(-a+b/x)^(1/2)*x/a+1/2*x^2*(-a+b/x)^(1/2)-_ + 1/4*b^2*atan((-a+b/x)^(1/2)/a^(1/2))/a^(3/2) +--R +--R +--R +---------+ +--R |- a x + b +--R |--------- +---------+ +--R 2 \| x 2 |- a x + b +-+ +--R - b atan(------------) + (2a x - b x) |--------- \|a +--R +-+ \| x +--R \|a +--R (305) ------------------------------------------------------ +--R +-+ +--R 4a\|a +--R Type: Expression Integer +--E 336 + +--S 337 of 554 +a0264:= integrate(t0264,x) +--R +--R +--R (306) +--R [ +--R +---------+ +--R 2 |- a x + b +---+ +--R b log(- 2a x |--------- + (- 2a x + b)\|- a ) +--R \| x +--R + +--R +---------+ +--R 2 +---+ |- a x + b +--R (4a x - 2b x)\|- a |--------- +--R \| x +--R / +--R +---+ +--R 8a\|- a +--R , +--R +---------+ +--R |- a x + b +-+ +--R |--------- \|a +---------+ +--R 2 \| x 2 |- a x + b +-+ +--R - b atan(----------------) + (2a x - b x) |--------- \|a +--R a \| x +--R ----------------------------------------------------------] +--R +-+ +--R 4a\|a +--R Type: Union(List Expression Integer,...) +--E 337 + +--S 338 of 554 +m0264a:= a0264.1-r0264 +--R +--R +--R (307) +--R +---------+ +--R 2 +-+ |- a x + b +---+ +--R b \|a log(- 2a x |--------- + (- 2a x + b)\|- a ) +--R \| x +--R + +--R +---------+ +--R |- a x + b +--R |--------- +--R 2 +---+ \| x +--R 2b \|- a atan(------------) +--R +-+ +--R \|a +--R / +--R +---+ +-+ +--R 8a\|- a \|a +--R Type: Expression Integer +--E 338 + +--S 339 of 554 +d0264a:= D(m0264a,x) +--R +--R +--R (308) 0 +--R Type: Expression Integer +--E 339 + +--S 340 of 554 +m0264b:= a0264.2-r0264 +--R +--R +--R +---------+ +---------+ +--R |- a x + b +-+ |- a x + b +--R |--------- \|a |--------- +--R 2 \| x 2 \| x +--R - b atan(----------------) + b atan(------------) +--R a +-+ +--R \|a +--R (309) ------------------------------------------------- +--R +-+ +--R 4a\|a +--R Type: Expression Integer +--E 340 + +--S 341 of 554 +d0264b:= D(m0264b,x) +--R +--R +--R (310) 0 +--R Type: Expression Integer +--E 341 + +--S 342 of 554 +t0265:= (-a+b/x)^(1/2) +--R +--R +--R +---------+ +--R |- a x + b +--R (311) |--------- +--R \| x +--R Type: Expression Integer +--E 342 + +--S 343 of 554 +r0265:= x*(-a+b/x)^(1/2)-b*atan((-a+b/x)^(1/2)/a^(1/2))/a^(1/2) +--R +--R +--R +---------+ +--R |- a x + b +--R |--------- +---------+ +--R \| x |- a x + b +-+ +--R - b atan(------------) + x |--------- \|a +--R +-+ \| x +--R \|a +--R (312) ------------------------------------------ +--R +-+ +--R \|a +--R Type: Expression Integer +--E 343 + +--S 344 of 554 +a0265:= integrate(t0265,x) +--R +--R +--R (313) +--R +---------+ +---------+ +--R |- a x + b +---+ +---+ |- a x + b +--R b log(- 2a x |--------- + (- 2a x + b)\|- a ) + 2x\|- a |--------- +--R \| x \| x +--R [---------------------------------------------------------------------, +--R +---+ +--R 2\|- a +--R +---------+ +--R |- a x + b +-+ +--R |--------- \|a +---------+ +--R \| x |- a x + b +-+ +--R - b atan(----------------) + x |--------- \|a +--R a \| x +--R ----------------------------------------------] +--R +-+ +--R \|a +--R Type: Union(List Expression Integer,...) +--E 344 + +--S 345 of 554 +m0265a:= a0265.1-r0265 +--R +--R +--R (314) +--R +---------+ +--R +-+ |- a x + b +---+ +--R b\|a log(- 2a x |--------- + (- 2a x + b)\|- a ) +--R \| x +--R + +--R +---------+ +--R |- a x + b +--R |--------- +--R +---+ \| x +--R 2b\|- a atan(------------) +--R +-+ +--R \|a +--R / +--R +---+ +-+ +--R 2\|- a \|a +--R Type: Expression Integer +--E 345 + +--S 346 of 554 +d0265a:= D(m0265a,x) +--R +--R +--R (315) 0 +--R Type: Expression Integer +--E 346 + +--S 347 of 554 +m0265b:= a0265.2-r0265 +--R +--R +--R +---------+ +---------+ +--R |- a x + b +-+ |- a x + b +--R |--------- \|a |--------- +--R \| x \| x +--R - b atan(----------------) + b atan(------------) +--R a +-+ +--R \|a +--R (316) ------------------------------------------------- +--R +-+ +--R \|a +--R Type: Expression Integer +--E 347 + +--S 348 of 554 +d0265b:= D(m0265b,x) +--R +--R +--R (317) 0 +--R Type: Expression Integer +--E 348 + +--S 349 of 554 +t0266:= (-a+b/x)^(1/2)/x +--R +--R +--R +---------+ +--R |- a x + b +--R |--------- +--R \| x +--R (318) ------------ +--R x +--R Type: Expression Integer +--E 349 + +--S 350 of 554 +r0266:= -2*(-a+b/x)^(1/2)+2*a^(1/2)*atan((-a+b/x)^(1/2)/a^(1/2)) +--R +--R +--R +---------+ +--R |- a x + b +--R |--------- +---------+ +--R +-+ \| x |- a x + b +--R (319) 2\|a atan(------------) - 2 |--------- +--R +-+ \| x +--R \|a +--R Type: Expression Integer +--E 350 + +--S 351 of 554 +a0266:= integrate(t0266,x) +--R +--R +--R (320) +--R +---------+ +---------+ +--R +---+ +---+ |- a x + b |- a x + b +--R [\|- a log(2x\|- a |--------- - 2a x + b) - 2 |---------, +--R \| x \| x +--R +-+ +---------+ +--R +-+ \|a |- a x + b +--R - 2\|a atan(------------) - 2 |---------] +--R +---------+ \| x +--R |- a x + b +--R |--------- +--R \| x +--R Type: Union(List Expression Integer,...) +--E 351 + +--S 352 of 554 +m0266a:= a0266.1-r0266 +--R +--R +--R +---------+ +--R |- a x + b +--R +---------+ |--------- +--R +---+ +---+ |- a x + b +-+ \| x +--R (321) \|- a log(2x\|- a |--------- - 2a x + b) - 2\|a atan(------------) +--R \| x +-+ +--R \|a +--R Type: Expression Integer +--E 352 + +--S 353 of 554 +d0266a:= D(m0266a,x) +--R +--R +--R (322) 0 +--R Type: Expression Integer +--E 353 + +--S 354 of 554 +m0266b:= a0266.2-r0266 +--R +--R +--R +---------+ +--R |- a x + b +--R +-+ |--------- +--R +-+ \|a +-+ \| x +--R (323) - 2\|a atan(------------) - 2\|a atan(------------) +--R +---------+ +-+ +--R |- a x + b \|a +--R |--------- +--R \| x +--R Type: Expression Integer +--E 354 + +--S 355 of 554 +d0266b:= D(m0266b,x) +--R +--R +--R (324) 0 +--R Type: Expression Integer +--E 355 + +--S 356 of 554 +t0267:= x^3/(a+b/x)^(1/2) +--R +--R +--R 3 +--R x +--R (325) ---------- +--R +-------+ +--R |a x + b +--R |------- +--R \| x +--R Type: Expression Integer +--E 356 + +--S 357 of 554 +r0267:= -35/64*b^3*(a+b/x)^(1/2)*x/a^4+35/96*b^2*(a+b/x)^(1/2)*x^2/a^3-_ + 7/24*b*(a+b/x)^(1/2)*x^3/a^2+1/4*(a+b/x)^(1/2)*x^4/a+_ + 35/64*b^4*atanh((a+b/x)^(1/2)/a^(1/2))/a^(9/2) +--R +--R +--R (326) +--R +-------+ +--R |a x + b +--R |------- +--R 4 \| x +--R 105b atanh(----------) +--R +-+ +--R \|a +--R + +--R +-------+ +--R 3 4 2 3 2 2 3 +-+ |a x + b +--R (48a x - 56a b x + 70a b x - 105b x)\|a |------- +--R \| x +--R / +--R 4 +-+ +--R 192a \|a +--R Type: Expression Integer +--E 357 + +--S 358 of 554 +a0267:= integrate(t0267,x) +--R +--R +--R (327) +--R [ +--R +-------+ +--R 4 |a x + b +-+ +--R 105b log(2a x |------- + (2a x + b)\|a ) +--R \| x +--R + +--R +-------+ +--R 3 4 2 3 2 2 3 +-+ |a x + b +--R (96a x - 112a b x + 140a b x - 210b x)\|a |------- +--R \| x +--R / +--R 4 +-+ +--R 384a \|a +--R , +--R +--R +-------+ +--R +---+ |a x + b +--R \|- a |------- +--R 4 \| x +--R 105b atan(----------------) +--R a +--R + +--R +-------+ +--R 3 4 2 3 2 2 3 +---+ |a x + b +--R (48a x - 56a b x + 70a b x - 105b x)\|- a |------- +--R \| x +--R / +--R 4 +---+ +--R 192a \|- a +--R ] +--R Type: Union(List Expression Integer,...) +--E 358 + +--S 359 of 554 +m0267a:= a0267.1-r0267 +--R +--R +--R +-------+ +--R |a x + b +--R +-------+ |------- +--R 4 |a x + b +-+ 4 \| x +--R 35b log(2a x |------- + (2a x + b)\|a ) - 70b atanh(----------) +--R \| x +-+ +--R \|a +--R (328) ---------------------------------------------------------------- +--R 4 +-+ +--R 128a \|a +--R Type: Expression Integer +--E 359 + +--S 360 of 554 +d0267a:= D(m0267a,x) +--R +--R +--R (329) 0 +--R Type: Expression Integer +--E 360 + +--S 361 of 554 +m0267b:= a0267.2-r0267 +--R +--R +--R +-------+ +-------+ +--R |a x + b +---+ |a x + b +--R |------- \|- a |------- +--R 4 +---+ \| x 4 +-+ \| x +--R - 35b \|- a atanh(----------) + 35b \|a atan(----------------) +--R +-+ a +--R \|a +--R (330) -------------------------------------------------------------- +--R 4 +---+ +-+ +--R 64a \|- a \|a +--R Type: Expression Integer +--E 361 + +--S 362 of 554 +d0267b:= D(m0267b,x) +--R +--R +--R (331) 0 +--R Type: Expression Integer +--E 362 + +--S 363 of 554 +t0268:= x^2/(a+b/x)^(1/2) +--R +--R +--R 2 +--R x +--R (332) ---------- +--R +-------+ +--R |a x + b +--R |------- +--R \| x +--R Type: Expression Integer +--E 363 + +--S 364 of 554 +r0268:= 5/8*b^2*(a+b/x)^(1/2)*x/a^3-5/12*b*(a+b/x)^(1/2)*x^2/a^2+_ + 1/3*(a+b/x)^(1/2)*x^3/a-5/8*b^3*atanh((a+b/x)^(1/2)/a^(1/2))/a^(7/2) +--R +--R +--R +-------+ +--R |a x + b +--R |------- +-------+ +--R 3 \| x 2 3 2 2 +-+ |a x + b +--R - 15b atanh(----------) + (8a x - 10a b x + 15b x)\|a |------- +--R +-+ \| x +--R \|a +--R (333) ------------------------------------------------------------------ +--R 3 +-+ +--R 24a \|a +--R Type: Expression Integer +--E 364 + +--S 365 of 554 +a0268:= integrate(t0268,x) +--R +--R +--R (334) +--R [ +--R +-------+ +--R 3 |a x + b +-+ +--R 15b log(- 2a x |------- + (2a x + b)\|a ) +--R \| x +--R + +--R +-------+ +--R 2 3 2 2 +-+ |a x + b +--R (16a x - 20a b x + 30b x)\|a |------- +--R \| x +--R / +--R 3 +-+ +--R 48a \|a +--R , +--R +-------+ +--R +---+ |a x + b +--R \|- a |------- +-------+ +--R 3 \| x 2 3 2 2 +---+ |a x + b +--R - 15b atan(----------------) + (8a x - 10a b x + 15b x)\|- a |------- +--R a \| x +--R -------------------------------------------------------------------------] +--R 3 +---+ +--R 24a \|- a +--R Type: Union(List Expression Integer,...) +--E 365 + +--S 366 of 554 +m0268a:= a0268.1-r0268 +--R +--R +--R +-------+ +--R |a x + b +--R +-------+ |------- +--R 3 |a x + b +-+ 3 \| x +--R 5b log(- 2a x |------- + (2a x + b)\|a ) + 10b atanh(----------) +--R \| x +-+ +--R \|a +--R (335) ----------------------------------------------------------------- +--R 3 +-+ +--R 16a \|a +--R Type: Expression Integer +--E 366 + +--S 367 of 554 +d0268a:= D(m0268a,x) +--R +--R +--R (336) 0 +--R Type: Expression Integer +--E 367 + +--S 368 of 554 +m0268b:= a0268.2-r0268 +--R +--R +--R +-------+ +-------+ +--R |a x + b +---+ |a x + b +--R |------- \|- a |------- +--R 3 +---+ \| x 3 +-+ \| x +--R 5b \|- a atanh(----------) - 5b \|a atan(----------------) +--R +-+ a +--R \|a +--R (337) ---------------------------------------------------------- +--R 3 +---+ +-+ +--R 8a \|- a \|a +--R Type: Expression Integer +--E 368 + +--S 369 of 554 +d0268b:= D(m0268b,x) +--R +--R +--R (338) 0 +--R Type: Expression Integer +--E 369 + +--S 370 of 554 +t0269:= x/(a+b/x)^(1/2) +--R +--R +--R x +--R (339) ---------- +--R +-------+ +--R |a x + b +--R |------- +--R \| x +--R Type: Expression Integer +--E 370 + +--S 371 of 554 +r0269:= -3/4*b*(a+b/x)^(1/2)*x/a^2+1/2*(a+b/x)^(1/2)*x^2/a+_ + 3/4*b^2*atanh((a+b/x)^(1/2)/a^(1/2))/a^(5/2) +--R +--R +--R +-------+ +--R |a x + b +--R |------- +-------+ +--R 2 \| x 2 +-+ |a x + b +--R 3b atanh(----------) + (2a x - 3b x)\|a |------- +--R +-+ \| x +--R \|a +--R (340) --------------------------------------------------- +--R 2 +-+ +--R 4a \|a +--R Type: Expression Integer +--E 371 + +--S 372 of 554 +a0269:= integrate(t0269,x) +--R +--R +--R (341) +--R +-------+ +-------+ +--R 2 |a x + b +-+ 2 +-+ |a x + b +--R 3b log(2a x |------- + (2a x + b)\|a ) + (4a x - 6b x)\|a |------- +--R \| x \| x +--R [----------------------------------------------------------------------, +--R 2 +-+ +--R 8a \|a +--R +-------+ +--R +---+ |a x + b +--R \|- a |------- +-------+ +--R 2 \| x 2 +---+ |a x + b +--R 3b atan(----------------) + (2a x - 3b x)\|- a |------- +--R a \| x +--R ----------------------------------------------------------] +--R 2 +---+ +--R 4a \|- a +--R Type: Union(List Expression Integer,...) +--E 372 + +--S 373 of 554 +m0269a:= a0269.1-r0269 +--R +--R +--R +-------+ +--R |a x + b +--R +-------+ |------- +--R 2 |a x + b +-+ 2 \| x +--R 3b log(2a x |------- + (2a x + b)\|a ) - 6b atanh(----------) +--R \| x +-+ +--R \|a +--R (342) -------------------------------------------------------------- +--R 2 +-+ +--R 8a \|a +--R Type: Expression Integer +--E 373 + +--S 374 of 554 +d0269a:= D(m0269a,x) +--R +--R +--R (343) 0 +--R Type: Expression Integer +--E 374 + +--S 375 of 554 +m0269b:= a0269.2-r0269 +--R +--R +--R +-------+ +-------+ +--R |a x + b +---+ |a x + b +--R |------- \|- a |------- +--R 2 +---+ \| x 2 +-+ \| x +--R - 3b \|- a atanh(----------) + 3b \|a atan(----------------) +--R +-+ a +--R \|a +--R (344) ------------------------------------------------------------ +--R 2 +---+ +-+ +--R 4a \|- a \|a +--R Type: Expression Integer +--E 375 + +--S 376 of 554 +d0269b:= D(m0269b,x) +--R +--R +--R (345) 0 +--R Type: Expression Integer +--E 376 + +--S 377 of 554 +t0270:= 1/(a+b/x)^(1/2) +--R +--R +--R 1 +--R (346) ---------- +--R +-------+ +--R |a x + b +--R |------- +--R \| x +--R Type: Expression Integer +--E 377 + +--S 378 of 554 +r0270:= (a+b/x)^(1/2)*x/a-b*atanh((a+b/x)^(1/2)/a^(1/2))/a^(3/2) +--R +--R +--R +-------+ +--R |a x + b +--R |------- +-------+ +--R \| x +-+ |a x + b +--R - b atanh(----------) + x\|a |------- +--R +-+ \| x +--R \|a +--R (347) --------------------------------------- +--R +-+ +--R a\|a +--R Type: Expression Integer +--E 378 + +--S 379 of 554 +a0270:= integrate(t0270,x) +--R +--R +--R (348) +--R +-------+ +-------+ +--R |a x + b +-+ +-+ |a x + b +--R b log(- 2a x |------- + (2a x + b)\|a ) + 2x\|a |------- +--R \| x \| x +--R [-----------------------------------------------------------, +--R +-+ +--R 2a\|a +--R +-------+ +--R +---+ |a x + b +--R \|- a |------- +-------+ +--R \| x +---+ |a x + b +--R - b atan(----------------) + x\|- a |------- +--R a \| x +--R ----------------------------------------------] +--R +---+ +--R a\|- a +--R Type: Union(List Expression Integer,...) +--E 379 + +--S 380 of 554 +m0270a:= a0270.1-r0270 +--R +--R +--R +-------+ +--R |a x + b +--R +-------+ |------- +--R |a x + b +-+ \| x +--R b log(- 2a x |------- + (2a x + b)\|a ) + 2b atanh(----------) +--R \| x +-+ +--R \|a +--R (349) --------------------------------------------------------------- +--R +-+ +--R 2a\|a +--R Type: Expression Integer +--E 380 + +--S 381 of 554 +d0270a:= D(m0270a,x) +--R +--R +--R (350) 0 +--R Type: Expression Integer +--E 381 + +--S 382 of 554 +m0270b:= a0270.2-r0270 +--R +--R +--R +-------+ +-------+ +--R |a x + b +---+ |a x + b +--R |------- \|- a |------- +--R +---+ \| x +-+ \| x +--R b\|- a atanh(----------) - b\|a atan(----------------) +--R +-+ a +--R \|a +--R (351) ------------------------------------------------------ +--R +---+ +-+ +--R a\|- a \|a +--R Type: Expression Integer +--E 382 + +--S 383 of 554 +d0270b:= D(m0270b,x) +--R +--R +--R (352) 0 +--R Type: Expression Integer +--E 383 + +--S 384 of 554 +t0271:= 1/x/(a+b/x)^(1/2) +--R +--R +--R 1 +--R (353) ----------- +--R +-------+ +--R |a x + b +--R x |------- +--R \| x +--R Type: Expression Integer +--E 384 + +--S 385 of 554 +r0271:= 2*atanh((a+b/x)^(1/2)/a^(1/2))/a^(1/2) +--R +--R +--R +-------+ +--R |a x + b +--R |------- +--R \| x +--R 2atanh(----------) +--R +-+ +--R \|a +--R (354) ------------------ +--R +-+ +--R \|a +--R Type: Expression Integer +--E 385 + +--S 386 of 554 +a0271:= integrate(t0271,x) +--R +--R +--R +-------+ +--R +---+ |a x + b +--R +-------+ \|- a |------- +--R |a x + b +-+ \| x +--R log(2a x |------- + (2a x + b)\|a ) 2atan(----------------) +--R \| x a +--R (355) [------------------------------------,-----------------------] +--R +-+ +---+ +--R \|a \|- a +--R Type: Union(List Expression Integer,...) +--E 386 + +--S 387 of 554 +m0271a:= a0271.1-r0271 +--R +--R +--R +-------+ +--R |a x + b +--R +-------+ |------- +--R |a x + b +-+ \| x +--R log(2a x |------- + (2a x + b)\|a ) - 2atanh(----------) +--R \| x +-+ +--R \|a +--R (356) --------------------------------------------------------- +--R +-+ +--R \|a +--R Type: Expression Integer +--E 387 + +--S 388 of 554 +d0271a:= D(m0271a,x) +--R +--R +--R (357) 0 +--R Type: Expression Integer +--E 388 + +--S 389 of 554 +m0271b:= a0271.2-r0271 +--R +--R +--R +-------+ +-------+ +--R |a x + b +---+ |a x + b +--R |------- \|- a |------- +--R +---+ \| x +-+ \| x +--R - 2\|- a atanh(----------) + 2\|a atan(----------------) +--R +-+ a +--R \|a +--R (358) -------------------------------------------------------- +--R +---+ +-+ +--R \|- a \|a +--R Type: Expression Integer +--E 389 + +--S 390 of 554 +d0271b:= D(m0271b,x) +--R +--R +--R (359) 0 +--R Type: Expression Integer +--E 390 + +--S 391 of 554 +t0272:= x^3/(-a+b/x)^(1/2) +--R +--R +--R 3 +--R x +--R (360) ------------ +--R +---------+ +--R |- a x + b +--R |--------- +--R \| x +--R Type: Expression Integer +--E 391 + +--S 392 of 554 +r0272:= -35/64*b^3*(-a+b/x)^(1/2)*x/a^4-35/96*b^2*(-a+b/x)^(1/2)*x^2/a^3-_ + 7/24*b*(-a+b/x)^(1/2)*x^3/a^2-1/4*(-a+b/x)^(1/2)*x^4/a-_ + 35/64*b^4*atan((-a+b/x)^(1/2)/a^(1/2))/a^(9/2) +--R +--R +--R (361) +--R +---------+ +--R |- a x + b +--R |--------- +--R 4 \| x +--R - 105b atan(------------) +--R +-+ +--R \|a +--R + +--R +---------+ +--R 3 4 2 3 2 2 3 |- a x + b +-+ +--R (- 48a x - 56a b x - 70a b x - 105b x) |--------- \|a +--R \| x +--R / +--R 4 +-+ +--R 192a \|a +--R Type: Expression Integer +--E 392 + +--S 393 of 554 +a0272:= integrate(t0272,x) +--R +--R +--R (362) +--R [ +--R +---------+ +--R 4 |- a x + b +---+ +--R 105b log(- 2a x |--------- + (- 2a x + b)\|- a ) +--R \| x +--R + +--R +---------+ +--R 3 4 2 3 2 2 3 +---+ |- a x + b +--R (- 96a x - 112a b x - 140a b x - 210b x)\|- a |--------- +--R \| x +--R / +--R 4 +---+ +--R 384a \|- a +--R , +--R +--R +---------+ +--R |- a x + b +-+ +--R |--------- \|a +--R 4 \| x +--R - 105b atan(----------------) +--R a +--R + +--R +---------+ +--R 3 4 2 3 2 2 3 |- a x + b +-+ +--R (- 48a x - 56a b x - 70a b x - 105b x) |--------- \|a +--R \| x +--R / +--R 4 +-+ +--R 192a \|a +--R ] +--R Type: Union(List Expression Integer,...) +--E 393 + +--S 394 of 554 +m0272a:= a0272.1-r0272 +--R +--R +--R (363) +--R +---------+ +--R 4 +-+ |- a x + b +---+ +--R 35b \|a log(- 2a x |--------- + (- 2a x + b)\|- a ) +--R \| x +--R + +--R +---------+ +--R |- a x + b +--R |--------- +--R 4 +---+ \| x +--R 70b \|- a atan(------------) +--R +-+ +--R \|a +--R / +--R 4 +---+ +-+ +--R 128a \|- a \|a +--R Type: Expression Integer +--E 394 + +--S 395 of 554 +d0272a:= D(m0272a,x) +--R +--R +--R (364) 0 +--R Type: Expression Integer +--E 395 + +--S 396 of 554 +m0272b:= a0272.2-r0272 +--R +--R +--R +---------+ +---------+ +--R |- a x + b +-+ |- a x + b +--R |--------- \|a |--------- +--R 4 \| x 4 \| x +--R - 35b atan(----------------) + 35b atan(------------) +--R a +-+ +--R \|a +--R (365) ----------------------------------------------------- +--R 4 +-+ +--R 64a \|a +--R Type: Expression Integer +--E 396 + +--S 397 of 554 +d0272b:= D(m0272b,x) +--R +--R +--R (366) 0 +--R Type: Expression Integer +--E 397 + +--S 398 of 554 +t0273:= x^2/(-a+b/x)^(1/2) +--R +--R +--R 2 +--R x +--R (367) ------------ +--R +---------+ +--R |- a x + b +--R |--------- +--R \| x +--R Type: Expression Integer +--E 398 + +--S 399 of 554 +r0273:= -5/8*b^2*(-a+b/x)^(1/2)*x/a^3-5/12*b*(-a+b/x)^(1/2)*x^2/a^2-_ + 1/3*(-a+b/x)^(1/2)*x^3/a-5/8*b^3*atan((-a+b/x)^(1/2)/a^(1/2))/a^(7/2) +--R +--R +--R (368) +--R +---------+ +--R |- a x + b +--R |--------- +---------+ +--R 3 \| x 2 3 2 2 |- a x + b +-+ +--R - 15b atan(------------) + (- 8a x - 10a b x - 15b x) |--------- \|a +--R +-+ \| x +--R \|a +--R ----------------------------------------------------------------------- +--R 3 +-+ +--R 24a \|a +--R Type: Expression Integer +--E 399 + +--S 400 of 554 +a0273:= integrate(t0273,x) +--R +--R +--R (369) +--R [ +--R +---------+ +--R 3 |- a x + b +---+ +--R 15b log(- 2a x |--------- + (- 2a x + b)\|- a ) +--R \| x +--R + +--R +---------+ +--R 2 3 2 2 +---+ |- a x + b +--R (- 16a x - 20a b x - 30b x)\|- a |--------- +--R \| x +--R / +--R 3 +---+ +--R 48a \|- a +--R , +--R +---------+ +--R |- a x + b +-+ +--R |--------- \|a +---------+ +--R 3 \| x 2 3 2 2 |- a x + b +-+ +--R - 15b atan(----------------) + (- 8a x - 10a b x - 15b x) |--------- \|a +--R a \| x +--R ---------------------------------------------------------------------------] +--R 3 +-+ +--R 24a \|a +--R Type: Union(List Expression Integer,...) +--E 400 + +--S 401 of 554 +m0273a:= a0273.1-r0273 +--R +--R +--R (370) +--R +---------+ +--R 3 +-+ |- a x + b +---+ +--R 5b \|a log(- 2a x |--------- + (- 2a x + b)\|- a ) +--R \| x +--R + +--R +---------+ +--R |- a x + b +--R |--------- +--R 3 +---+ \| x +--R 10b \|- a atan(------------) +--R +-+ +--R \|a +--R / +--R 3 +---+ +-+ +--R 16a \|- a \|a +--R Type: Expression Integer +--E 401 + +--S 402 of 554 +d0273a:= D(m0273a,x) +--R +--R +--R (371) 0 +--R Type: Expression Integer +--E 402 + +--S 403 of 554 +m0273b:= a0273.2-r0273 +--R +--R +--R +---------+ +---------+ +--R |- a x + b +-+ |- a x + b +--R |--------- \|a |--------- +--R 3 \| x 3 \| x +--R - 5b atan(----------------) + 5b atan(------------) +--R a +-+ +--R \|a +--R (372) --------------------------------------------------- +--R 3 +-+ +--R 8a \|a +--R Type: Expression Integer +--E 403 + +--S 404 of 554 +d0273b:= D(m0273b,x) +--R +--R +--R (373) 0 +--R Type: Expression Integer +--E 404 + +--S 405 of 554 +t0274:= x/(-a+b/x)^(1/2) +--R +--R +--R x +--R (374) ------------ +--R +---------+ +--R |- a x + b +--R |--------- +--R \| x +--R Type: Expression Integer +--E 405 + +--S 406 of 554 +r0274:= -3/4*b*(-a+b/x)^(1/2)*x/a^2-1/2*(-a+b/x)^(1/2)*x^2/a-_ + 3/4*b^2*atan((-a+b/x)^(1/2)/a^(1/2))/a^(5/2) +--R +--R +--R +---------+ +--R |- a x + b +--R |--------- +---------+ +--R 2 \| x 2 |- a x + b +-+ +--R - 3b atan(------------) + (- 2a x - 3b x) |--------- \|a +--R +-+ \| x +--R \|a +--R (375) ---------------------------------------------------------- +--R 2 +-+ +--R 4a \|a +--R Type: Expression Integer +--E 406 + +--S 407 of 554 +a0274:= integrate(t0274,x) +--R +--R +--R (376) +--R [ +--R +---------+ +--R 2 |- a x + b +---+ +--R 3b log(- 2a x |--------- + (- 2a x + b)\|- a ) +--R \| x +--R + +--R +---------+ +--R 2 +---+ |- a x + b +--R (- 4a x - 6b x)\|- a |--------- +--R \| x +--R / +--R 2 +---+ +--R 8a \|- a +--R , +--R +---------+ +--R |- a x + b +-+ +--R |--------- \|a +---------+ +--R 2 \| x 2 |- a x + b +-+ +--R - 3b atan(----------------) + (- 2a x - 3b x) |--------- \|a +--R a \| x +--R --------------------------------------------------------------] +--R 2 +-+ +--R 4a \|a +--R Type: Union(List Expression Integer,...) +--E 407 + +--S 408 of 554 +m0274a:= a0274.1-r0274 +--R +--R +--R (377) +--R +---------+ +--R 2 +-+ |- a x + b +---+ +--R 3b \|a log(- 2a x |--------- + (- 2a x + b)\|- a ) +--R \| x +--R + +--R +---------+ +--R |- a x + b +--R |--------- +--R 2 +---+ \| x +--R 6b \|- a atan(------------) +--R +-+ +--R \|a +--R / +--R 2 +---+ +-+ +--R 8a \|- a \|a +--R Type: Expression Integer +--E 408 + +--S 409 of 554 +d0274a:= D(m0274a,x) +--R +--R +--R (378) 0 +--R Type: Expression Integer +--E 409 + +--S 410 of 554 +m0274b:= a0274.2-r0274 +--R +--R +--R +---------+ +---------+ +--R |- a x + b +-+ |- a x + b +--R |--------- \|a |--------- +--R 2 \| x 2 \| x +--R - 3b atan(----------------) + 3b atan(------------) +--R a +-+ +--R \|a +--R (379) --------------------------------------------------- +--R 2 +-+ +--R 4a \|a +--R Type: Expression Integer +--E 410 + +--S 411 of 554 +d0274b:= D(m0274b,x) +--R +--R +--R (380) 0 +--R Type: Expression Integer +--E 411 + +--S 412 of 554 +t0275:= 1/(-a+b/x)^(1/2) +--R +--R +--R 1 +--R (381) ------------ +--R +---------+ +--R |- a x + b +--R |--------- +--R \| x +--R Type: Expression Integer +--E 412 + +--S 413 of 554 +r0275:= -(-a+b/x)^(1/2)*x/a-b*atan((-a+b/x)^(1/2)/a^(1/2))/a^(3/2) +--R +--R +--R +---------+ +--R |- a x + b +--R |--------- +---------+ +--R \| x |- a x + b +-+ +--R - b atan(------------) - x |--------- \|a +--R +-+ \| x +--R \|a +--R (382) ------------------------------------------ +--R +-+ +--R a\|a +--R Type: Expression Integer +--E 413 + +--S 414 of 554 +a0275:= integrate(t0275,x) +--R +--R +--R (383) +--R +---------+ +---------+ +--R |- a x + b +---+ +---+ |- a x + b +--R b log(- 2a x |--------- + (- 2a x + b)\|- a ) - 2x\|- a |--------- +--R \| x \| x +--R [---------------------------------------------------------------------, +--R +---+ +--R 2a\|- a +--R +---------+ +--R |- a x + b +-+ +--R |--------- \|a +---------+ +--R \| x |- a x + b +-+ +--R - b atan(----------------) - x |--------- \|a +--R a \| x +--R ----------------------------------------------] +--R +-+ +--R a\|a +--R Type: Union(List Expression Integer,...) +--E 414 + +--S 415 of 554 +m0275a:= a0275.1-r0275 +--R +--R +--R (384) +--R +---------+ +--R +-+ |- a x + b +---+ +--R b\|a log(- 2a x |--------- + (- 2a x + b)\|- a ) +--R \| x +--R + +--R +---------+ +--R |- a x + b +--R |--------- +--R +---+ \| x +--R 2b\|- a atan(------------) +--R +-+ +--R \|a +--R / +--R +---+ +-+ +--R 2a\|- a \|a +--R Type: Expression Integer +--E 415 + +--S 416 of 554 +d0275a:= D(m0275a,x) +--R +--R +--R (385) 0 +--R Type: Expression Integer +--E 416 + +--S 417 of 554 +m0275b:= a0275.2-r0275 +--R +--R +--R +---------+ +---------+ +--R |- a x + b +-+ |- a x + b +--R |--------- \|a |--------- +--R \| x \| x +--R - b atan(----------------) + b atan(------------) +--R a +-+ +--R \|a +--R (386) ------------------------------------------------- +--R +-+ +--R a\|a +--R Type: Expression Integer +--E 417 + +--S 418 of 554 +d0275b:= D(m0275b,x) +--R +--R +--R (387) 0 +--R Type: Expression Integer +--E 418 + +--S 419 of 554 +t0276:= 1/x/(-a+b/x)^(1/2) +--R +--R +--R 1 +--R (388) ------------- +--R +---------+ +--R |- a x + b +--R x |--------- +--R \| x +--R Type: Expression Integer +--E 419 + +--S 420 of 554 +r0276:= -2*atan((-a+b/x)^(1/2)/a^(1/2))/a^(1/2) +--R +--R +--R +---------+ +--R |- a x + b +--R |--------- +--R \| x +--R 2atan(------------) +--R +-+ +--R \|a +--R (389) - ------------------- +--R +-+ +--R \|a +--R Type: Expression Integer +--E 420 + +--S 421 of 554 +a0276:= integrate(t0276,x) +--R +--R +--R (390) +--R +---------+ +--R |- a x + b +-+ +--R +---------+ |--------- \|a +--R |- a x + b +---+ \| x +--R log(- 2a x |--------- + (- 2a x + b)\|- a ) 2atan(----------------) +--R \| x a +--R [--------------------------------------------,- -----------------------] +--R +---+ +-+ +--R \|- a \|a +--R Type: Union(List Expression Integer,...) +--E 421 + +--S 422 of 554 +m0276a:= a0276.1-r0276 +--R +--R +--R (391) +--R +---------+ +--R |- a x + b +--R +---------+ |--------- +--R +-+ |- a x + b +---+ +---+ \| x +--R \|a log(- 2a x |--------- + (- 2a x + b)\|- a ) + 2\|- a atan(------------) +--R \| x +-+ +--R \|a +--R ---------------------------------------------------------------------------- +--R +---+ +-+ +--R \|- a \|a +--R Type: Expression Integer +--E 422 + +--S 423 of 554 +d0276a:= D(m0276a,x) +--R +--R +--R (392) 0 +--R Type: Expression Integer +--E 423 + +--S 424 of 554 +m0276b:= a0276.2-r0276 +--R +--R +--R +---------+ +---------+ +--R |- a x + b +-+ |- a x + b +--R |--------- \|a |--------- +--R \| x \| x +--R - 2atan(----------------) + 2atan(------------) +--R a +-+ +--R \|a +--R (393) ----------------------------------------------- +--R +-+ +--R \|a +--R Type: Expression Integer +--E 424 + +--S 425 of 554 +d0276b:= D(m0276b,x) +--R +--R +--R (394) 0 +--R Type: Expression Integer +--E 425 + +--S 426 of 554 +t0277:= x^3/(a+b/x^2)^(1/2) +--R +--R +--R 3 +--R x +--R (395) ----------- +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R Type: Expression Integer +--E 426 + +--S 427 of 554 +r0277:= -3/8*b*(a+b/x^2)^(1/2)*x^2/a^2+1/4*(a+b/x^2)^(1/2)*x^4/a+_ + 3/8*b^2*atanh((a+b/x^2)^(1/2)/a^(1/2))/a^(5/2) +--R +--R +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--------+ +--R | 2 | 2 +--R 2 \| x 4 2 +-+ |a x + b +--R 3b atanh(-----------) + (2a x - 3b x )\|a |-------- +--R +-+ | 2 +--R \|a \| x +--R (396) ------------------------------------------------------ +--R 2 +-+ +--R 8a \|a +--R Type: Expression Integer +--E 427 + +--S 428 of 554 +a0277:= integrate(t0277,x) +--R +--R +--R (397) +--R [ +--R +--------+ +--R 2 2 3 +-+ | 2 2 2 4 3 2 4 +--R ((12a b x + 24b )\|b \|a x + b - 3a b x - 24a b x - 24b ) +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ 2 +-+ +--R (\|a \|b - a x)\|a x + b + a x\|b + (- a x - b)\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R 3 7 2 5 2 3 3 +-+ | 2 +--R (- 2a x - 13a b x + 8a b x + 24b x)\|a \|a x + b +--R + +--R 3 7 2 5 2 3 3 +-+ +-+ +--R (8a x + 12a b x - 20a b x - 24b x)\|a \|b +--R / +--R +--------+ +--R 3 2 2 +-+ +-+ | 2 4 4 3 2 2 2 +-+ +--R (32a x + 64a b)\|a \|b \|a x + b + (- 8a x - 64a b x - 64a b )\|a +--R , +--R +--R +--------+ +--R 2 2 3 +-+ | 2 2 2 4 3 2 4 +--R ((24a b x + 48b )\|b \|a x + b - 6a b x - 48a b x - 48b ) +--R * +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R \|- a \|a x + b - \|- a \|b +--R atan(------------------------------) +--R a x +--R + +--R +--------+ +--R 3 7 2 5 2 3 3 +---+ | 2 +--R (- 2a x - 13a b x + 8a b x + 24b x)\|- a \|a x + b +--R + +--R 3 7 2 5 2 3 3 +---+ +-+ +--R (8a x + 12a b x - 20a b x - 24b x)\|- a \|b +--R / +--R +--------+ +--R 3 2 2 +---+ +-+ | 2 +--R (32a x + 64a b)\|- a \|b \|a x + b +--R + +--R 4 4 3 2 2 2 +---+ +--R (- 8a x - 64a b x - 64a b )\|- a +--R ] +--R Type: Union(List Expression Integer,...) +--E 428 + +--S 429 of 554 +m0277a:= a0277.1-r0277 +--R +--R +--R (398) +--R +--------+ +--R 2 2 3 +-+ | 2 2 2 4 3 2 4 +--R ((12a b x + 24b )\|b \|a x + b - 3a b x - 24a b x - 24b ) +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ 2 +-+ +--R (\|a \|b - a x)\|a x + b + a x\|b + (- a x - b)\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R 2 2 3 +-+ | 2 2 2 4 3 2 4 +--R ((- 12a b x - 24b )\|b \|a x + b + 3a b x + 24a b x + 24b ) +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R | 2 +--R 2 6 4 2 2 +-+ |a x + b +-+ +--R (- 8a x - 4a b x + 24b x )\|a |-------- \|b +--R | 2 +--R \| x +--R + +--R 3 7 2 5 2 3 3 +-+ +--R (- 2a x - 13a b x + 8a b x + 24b x)\|a +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 3 7 2 5 2 3 3 +-+ +-+ +--R (8a x + 12a b x - 20a b x - 24b x)\|a \|b +--R + +--R +--------+ +--R | 2 +--R 3 8 2 6 2 4 3 2 +-+ |a x + b +--R (2a x + 13a b x - 8a b x - 24b x )\|a |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R 3 2 2 +-+ +-+ | 2 4 4 3 2 2 2 +-+ +--R (32a x + 64a b)\|a \|b \|a x + b + (- 8a x - 64a b x - 64a b )\|a +--R Type: Expression Integer +--E 429 + +--S 430 of 554 +d0277a:= D(m0277a,x) +--R +--R +--R (399) +--R 5 14 4 12 3 2 10 2 3 8 4 6 +--R 11a x + 220a b x + 1232a b x + 2816a b x + 2816a b x +--R + +--R 5 4 +--R 1024b x +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +--R \|a |-------- +--R | 2 +--R \| x +--R + +--R 6 14 5 12 4 2 10 3 3 8 2 4 6 +--R - 11a x - 220a b x - 1232a b x - 2816a b x - 2816a b x +--R + +--R 5 4 +--R - 1024a b x +--R * +--R +-+ +--R \|b +--R + +--R 6 15 5 13 4 2 11 3 3 9 2 4 7 +--R - a x - 60a b x - 560a b x - 1792a b x - 2304a b x +--R + +--R 5 5 +--R - 1024a b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R + +--R 6 15 5 13 4 2 11 3 3 9 2 4 7 +--R a x + 61a b x + 620a b x + 2352a b x + 4096a b x +--R + +--R 5 5 6 3 +--R 3328a b x + 1024b x +--R * +--R +-+ +--R \|a +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 6 15 5 13 4 2 11 3 3 9 2 4 7 +--R 11a x + 220a b x + 1232a b x + 2816a b x + 2816a b x +--R + +--R 5 5 +--R 1024a b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R + +--R 6 15 5 13 4 2 11 3 3 9 2 4 7 +--R - 11a x - 231a b x - 1452a b x - 4048a b x - 5632a b x +--R + +--R 5 5 6 3 +--R - 3840a b x - 1024b x +--R * +--R +-+ +--R \|a +--R * +--R +-+ +--R \|b +--R + +--R 6 16 5 14 4 2 12 3 3 10 2 4 8 +--R - a x - 61a b x - 620a b x - 2352a b x - 4096a b x +--R + +--R 5 6 6 4 +--R - 3328a b x - 1024b x +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +--R \|a |-------- +--R | 2 +--R \| x +--R + +--R 7 16 6 14 5 2 12 4 3 10 3 4 8 2 5 6 +--R a x + 61a b x + 620a b x + 2352a b x + 4096a b x + 3328a b x +--R + +--R 6 4 +--R 1024a b x +--R / +--R 6 11 5 9 4 2 7 3 3 5 2 4 3 +--R 11a x + 220a b x + 1232a b x + 2816a b x + 2816a b x +--R + +--R 5 +--R 1024a b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R + +--R 6 12 5 10 4 2 8 3 3 6 2 4 4 +--R - a x - 61a b x - 620a b x - 2352a b x - 4096a b x +--R + +--R 5 2 6 +--R - 3328a b x - 1024b +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +--R \|a |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 6 12 5 10 4 2 8 3 3 6 2 4 4 +--R 11a x + 231a b x + 1452a b x + 4048a b x + 5632a b x +--R + +--R 5 2 6 +--R 3840a b x + 1024b +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +-+ +--R \|a |-------- \|b +--R | 2 +--R \| x +--R + +--R 7 13 6 11 5 2 9 4 3 7 3 4 5 +--R - a x - 61a b x - 620a b x - 2352a b x - 4096a b x +--R + +--R 2 5 3 6 +--R - 3328a b x - 1024a b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R Type: Expression Integer +--E 430 + +--S 431 of 554 +m0277b:= a0277.2-r0277 +--R +--R +--R (400) +--R +--------+ +--R 2 2 3 +---+ +-+ | 2 +--R (- 12a b x - 24b )\|- a \|b \|a x + b +--R + +--R 2 2 4 3 2 4 +---+ +--R (3a b x + 24a b x + 24b )\|- a +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R 2 2 3 +-+ +-+ | 2 +--R (24a b x + 48b )\|a \|b \|a x + b +--R + +--R 2 2 4 3 2 4 +-+ +--R (- 6a b x - 48a b x - 48b )\|a +--R * +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R \|- a \|a x + b - \|- a \|b +--R atan(------------------------------) +--R a x +--R + +--R +--------+ +--R | 2 +--R 2 6 4 2 2 +---+ +-+ |a x + b +-+ +--R (- 8a x - 4a b x + 24b x )\|- a \|a |-------- \|b +--R | 2 +--R \| x +--R + +--R 3 7 2 5 2 3 3 +---+ +-+ +--R (- 2a x - 13a b x + 8a b x + 24b x)\|- a \|a +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 3 7 2 5 2 3 3 +---+ +-+ +-+ +--R (8a x + 12a b x - 20a b x - 24b x)\|- a \|a \|b +--R + +--R +--------+ +--R | 2 +--R 3 8 2 6 2 4 3 2 +---+ +-+ |a x + b +--R (2a x + 13a b x - 8a b x - 24b x )\|- a \|a |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R 3 2 2 +---+ +-+ +-+ | 2 +--R (32a x + 64a b)\|- a \|a \|b \|a x + b +--R + +--R 4 4 3 2 2 2 +---+ +-+ +--R (- 8a x - 64a b x - 64a b )\|- a \|a +--R Type: Expression Integer +--E 431 + +--S 432 of 554 +d0277b:= D(m0277b,x) +--R +--R +--R (401) +--R +--------+ +--R | 2 +--R 3 10 2 8 2 6 3 4 |a x + b +-+ 4 11 +--R (- 8a x - 80a b x - 192a b x - 128b x ) |-------- \|b - a x +--R | 2 +--R \| x +--R + +--R 3 9 2 2 7 3 5 4 3 +--R - 32a b x - 160a b x - 256a b x - 128b x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 4 11 3 9 2 2 7 3 5 4 3 +-+ +--R (8a x + 88a b x + 272a b x + 320a b x + 128b x )\|b +--R + +--R +--------+ +--R | 2 +--R 4 12 3 10 2 2 8 3 6 4 4 |a x + b +--R (a x + 32a b x + 160a b x + 256a b x + 128b x ) |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R | 2 +--------+ +--R 4 8 3 6 2 2 4 3 2 4 |a x + b | 2 +--R (a x + 32a b x + 160a b x + 256a b x + 128b ) |-------- \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 4 8 3 6 2 2 4 3 2 4 |a x + b +-+ +--R (- 8a x - 88a b x - 272a b x - 320a b x - 128b ) |-------- \|b +--R | 2 +--R \| x +--R Type: Expression Integer +--E 432 + +--S 433 of 554 +t0278:= x/(a+b/x^2)^(1/2) +--R +--R +--R x +--R (402) ----------- +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R Type: Expression Integer +--E 433 + +--S 434 of 554 +r0278:= 1/2*(a+b/x^2)^(1/2)*x^2/a-1/2*b*atanh((a+b/x^2)^(1/2)/a^(1/2))/a^(3/2) +--R +--R +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--------+ +--R | 2 | 2 +--R \| x 2 +-+ |a x + b +--R - b atanh(-----------) + x \|a |-------- +--R +-+ | 2 +--R \|a \| x +--R (403) ------------------------------------------ +--R +-+ +--R 2a\|a +--R Type: Expression Integer +--E 434 + +--S 435 of 554 +a0278:= integrate(t0278,x) +--R +--R +--R (404) +--R [ +--R +--------+ +--R +-+ | 2 2 2 +--R (2b\|b \|a x + b - a b x - 2b ) +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ 2 +-+ +--R (\|a \|b + a x)\|a x + b - a x\|b + (- a x - b)\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R 3 +-+ | 2 3 +-+ +-+ +--R (- a x - 2b x)\|a \|a x + b + (2a x + 2b x)\|a \|b +--R / +--R +--------+ +--R +-+ +-+ | 2 2 2 +-+ +--R 4a\|a \|b \|a x + b + (- 2a x - 4a b)\|a +--R , +--R +--R +--------+ +--R +-+ | 2 2 2 +--R (- 4b\|b \|a x + b + 2a b x + 4b ) +--R * +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R \|- a \|a x + b - \|- a \|b +--R atan(------------------------------) +--R a x +--R + +--R +--------+ +--R 3 +---+ | 2 3 +---+ +-+ +--R (- a x - 2b x)\|- a \|a x + b + (2a x + 2b x)\|- a \|b +--R / +--R +--------+ +--R +---+ +-+ | 2 2 2 +---+ +--R 4a\|- a \|b \|a x + b + (- 2a x - 4a b)\|- a +--R ] +--R Type: Union(List Expression Integer,...) +--E 435 + +--S 436 of 554 +m0278a:= a0278.1-r0278 +--R +--R +--R (405) +--R +--------+ +--R +-+ | 2 2 2 +--R (2b\|b \|a x + b - a b x - 2b ) +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ 2 +-+ +--R (\|a \|b + a x)\|a x + b - a x\|b + (- a x - b)\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R +--------+ | 2 +--R +-+ | 2 2 2 \| x +--R (2b\|b \|a x + b - a b x - 2b )atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R | 2 +--------+ +--R 2 +-+ |a x + b +-+ 3 +-+ | 2 +--R (- 2x \|a |-------- \|b + (- a x - 2b x)\|a )\|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 +-+ +-+ 4 2 +-+ |a x + b +--R (2a x + 2b x)\|a \|b + (a x + 2b x )\|a |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R +-+ +-+ | 2 2 2 +-+ +--R 4a\|a \|b \|a x + b + (- 2a x - 4a b)\|a +--R Type: Expression Integer +--E 436 + +--S 437 of 554 +d0278a:= D(m0278a,x) +--R +--R +--R (406) +--R +--------+ +--R | 2 +--R 3 8 2 6 2 4 3 2 +-+ |a x + b 4 8 +--R (- 7a x - 56a b x - 112a b x - 64b x )\|a |-------- - 7a x +--R | 2 +--R \| x +--R + +--R 3 6 2 2 4 3 2 +--R - 56a b x - 112a b x - 64a b x +--R * +--R +-+ +--R \|b +--R + +--R +--------+ +--R | 2 +--R 4 9 3 7 2 2 5 3 3 |a x + b +--R (- a x - 24a b x - 80a b x - 64a b x ) |-------- +--R | 2 +--R \| x +--R + +--R 4 9 3 7 2 2 5 3 3 4 +-+ +--R (- a x - 25a b x - 104a b x - 144a b x - 64b x)\|a +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 4 9 3 7 2 2 5 3 3 |a x + b +--R (7a x + 56a b x + 112a b x + 64a b x ) |-------- +--R | 2 +--R \| x +--R + +--R 4 9 3 7 2 2 5 3 3 4 +-+ +--R (7a x + 63a b x + 168a b x + 176a b x + 64b x)\|a +--R * +--R +-+ +--R \|b +--R + +--R +--------+ +--R | 2 +--R 4 10 3 8 2 2 6 3 4 4 2 +-+ |a x + b +--R (a x + 25a b x + 104a b x + 144a b x + 64b x )\|a |-------- +--R | 2 +--R \| x +--R + +--R 5 10 4 8 3 2 6 2 3 4 4 2 +--R a x + 25a b x + 104a b x + 144a b x + 64a b x +--R / +--R +--------+ +--R | 2 +--R 4 7 3 5 2 2 3 3 |a x + b +-+ +--R (7a x + 56a b x + 112a b x + 64a b x) |-------- \|b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 4 8 3 6 2 2 4 3 2 4 +-+ |a x + b +--R (a x + 25a b x + 104a b x + 144a b x + 64b )\|a |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 4 8 3 6 2 2 4 3 2 4 +-+ |a x + b +-+ +--R (- 7a x - 63a b x - 168a b x - 176a b x - 64b )\|a |-------- \|b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 5 9 4 7 3 2 5 2 3 3 4 |a x + b +--R (- a x - 25a b x - 104a b x - 144a b x - 64a b x) |-------- +--R | 2 +--R \| x +--R Type: Expression Integer +--E 437 + +--S 438 of 554 +m0278b:= a0278.2-r0278 +--R +--R +--R (407) +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R +--------+ | 2 +--R +---+ +-+ | 2 2 2 +---+ \| x +--R (2b\|- a \|b \|a x + b + (- a b x - 2b )\|- a )atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R +-+ +-+ | 2 2 2 +-+ +--R (- 4b\|a \|b \|a x + b + (2a b x + 4b )\|a ) +--R * +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R \|- a \|a x + b - \|- a \|b +--R atan(------------------------------) +--R a x +--R + +--R +--------+ +--R | 2 +--------+ +--R 2 +---+ +-+ |a x + b +-+ 3 +---+ +-+ | 2 +--R (- 2x \|- a \|a |-------- \|b + (- a x - 2b x)\|- a \|a )\|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 +---+ +-+ +-+ 4 2 +---+ +-+ |a x + b +--R (2a x + 2b x)\|- a \|a \|b + (a x + 2b x )\|- a \|a |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R +---+ +-+ +-+ | 2 2 2 +---+ +-+ +--R 4a\|- a \|a \|b \|a x + b + (- 2a x - 4a b)\|- a \|a +--R Type: Expression Integer +--E 438 + +--S 439 of 554 +d0278b:= D(m0278b,x) +--R +--R +--R (408) +--R +--------+ +--R | 2 +--------+ +--R 4 2 |a x + b +-+ 2 5 3 2 | 2 +--R ((- 4a x - 8b x ) |-------- \|b - a x - 8a b x - 8b x)\|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 2 5 3 2 +-+ 2 6 4 2 2 |a x + b +--R (4a x + 12a b x + 8b x)\|b + (a x + 8a b x + 8b x ) |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R | 2 +--------+ +--R 2 4 2 2 |a x + b | 2 +--R (a x + 8a b x + 8b ) |-------- \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 2 4 2 2 |a x + b +-+ +--R (- 4a x - 12a b x - 8b ) |-------- \|b +--R | 2 +--R \| x +--R Type: Expression Integer +--E 439 + +--S 440 of 554 +t0279:= 1/x/(a+b/x^2)^(1/2) +--R +--R +--R 1 +--R (409) ------------ +--R +--------+ +--R | 2 +--R |a x + b +--R x |-------- +--R | 2 +--R \| x +--R Type: Expression Integer +--E 440 + +--S 441 of 554 +r0279:= atanh((a+b/x^2)^(1/2)/a^(1/2))/a^(1/2) +--R +--R +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R atanh(-----------) +--R +-+ +--R \|a +--R (410) ------------------ +--R +-+ +--R \|a +--R Type: Expression Integer +--E 441 + +--S 442 of 554 +a0279:= integrate(t0279,x) +--R +--R +--R (411) +--R +--------+ +--R +-+ +-+ | 2 +-+ 2 +-+ +--R (\|a \|b - a x)\|a x + b + a x\|b + (- a x - b)\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R [-------------------------------------------------------------, +--R +-+ +--R \|a +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R \|- a \|a x + b - \|- a \|b +--R 2atan(------------------------------) +--R a x +--R -------------------------------------] +--R +---+ +--R \|- a +--R Type: Union(List Expression Integer,...) +--E 442 + +--S 443 of 554 +m0279a:= a0279.1-r0279 +--R +--R +--R (412) +--R +--------+ +--R +-+ +-+ | 2 +-+ 2 +-+ +--R (\|a \|b - a x)\|a x + b + a x\|b + (- a x - b)\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R - atanh(-----------) +--R +-+ +--R \|a +--R / +--R +-+ +--R \|a +--R Type: Expression Integer +--E 443 + +--S 444 of 554 +d0279a:= D(m0279a,x) +--R +--R +--R (413) +--R +--------+ +--R | 2 +--R 3 +-+ |a x + b 2 3 +-+ +--R ((3a x + 4b x)\|a |-------- - 3a x - 4a b x)\|b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 2 4 2 |a x + b 2 4 2 2 +-+ +--R (- a x - 4a b x ) |-------- + (a x + 5a b x + 4b )\|a +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 2 4 2 |a x + b 2 4 2 2 +-+ +-+ +--R ((3a x + 4a b x ) |-------- + (- 3a x - 7a b x - 4b )\|a )\|b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 2 5 3 2 +-+ |a x + b 3 5 2 3 2 +--R (- a x - 5a b x - 4b x)\|a |-------- + a x + 5a b x + 4a b x +--R | 2 +--R \| x +--R / +--R +--------+ +--R | 2 +--R 2 4 2 |a x + b +-+ +--R (3a x + 4a b x ) |-------- \|b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 2 5 3 2 +-+ |a x + b +--R (- a x - 5a b x - 4b x)\|a |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 2 5 3 2 +-+ |a x + b +-+ +--R (3a x + 7a b x + 4b x)\|a |-------- \|b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 6 2 4 2 2 |a x + b +--R (- a x - 5a b x - 4a b x ) |-------- +--R | 2 +--R \| x +--R Type: Expression Integer +--E 444 + +--S 445 of 554 +m0279b:= a0279.2-r0279 +--R +--R +--R (414) +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--------+ +--R | 2 +---+ | 2 +---+ +-+ +--R +---+ \| x +-+ \|- a \|a x + b - \|- a \|b +--R - \|- a atanh(-----------) + 2\|a atan(------------------------------) +--R +-+ a x +--R \|a +--R ---------------------------------------------------------------------- +--R +---+ +-+ +--R \|- a \|a +--R Type: Expression Integer +--E 445 + +--S 446 of 554 +d0279b:= D(m0279b,x) +--R +--R +--R +--------+ +--R +--------+ | 2 +--R | 2 |a x + b +--R - \|a x + b + x |-------- +--R | 2 +--R \| x +--R (415) ---------------------------- +--R +--------+ +--R | 2 +--------+ +--R |a x + b | 2 +--R x |-------- \|a x + b +--R | 2 +--R \| x +--R Type: Expression Integer +--E 446 + +--S 447 of 554 +t0280:= 1/x/(-a+b/x^2)^(1/2) +--R +--R +--R 1 +--R (416) -------------- +--R +----------+ +--R | 2 +--R |- a x + b +--R x |---------- +--R | 2 +--R \| x +--R Type: Expression Integer +--E 447 + +--S 448 of 554 +r0280:= -atan((-a+b/x^2)^(1/2)/a^(1/2))/a^(1/2) +--R +--R +--R +----------+ +--R | 2 +--R |- a x + b +--R |---------- +--R | 2 +--R \| x +--R atan(-------------) +--R +-+ +--R \|a +--R (417) - ------------------- +--R +-+ +--R \|a +--R Type: Expression Integer +--E 448 + +--S 449 of 554 +a0280:= integrate(t0280,x) +--R +--R +--R (418) +--R +----------+ +----------+ +--R | 2 +---+ +-+ 2 +---+ | 2 +--R (\|- a x + b \|- a - a x)\|b + (a x - b)\|- a + a x\|- a x + b +--R log(---------------------------------------------------------------------) +--R +----------+ +--R | 2 +-+ +--R \|- a x + b \|b - b +--R [--------------------------------------------------------------------------, +--R +---+ +--R \|- a +--R +----------+ +--R +-+ +-+ | 2 +-+ +--R \|a \|b - \|- a x + b \|a +--R 2atan(----------------------------) +--R a x +--R -----------------------------------] +--R +-+ +--R \|a +--R Type: Union(List Expression Integer,...) +--E 449 + +--S 450 of 554 +m0280a:= a0280.1-r0280 +--R +--R +--R (419) +--R +-+ +--R \|a +--R * +--R log +--R +----------+ +--R | 2 +---+ +-+ 2 +---+ +--R (\|- a x + b \|- a - a x)\|b + (a x - b)\|- a +--R + +--R +----------+ +--R | 2 +--R a x\|- a x + b +--R / +--R +----------+ +--R | 2 +-+ +--R \|- a x + b \|b - b +--R + +--R +----------+ +--R | 2 +--R |- a x + b +--R |---------- +--R | 2 +--R +---+ \| x +--R \|- a atan(-------------) +--R +-+ +--R \|a +--R / +--R +---+ +-+ +--R \|- a \|a +--R Type: Expression Integer +--E 450 + +--S 451 of 554 +d0280a:= D(m0280a,x) +--R +--R +--R (420) +--R +----------+ +--R +----------+ | 2 +--R 3 | 2 +---+ 2 4 2 |- a x + b +--R ((- 3a x + 4b x)\|- a x + b \|- a + 3a x - 4a b x ) |---------- +--R | 2 +--R \| x +--R + +--R +----------+ +--R 2 4 2 2 +---+ 2 3 | 2 +--R (- 3a x + 7a b x - 4b )\|- a + (- 3a x + 4a b x)\|- a x + b +--R * +--R +-+ +--R \|b +--R + +--R +----------+ +--R 2 5 3 2 +---+ 2 4 2 | 2 +--R ((- a x + 5a b x - 4b x)\|- a + (- a x + 4a b x )\|- a x + b ) +--R * +--R +----------+ +--R | 2 +--R |- a x + b +--R |---------- +--R | 2 +--R \| x +--R + +--R +----------+ +--R 2 4 2 2 | 2 +---+ 3 5 2 3 2 +--R (a x - 5a b x + 4b )\|- a x + b \|- a - a x + 5a b x - 4a b x +--R / +--R +----------+ +--R 2 5 3 2 +---+ 2 4 2 | 2 +--R ((3a x - 7a b x + 4b x)\|- a + (3a x - 4a b x )\|- a x + b ) +--R * +--R +----------+ +--R | 2 +--R |- a x + b +-+ +--R |---------- \|b +--R | 2 +--R \| x +--R + +--R +----------+ +--R 2 5 3 2 | 2 +---+ 3 6 2 4 +--R (- a x + 5a b x - 4b x)\|- a x + b \|- a + a x - 5a b x +--R + +--R 2 2 +--R 4a b x +--R * +--R +----------+ +--R | 2 +--R |- a x + b +--R |---------- +--R | 2 +--R \| x +--R Type: Expression Integer +--E 451 + +--S 452 of 554 +m0280b:= a0280.2-r0280 +--R +--R +--R +----------+ +--R | 2 +--R |- a x + b +--R +----------+ |---------- +--R +-+ +-+ | 2 +-+ | 2 +--R \|a \|b - \|- a x + b \|a \| x +--R 2atan(----------------------------) + atan(-------------) +--R a x +-+ +--R \|a +--R (421) --------------------------------------------------------- +--R +-+ +--R \|a +--R Type: Expression Integer +--E 452 + +--S 453 of 554 +d0280b:= D(m0280b,x) +--R +--R +--R +----------+ +--R | 2 +----------+ +--R |- a x + b | 2 +--R x |---------- - \|- a x + b +--R | 2 +--R \| x +--R (422) ------------------------------ +--R +----------+ +--R +----------+ | 2 +--R | 2 |- a x + b +--R x\|- a x + b |---------- +--R | 2 +--R \| x +--R Type: Expression Integer +--E 453 + +--S 454 of 554 +t0281:= 1/x^2/(2+b/x^2)^(1/2) +--R +--R +--R 1 +--R (423) ------------ +--R +-------+ +--R | 2 +--R 2 |2x + b +--R x |------- +--R | 2 +--R \| x +--R Type: Expression Integer +--E 454 + +--S 455 of 554 +r0281:= -asinh(1/2*b^(1/2)*2^(1/2)/x)/b^(1/2) +--R +--R +--R +-+ +-+ +--R \|2 \|b +--R asinh(--------) +--R 2x +--R (424) - --------------- +--R +-+ +--R \|b +--R Type: Expression Integer +--E 455 + +--S 456 of 554 +a0281:= integrate(t0281,x) +--R +--R +--R +-------+ +--R | 2 +-+ +--R +-+ \|2x + b - \|b +--R \|b log(-----------------) +--R x +--R (425) -------------------------- +--R b +--R Type: Union(Expression Integer,...) +--E 456 + +--S 457 of 554 +m0281:= a0281-r0281 +--R +--R +--R +-------+ +--R | 2 +-+ +-+ +-+ +--R \|2x + b - \|b \|2 \|b +--R log(-----------------) + asinh(--------) +--R x 2x +--R (426) ---------------------------------------- +--R +-+ +--R \|b +--R Type: Expression Integer +--E 457 + +--S 458 of 554 +d0281:= D(m0281,x) +--R +--R +--R (427) +--R +-------+ +-------+ +--R | 2 +-------+ | 2 +--R +-+ +-+ |2x + b | 2 |2x + b +-+ 2 +-+ +--R (- \|2 \|b - 2x |------- )\|2x + b + 2x |------- \|b + (2x + b)\|2 +--R | 2 | 2 +--R \| 2x \| 2x +--R ------------------------------------------------------------------------ +--R +-------+ +-------+ +--R | 2 +-------+ | 2 +--R 2 |2x + b +-+ | 2 4 2 |2x + b +--R 2x |------- \|b \|2x + b + (- 4x - 2b x ) |------- +--R | 2 | 2 +--R \| 2x \| 2x +--R Type: Expression Integer +--E 458 + +--S 459 of 554 +t0282:= 1/x^2/(2-b/x^2)^(1/2) +--R +--R +--R 1 +--R (428) ------------ +--R +-------+ +--R | 2 +--R 2 |2x - b +--R x |------- +--R | 2 +--R \| x +--R Type: Expression Integer +--E 459 + +--S 460 of 554 +r0282:= -asin(1/2*b^(1/2)*2^(1/2)/x)/b^(1/2) +--R +--R +--R +-+ +-+ +--R \|2 \|b +--R asin(--------) +--R 2x +--R (429) - -------------- +--R +-+ +--R \|b +--R Type: Expression Integer +--E 460 + +--S 461 of 554 +a0282:= integrate(t0282,x) +--R +--R +--R +-------+ +--R | 2 +---+ +--R +---+ \|2x - b - \|- b +--R \|- b log(-------------------) +--R x +--R (430) - ------------------------------ +--R b +--R Type: Union(Expression Integer,...) +--E 461 + +--S 462 of 554 +m0282:= a0282-r0282 +--R +--R +--R +-------+ +--R | 2 +---+ +-+ +-+ +--R +---+ +-+ \|2x - b - \|- b \|2 \|b +--R - \|- b \|b log(-------------------) + b asin(--------) +--R x 2x +--R (431) ------------------------------------------------------- +--R +-+ +--R b\|b +--R Type: Expression Integer +--E 462 + +--S 463 of 554 +d0282:= D(m0282,x) +--R +--R +--R (432) +--R +-------+ +-------+ +--R | 2 +-------+ | 2 +--R |2x - b +-+ +---+ | 2 +---+ |2x - b 2 +-+ +--R (- 2x |------- - \|2 \|- b )\|2x - b + 2x\|- b |------- + (2x - b)\|2 +--R | 2 | 2 +--R \| 2x \| 2x +--R ---------------------------------------------------------------------------- +--R +-------+ +-------+ +--R | 2 +-------+ | 2 +--R 2 +---+ |2x - b | 2 4 2 |2x - b +--R 2x \|- b |------- \|2x - b + (- 4x + 2b x ) |------- +--R | 2 | 2 +--R \| 2x \| 2x +--R Type: Expression Integer +--E 463 + +--S 464 of 554 +t0283:= 1/x^2/(a+b/x^2)^(1/2) +--R +--R +--R 1 +--R (433) ------------- +--R +--------+ +--R | 2 +--R 2 |a x + b +--R x |-------- +--R | 2 +--R \| x +--R Type: Expression Integer +--E 464 + +--S 465 of 554 +r0283:= -atanh((a+b/x^2)^(1/2)*x/b^(1/2))/b^(1/2) +--R +--R +--R +--------+ +--R | 2 +--R |a x + b +--R x |-------- +--R | 2 +--R \| x +--R atanh(------------) +--R +-+ +--R \|b +--R (434) - ------------------- +--R +-+ +--R \|b +--R Type: Expression Integer +--E 465 + +--S 466 of 554 +a0283:= integrate(t0283,x) +--R +--R +--R +--------+ +--R | 2 +-+ +--R +-+ \|a x + b - \|b +--R \|b log(------------------) +--R x +--R (435) --------------------------- +--R b +--R Type: Union(Expression Integer,...) +--E 466 + +--S 467 of 554 +m0283:= a0283-r0283 +--R +--R +--R +--------+ +--R | 2 +--R |a x + b +--R +--------+ x |-------- +--R | 2 +-+ | 2 +--R \|a x + b - \|b \| x +--R log(------------------) + atanh(------------) +--R x +-+ +--R \|b +--R (436) --------------------------------------------- +--R +-+ +--R \|b +--R Type: Expression Integer +--E 467 + +--S 468 of 554 +d0283:= D(m0283,x) +--R +--R +--R +--------+ +--------+ +--R | 2 +--------+ | 2 +--R +-+ |a x + b | 2 |a x + b +-+ 2 +--R (- \|b - x |-------- )\|a x + b + x |-------- \|b + a x + b +--R | 2 | 2 +--R \| x \| x +--R (437) ---------------------------------------------------------------- +--R +--------+ +--------+ +--R | 2 +--------+ | 2 +--R 2 |a x + b +-+ | 2 4 2 |a x + b +--R x |-------- \|b \|a x + b + (- a x - b x ) |-------- +--R | 2 | 2 +--R \| x \| x +--R Type: Expression Integer +--E 468 + +--S 469 of 554 +t0284:= x^3*(a+b/x^2)^(1/2) +--R +--R +--R +--------+ +--R | 2 +--R 3 |a x + b +--R (438) x |-------- +--R | 2 +--R \| x +--R Type: Expression Integer +--E 469 + +--S 470 of 554 +r0284:= 1/8*b*(a+b/x^2)^(1/2)*x^2/a+1/4*(a+b/x^2)^(1/2)*x^4-_ + 1/8*b^2*atanh((a+b/x^2)^(1/2)/a^(1/2))/a^(3/2) +--R +--R +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--------+ +--R | 2 | 2 +--R 2 \| x 4 2 +-+ |a x + b +--R - b atanh(-----------) + (2a x + b x )\|a |-------- +--R +-+ | 2 +--R \|a \| x +--R (439) ------------------------------------------------------ +--R +-+ +--R 8a\|a +--R Type: Expression Integer +--E 470 + +--S 471 of 554 +a0284:= integrate(t0284,x) +--R +--R +--R (440) +--R [ +--R +--------+ +--R 2 2 3 +-+ | 2 2 2 4 3 2 4 +--R ((4a b x + 8b )\|b \|a x + b - a b x - 8a b x - 8b ) +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ 2 +-+ +--R (\|a \|b + a x)\|a x + b - a x\|b + (- a x - b)\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R 3 7 2 5 2 3 3 +-+ | 2 +--R (- 2a x - 17a b x - 24a b x - 8b x)\|a \|a x + b +--R + +--R 3 7 2 5 2 3 3 +-+ +-+ +--R (8a x + 28a b x + 28a b x + 8b x)\|a \|b +--R / +--R +--------+ +--R 2 2 +-+ +-+ | 2 3 4 2 2 2 +-+ +--R (32a x + 64a b)\|a \|b \|a x + b + (- 8a x - 64a b x - 64a b )\|a +--R , +--R +--R +--------+ +--R 2 2 3 +-+ | 2 2 2 4 3 2 4 +--R ((- 8a b x - 16b )\|b \|a x + b + 2a b x + 16a b x + 16b ) +--R * +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R \|- a \|a x + b - \|- a \|b +--R atan(------------------------------) +--R a x +--R + +--R +--------+ +--R 3 7 2 5 2 3 3 +---+ | 2 +--R (- 2a x - 17a b x - 24a b x - 8b x)\|- a \|a x + b +--R + +--R 3 7 2 5 2 3 3 +---+ +-+ +--R (8a x + 28a b x + 28a b x + 8b x)\|- a \|b +--R / +--R +--------+ +--R 2 2 +---+ +-+ | 2 +--R (32a x + 64a b)\|- a \|b \|a x + b +--R + +--R 3 4 2 2 2 +---+ +--R (- 8a x - 64a b x - 64a b )\|- a +--R ] +--R Type: Union(List Expression Integer,...) +--E 471 + +--S 472 of 554 +m0284a:= a0284.1-r0284 +--R +--R +--R (441) +--R +--------+ +--R 2 2 3 +-+ | 2 2 2 4 3 2 4 +--R ((4a b x + 8b )\|b \|a x + b - a b x - 8a b x - 8b ) +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ 2 +-+ +--R (\|a \|b + a x)\|a x + b - a x\|b + (- a x - b)\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R 2 2 3 +-+ | 2 2 2 4 3 2 4 +--R ((4a b x + 8b )\|b \|a x + b - a b x - 8a b x - 8b ) +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R | 2 +--R 2 6 4 2 2 +-+ |a x + b +-+ +--R (- 8a x - 20a b x - 8b x )\|a |-------- \|b +--R | 2 +--R \| x +--R + +--R 3 7 2 5 2 3 3 +-+ +--R (- 2a x - 17a b x - 24a b x - 8b x)\|a +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 3 7 2 5 2 3 3 +-+ +-+ +--R (8a x + 28a b x + 28a b x + 8b x)\|a \|b +--R + +--R +--------+ +--R | 2 +--R 3 8 2 6 2 4 3 2 +-+ |a x + b +--R (2a x + 17a b x + 24a b x + 8b x )\|a |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R 2 2 +-+ +-+ | 2 3 4 2 2 2 +-+ +--R (32a x + 64a b)\|a \|b \|a x + b + (- 8a x - 64a b x - 64a b )\|a +--R Type: Expression Integer +--E 472 + +--S 473 of 554 +d0284a:= D(m0284a,x) +--R +--R +--R (442) +--R 6 14 5 12 4 2 10 3 3 8 +--R - 11a x - 231a b x - 1452a b x - 4048a b x +--R + +--R 2 4 6 5 4 6 2 +--R - 5632a b x - 3840a b x - 1024b x +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +--R \|a |-------- +--R | 2 +--R \| x +--R + +--R 7 14 6 12 5 2 10 4 3 8 3 4 6 +--R - 11a x - 231a b x - 1452a b x - 4048a b x - 5632a b x +--R + +--R 2 5 4 6 2 +--R - 3840a b x - 1024a b x +--R * +--R +-+ +--R \|b +--R + +--R 7 15 6 13 5 2 11 4 3 9 3 4 7 +--R - a x - 61a b x - 620a b x - 2352a b x - 4096a b x +--R + +--R 2 5 5 6 3 +--R - 3328a b x - 1024a b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R + +--R 7 15 6 13 5 2 11 4 3 9 3 4 7 +--R - a x - 62a b x - 681a b x - 2972a b x - 6448a b x +--R + +--R 2 5 5 6 3 7 +--R - 7424a b x - 4352a b x - 1024b x +--R * +--R +-+ +--R \|a +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 7 15 6 13 5 2 11 4 3 9 3 4 7 +--R 11a x + 231a b x + 1452a b x + 4048a b x + 5632a b x +--R + +--R 2 5 5 6 3 +--R 3840a b x + 1024a b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R + +--R 7 15 6 13 5 2 11 4 3 9 3 4 7 +--R 11a x + 242a b x + 1683a b x + 5500a b x + 9680a b x +--R + +--R 2 5 5 6 3 7 +--R 9472a b x + 4864a b x + 1024b x +--R * +--R +-+ +--R \|a +--R * +--R +-+ +--R \|b +--R + +--R 7 16 6 14 5 2 12 4 3 10 3 4 8 +--R a x + 62a b x + 681a b x + 2972a b x + 6448a b x +--R + +--R 2 5 6 6 4 7 2 +--R 7424a b x + 4352a b x + 1024b x +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +--R \|a |-------- +--R | 2 +--R \| x +--R + +--R 8 16 7 14 6 2 12 5 3 10 4 4 8 3 5 6 +--R a x + 62a b x + 681a b x + 2972a b x + 6448a b x + 7424a b x +--R + +--R 2 6 4 7 2 +--R 4352a b x + 1024a b x +--R / +--R 6 11 5 9 4 2 7 3 3 5 2 4 3 +--R 11a x + 220a b x + 1232a b x + 2816a b x + 2816a b x +--R + +--R 5 +--R 1024a b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R + +--R 6 12 5 10 4 2 8 3 3 6 2 4 4 +--R a x + 61a b x + 620a b x + 2352a b x + 4096a b x +--R + +--R 5 2 6 +--R 3328a b x + 1024b +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +--R \|a |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 6 12 5 10 4 2 8 3 3 6 2 4 4 +--R - 11a x - 231a b x - 1452a b x - 4048a b x - 5632a b x +--R + +--R 5 2 6 +--R - 3840a b x - 1024b +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +-+ +--R \|a |-------- \|b +--R | 2 +--R \| x +--R + +--R 7 13 6 11 5 2 9 4 3 7 3 4 5 +--R - a x - 61a b x - 620a b x - 2352a b x - 4096a b x +--R + +--R 2 5 3 6 +--R - 3328a b x - 1024a b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R Type: Expression Integer +--E 473 + +--S 474 of 554 +m0284b:= a0284.2-r0284 +--R +--R +--R (443) +--R +--------+ +--R 2 2 3 +---+ +-+ | 2 +--R (4a b x + 8b )\|- a \|b \|a x + b +--R + +--R 2 2 4 3 2 4 +---+ +--R (- a b x - 8a b x - 8b )\|- a +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R 2 2 3 +-+ +-+ | 2 +--R (- 8a b x - 16b )\|a \|b \|a x + b +--R + +--R 2 2 4 3 2 4 +-+ +--R (2a b x + 16a b x + 16b )\|a +--R * +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R \|- a \|a x + b - \|- a \|b +--R atan(------------------------------) +--R a x +--R + +--R +--------+ +--R | 2 +--R 2 6 4 2 2 +---+ +-+ |a x + b +-+ +--R (- 8a x - 20a b x - 8b x )\|- a \|a |-------- \|b +--R | 2 +--R \| x +--R + +--R 3 7 2 5 2 3 3 +---+ +-+ +--R (- 2a x - 17a b x - 24a b x - 8b x)\|- a \|a +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 3 7 2 5 2 3 3 +---+ +-+ +-+ +--R (8a x + 28a b x + 28a b x + 8b x)\|- a \|a \|b +--R + +--R +--------+ +--R | 2 +--R 3 8 2 6 2 4 3 2 +---+ +-+ |a x + b +--R (2a x + 17a b x + 24a b x + 8b x )\|- a \|a |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R 2 2 +---+ +-+ +-+ | 2 +--R (32a x + 64a b)\|- a \|a \|b \|a x + b +--R + +--R 3 4 2 2 2 +---+ +-+ +--R (- 8a x - 64a b x - 64a b )\|- a \|a +--R Type: Expression Integer +--E 474 + +--S 475 of 554 +d0284b:= D(m0284b,x) +--R +--R +--R (444) +--R +--------+ +--R | 2 +--R 4 10 3 8 2 2 6 3 4 4 2 |a x + b +--R (- 8a x - 88a b x - 272a b x - 320a b x - 128b x ) |-------- +--R | 2 +--R \| x +--R * +--R +-+ +--R \|b +--R + +--R 5 11 4 9 3 2 7 2 3 5 4 3 5 +--R - a x - 33a b x - 192a b x - 416a b x - 384a b x - 128b x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 5 11 4 9 3 2 7 2 3 5 4 3 5 +-+ +--R (8a x + 96a b x + 360a b x + 592a b x + 448a b x + 128b x)\|b +--R + +--R 5 12 4 10 3 2 8 2 3 6 4 4 5 2 +--R (a x + 33a b x + 192a b x + 416a b x + 384a b x + 128b x ) +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R | 2 +--------+ +--R 4 8 3 6 2 2 4 3 2 4 |a x + b | 2 +--R (a x + 32a b x + 160a b x + 256a b x + 128b ) |-------- \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 4 8 3 6 2 2 4 3 2 4 |a x + b +-+ +--R (- 8a x - 88a b x - 272a b x - 320a b x - 128b ) |-------- \|b +--R | 2 +--R \| x +--R Type: Expression Integer +--E 475 + +--S 476 of 554 +t0285:= x*(a+b/x^2)^(1/2) +--R +--R +--R +--------+ +--R | 2 +--R |a x + b +--R (445) x |-------- +--R | 2 +--R \| x +--R Type: Expression Integer +--E 476 + +--S 477 of 554 +r0285:= 1/2*x^2*(a+b/x^2)^(1/2)+1/2*b*atanh((a+b/x^2)^(1/2)/a^(1/2))/a^(1/2) +--R +--R +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--------+ +--R | 2 | 2 +--R \| x 2 +-+ |a x + b +--R b atanh(-----------) + x \|a |-------- +--R +-+ | 2 +--R \|a \| x +--R (446) ---------------------------------------- +--R +-+ +--R 2\|a +--R Type: Expression Integer +--E 477 + +--S 478 of 554 +a0285:= integrate(t0285,x) +--R +--R +--R (447) +--R [ +--R +--------+ +--R +-+ | 2 2 2 +--R (2b\|b \|a x + b - a b x - 2b ) +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ 2 +-+ +--R (\|a \|b - a x)\|a x + b + a x\|b + (- a x - b)\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R 3 +-+ | 2 3 +-+ +-+ +--R (- a x - 2b x)\|a \|a x + b + (2a x + 2b x)\|a \|b +--R / +--R +--------+ +--R +-+ +-+ | 2 2 +-+ +--R 4\|a \|b \|a x + b + (- 2a x - 4b)\|a +--R , +--R +--R +--------+ +--R +--------+ +---+ | 2 +---+ +-+ +--R +-+ | 2 2 2 \|- a \|a x + b - \|- a \|b +--R (4b\|b \|a x + b - 2a b x - 4b )atan(------------------------------) +--R a x +--R + +--R +--------+ +--R 3 +---+ | 2 3 +---+ +-+ +--R (- a x - 2b x)\|- a \|a x + b + (2a x + 2b x)\|- a \|b +--R / +--R +--------+ +--R +---+ +-+ | 2 2 +---+ +--R 4\|- a \|b \|a x + b + (- 2a x - 4b)\|- a +--R ] +--R Type: Union(List Expression Integer,...) +--E 478 + +--S 479 of 554 +m0285a:= a0285.1-r0285 +--R +--R +--R (448) +--R +--------+ +--R +-+ | 2 2 2 +--R (2b\|b \|a x + b - a b x - 2b ) +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ 2 +-+ +--R (\|a \|b - a x)\|a x + b + a x\|b + (- a x - b)\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R +--------+ | 2 +--R +-+ | 2 2 2 \| x +--R (- 2b\|b \|a x + b + a b x + 2b )atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R | 2 +--------+ +--R 2 +-+ |a x + b +-+ 3 +-+ | 2 +--R (- 2x \|a |-------- \|b + (- a x - 2b x)\|a )\|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 +-+ +-+ 4 2 +-+ |a x + b +--R (2a x + 2b x)\|a \|b + (a x + 2b x )\|a |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R +-+ +-+ | 2 2 +-+ +--R 4\|a \|b \|a x + b + (- 2a x - 4b)\|a +--R Type: Expression Integer +--E 479 + +--S 480 of 554 +d0285a:= D(m0285a,x) +--R +--R +--R (449) +--R +--------+ +--R | 2 +--R 4 9 3 7 2 2 5 3 3 4 +-+ |a x + b +--R (7a x + 63a b x + 168a b x + 176a b x + 64b x)\|a |-------- +--R | 2 +--R \| x +--R + +--R 5 9 4 7 3 2 5 2 3 3 4 +--R - 7a x - 63a b x - 168a b x - 176a b x - 64a b x +--R * +--R +-+ +--R \|b +--R + +--R +--------+ +--R | 2 +--R 5 10 4 8 3 2 6 2 3 4 4 2 |a x + b +--R (- a x - 25a b x - 104a b x - 144a b x - 64a b x ) |-------- +--R | 2 +--R \| x +--R + +--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +-+ +--R (a x + 26a b x + 129a b x + 248a b x + 208a b x + 64b )\|a +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 5 10 4 8 3 2 6 2 3 4 4 2 |a x + b +--R (7a x + 63a b x + 168a b x + 176a b x + 64a b x ) |-------- +--R | 2 +--R \| x +--R + +--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +-+ +--R (- 7a x - 70a b x - 231a b x - 344a b x - 240a b x - 64b )\|a +--R * +--R +-+ +--R \|b +--R + +--R 5 11 4 9 3 2 7 2 3 5 4 3 5 +-+ +--R (- a x - 26a b x - 129a b x - 248a b x - 208a b x - 64b x)\|a +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R + +--R 6 11 5 9 4 2 7 3 3 5 2 4 3 5 +--R a x + 26a b x + 129a b x + 248a b x + 208a b x + 64a b x +--R / +--R +--------+ +--R | 2 +--R 4 8 3 6 2 2 4 3 2 |a x + b +-+ +--R (7a x + 56a b x + 112a b x + 64a b x ) |-------- \|b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 4 9 3 7 2 2 5 3 3 4 +-+ |a x + b +--R (- a x - 25a b x - 104a b x - 144a b x - 64b x)\|a |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 4 9 3 7 2 2 5 3 3 4 +-+ |a x + b +-+ +--R (7a x + 63a b x + 168a b x + 176a b x + 64b x)\|a |-------- \|b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 5 10 4 8 3 2 6 2 3 4 4 2 |a x + b +--R (- a x - 25a b x - 104a b x - 144a b x - 64a b x ) |-------- +--R | 2 +--R \| x +--R Type: Expression Integer +--E 480 + +--S 481 of 554 +m0285b:= a0285.2-r0285 +--R +--R +--R (450) +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R +--------+ | 2 +--R +---+ +-+ | 2 2 2 +---+ \| x +--R (- 2b\|- a \|b \|a x + b + (a b x + 2b )\|- a )atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R +-+ +-+ | 2 2 2 +-+ +--R (4b\|a \|b \|a x + b + (- 2a b x - 4b )\|a ) +--R * +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R \|- a \|a x + b - \|- a \|b +--R atan(------------------------------) +--R a x +--R + +--R +--------+ +--R | 2 +--------+ +--R 2 +---+ +-+ |a x + b +-+ 3 +---+ +-+ | 2 +--R (- 2x \|- a \|a |-------- \|b + (- a x - 2b x)\|- a \|a )\|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 +---+ +-+ +-+ 4 2 +---+ +-+ |a x + b +--R (2a x + 2b x)\|- a \|a \|b + (a x + 2b x )\|- a \|a |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R +---+ +-+ +-+ | 2 2 +---+ +-+ +--R 4\|- a \|a \|b \|a x + b + (- 2a x - 4b)\|- a \|a +--R Type: Expression Integer +--E 481 + +--S 482 of 554 +d0285b:= D(m0285b,x) +--R +--R +--R (451) +--R +--------+ +--R | 2 +--R 2 5 3 2 |a x + b +-+ 3 6 2 4 +--R (- 4a x - 12a b x - 8b x) |-------- \|b - a x - 9a b x +--R | 2 +--R \| x +--R + +--R 2 2 3 +--R - 16a b x - 8b +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 3 6 2 4 2 2 3 +-+ +--R (4a x + 16a b x + 20a b x + 8b )\|b +--R + +--R +--------+ +--R | 2 +--R 3 7 2 5 2 3 3 |a x + b +--R (a x + 9a b x + 16a b x + 8b x) |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R | 2 +--------+ +--R 2 5 3 2 |a x + b | 2 +--R (a x + 8a b x + 8b x) |-------- \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 2 5 3 2 |a x + b +-+ +--R (- 4a x - 12a b x - 8b x) |-------- \|b +--R | 2 +--R \| x +--R Type: Expression Integer +--E 482 + +--S 483 of 554 +t0286:= (a+b/x^2)^(1/2) +--R +--R +--R +--------+ +--R | 2 +--R |a x + b +--R (452) |-------- +--R | 2 +--R \| x +--R Type: Expression Integer +--E 483 + +--S 484 of 554 +r0286:= x*(a+b/x^2)^(1/2)-b^(1/2)*atanh((a+b/x^2)^(1/2)*x/b^(1/2)) +--R +--R +--R +--------+ +--R | 2 +--R |a x + b +--R x |-------- +--------+ +--R | 2 | 2 +--R +-+ \| x |a x + b +--R (453) - \|b atanh(------------) + x |-------- +--R +-+ | 2 +--R \|b \| x +--R Type: Expression Integer +--E 484 + +--S 485 of 554 +a0286:= integrate(t0286,x) +--R +--R +--R +--------+ +--R +--------+ | 2 +-+ +--R | 2 +-+ \|a x + b - \|b 2 +-+ +--R (b\|a x + b - b\|b )log(------------------) + a x \|b +--R x +--R (454) -------------------------------------------------------- +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R Type: Union(Expression Integer,...) +--E 485 + +--S 486 of 554 +m0286:= a0286-r0286 +--R +--R +--R (455) +--R +--------+ +--R +--------+ | 2 +-+ +--R | 2 +-+ \|a x + b - \|b +--R (b\|a x + b - b\|b )log(------------------) +--R x +--R + +--R +--------+ +--R | 2 +--R |a x + b +--R x |-------- +--------+ +--R +--------+ | 2 | 2 +--------+ +--R | 2 +-+ \| x |a x + b +-+ | 2 +--R (b\|a x + b - b\|b )atanh(------------) - x |-------- \|b \|a x + b +--R +-+ | 2 +--R \|b \| x +--R + +--R +--------+ +--R | 2 +--R 2 +-+ |a x + b +--R a x \|b + b x |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R Type: Expression Integer +--E 486 + +--S 487 of 554 +d0286:= D(m0286,x) +--R +--R +--R (456) +--R +--------+ +--R | 2 +--R 2 4 2 2 +-+ 2 5 3 2 |a x + b +--R ((- 3a x - 7a b x - 4b )\|b + (- a x - 5a b x - 4b x) |-------- ) +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 2 5 3 2 |a x + b +-+ 3 6 2 4 2 2 3 +--R (3a x + 7a b x + 4b x) |-------- \|b + a x + 6a b x + 9a b x + 4b +--R | 2 +--R \| x +--R / +--R +--------+ +--R | 2 +--------+ +--R 4 2 |a x + b +-+ | 2 +--R (3a x + 4b x ) |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 2 6 4 2 2 |a x + b +--R (- a x - 5a b x - 4b x ) |-------- +--R | 2 +--R \| x +--R Type: Expression Integer +--E 487 + +--S 488 of 554 +t0287:= (a+b/x^2)^(1/2)/x +--R +--R +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R (457) ----------- +--R x +--R Type: Expression Integer +--E 488 + +--S 489 of 554 +r0287:= -(a+b/x^2)^(1/2)+a^(1/2)*atanh((a+b/x^2)^(1/2)/a^(1/2)) +--R +--R +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--------+ +--R | 2 | 2 +--R +-+ \| x |a x + b +--R (458) \|a atanh(-----------) - |-------- +--R +-+ | 2 +--R \|a \| x +--R Type: Expression Integer +--E 489 + +--S 490 of 554 +a0287:= integrate(t0287,x) +--R +--R +--R (459) +--R [ +--R +--------+ +--R +-+ | 2 +-+ +-+ +--R (x\|a \|a x + b - x\|a \|b ) +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ +-+ 2 +--R (\|b - x\|a )\|a x + b + x\|a \|b - a x - b +--R log(------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R +-+ | 2 2 +--R \|b \|a x + b - a x - b +--R / +--R +--------+ +--R | 2 +-+ +--R x\|a x + b - x\|b +--R , +--R +--R +--------+ +--R +--------+ | 2 +-+ +--R +---+ | 2 +---+ +-+ \|a x + b - \|b +--R (2x\|- a \|a x + b - 2x\|- a \|b )atan(------------------) +--R +---+ +--R x\|- a +--R + +--R +--------+ +--R +-+ | 2 2 +--R \|b \|a x + b - a x - b +--R / +--R +--------+ +--R | 2 +-+ +--R x\|a x + b - x\|b +--R ] +--R Type: Union(List Expression Integer,...) +--E 490 + +--S 491 of 554 +m0287a:= a0287.1-r0287 +--R +--R +--R (460) +--R +--------+ +--R +-+ | 2 +-+ +-+ +--R (x\|a \|a x + b - x\|a \|b ) +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ +-+ 2 +--R (\|b - x\|a )\|a x + b + x\|a \|b - a x - b +--R log(------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R +--------+ | 2 +--R +-+ | 2 +-+ +-+ \| x +--R (- x\|a \|a x + b + x\|a \|b )atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--------+ +--R | 2 +--------+ | 2 +--R +-+ |a x + b | 2 |a x + b +-+ 2 +--R (\|b + x |-------- )\|a x + b - x |-------- \|b - a x - b +--R | 2 | 2 +--R \| x \| x +--R / +--R +--------+ +--R | 2 +-+ +--R x\|a x + b - x\|b +--R Type: Expression Integer +--E 491 + +--S 492 of 554 +d0287a:= D(m0287a,x) +--R +--R +--R (461) +--R +--------+ +--R | 2 +--R 3 7 2 5 2 3 3 |a x + b +--R (5a x + 25a b x + 36a b x + 16b x) |-------- +--R | 2 +--R \| x +--R + +--R 3 7 2 5 2 3 3 +-+ +--R (- 5a x - 25a b x - 36a b x - 16b x)\|a +--R * +--R +-+ +--R \|b +--R + +--R +--------+ +--R | 2 +--R 3 8 2 6 2 4 3 2 +-+ |a x + b 4 8 +--R (- a x - 13a b x - 28a b x - 16b x )\|a |-------- + a x +--R | 2 +--R \| x +--R + +--R 3 6 2 2 4 3 2 4 +--R 14a b x + 41a b x + 44a b x + 16b +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 3 8 2 6 2 4 3 2 +-+ |a x + b 4 8 +--R (5a x + 25a b x + 36a b x + 16b x )\|a |-------- - 5a x +--R | 2 +--R \| x +--R + +--R 3 6 2 2 4 3 2 4 +--R - 30a b x - 61a b x - 52a b x - 16b +--R * +--R +-+ +--R \|b +--R + +--R +--------+ +--R | 2 +--R 4 9 3 7 2 2 5 3 3 4 |a x + b +--R (- a x - 14a b x - 41a b x - 44a b x - 16b x) |-------- +--R | 2 +--R \| x +--R + +--R 4 9 3 7 2 2 5 3 3 4 +-+ +--R (a x + 14a b x + 41a b x + 44a b x + 16b x)\|a +--R / +--R +--------+ +--R | 2 +--R 2 8 6 2 4 +-+ |a x + b +-+ +--R (5a x + 20a b x + 16b x )\|a |-------- \|b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 9 2 7 2 5 3 3 |a x + b +--R (- a x - 13a b x - 28a b x - 16b x ) |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 3 9 2 7 2 5 3 3 |a x + b +-+ +--R (5a x + 25a b x + 36a b x + 16b x ) |-------- \|b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 10 2 8 2 6 3 4 +-+ |a x + b +--R (- a x - 13a b x - 28a b x - 16b x )\|a |-------- +--R | 2 +--R \| x +--R Type: Expression Integer +--E 492 + +--S 493 of 554 +m0287b:= a0287.2-r0287 +--R +--R +--R (462) +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R +--------+ | 2 +--R +-+ | 2 +-+ +-+ \| x +--R (- x\|a \|a x + b + x\|a \|b )atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R +--------+ | 2 +-+ +--R +---+ | 2 +---+ +-+ \|a x + b - \|b +--R (2x\|- a \|a x + b - 2x\|- a \|b )atan(------------------) +--R +---+ +--R x\|- a +--R + +--R +--------+ +--------+ +--R | 2 +--------+ | 2 +--R +-+ |a x + b | 2 |a x + b +-+ 2 +--R (\|b + x |-------- )\|a x + b - x |-------- \|b - a x - b +--R | 2 | 2 +--R \| x \| x +--R / +--R +--------+ +--R | 2 +-+ +--R x\|a x + b - x\|b +--R Type: Expression Integer +--E 493 + +--S 494 of 554 +d0287b:= D(m0287b,x) +--R +--R +--R (463) +--R +--------+ +--R | 2 +--------+ +--R 3 |a x + b +-+ 2 4 2 2 | 2 +--R ((- 2a x - 2b x) |-------- \|b - a x - 3a b x - 2b )\|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 2 4 2 2 +-+ 2 5 3 2 |a x + b +--R (2a x + 4a b x + 2b )\|b + (a x + 3a b x + 2b x) |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--------+ +--R | 2 +--------+ | 2 +--R 5 3 |a x + b | 2 5 3 |a x + b +-+ +--R (a x + 2b x ) |-------- \|a x + b + (- 2a x - 2b x ) |-------- \|b +--R | 2 | 2 +--R \| x \| x +--R Type: Expression Integer +--E 494 + +--S 495 of 554 +t0288:= (a+b/x^2)^(1/2)/x^2 +--R +--R +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R (464) ----------- +--R 2 +--R x +--R Type: Expression Integer +--E 495 + +--S 496 of 554 +r0288:= -1/2*(a+b/x^2)^(1/2)/x-1/2*a*atanh((a+b/x^2)^(1/2)*x/b^(1/2))/b^(1/2) +--R +--R +--R +--------+ +--R | 2 +--R |a x + b +--R x |-------- +--------+ +--R | 2 | 2 +--R \| x |a x + b +-+ +--R - a x atanh(------------) - |-------- \|b +--R +-+ | 2 +--R \|b \| x +--R (465) ------------------------------------------- +--R +-+ +--R 2x\|b +--R Type: Expression Integer +--E 496 + +--S 497 of 554 +a0288:= integrate(t0288,x) +--R +--R +--R (466) +--R +--------+ +--R +--------+ | 2 +-+ +--R 2 | 2 2 4 2 +-+ \|a x + b - \|b +--R (2a b x \|a x + b + (- a x - 2a b x )\|b )log(------------------) +--R x +--R + +--R +--------+ +--R 2 2 | 2 2 2 +-+ +--R (a b x + 2b )\|a x + b + (- 2a b x - 2b )\|b +--R / +--R +--------+ +--R 2 +-+ | 2 4 2 2 +--R 4b x \|b \|a x + b - 2a b x - 4b x +--R Type: Union(Expression Integer,...) +--E 497 + +--S 498 of 554 +m0288:= a0288-r0288 +--R +--R +--R (467) +--R +--------+ +--R +--------+ | 2 +-+ +--R 2 +-+ | 2 2 4 2 \|a x + b - \|b +--R (2a x \|b \|a x + b - a x - 2a b x )log(------------------) +--R x +--R + +--R +--------+ +--R | 2 +--R |a x + b +--R x |-------- +--R +--------+ | 2 +--R 2 +-+ | 2 2 4 2 \| x +--R (2a x \|b \|a x + b - a x - 2a b x )atanh(------------) +--R +-+ +--R \|b +--R + +--R +--------+ +--R | 2 +--------+ +--R 2 +-+ |a x + b | 2 +--R ((a x + 2b)\|b + 2b x |-------- )\|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 |a x + b +-+ 2 2 +--R (- a x - 2b x) |-------- \|b - 2a b x - 2b +--R | 2 +--R \| x +--R / +--R +--------+ +--R 2 | 2 4 2 +-+ +--R 4b x \|a x + b + (- 2a x - 4b x )\|b +--R Type: Expression Integer +--E 498 + +--S 499 of 554 +d0288:= D(m0288,x) +--R +--R +--R (468) +--R 3 6 2 4 2 2 3 +-+ +--R (- 5a x - 25a b x - 36a b x - 16b )\|b +--R + +--R +--------+ +--R | 2 +--R 3 7 2 5 2 3 3 |a x + b +--R (- a x - 13a b x - 28a b x - 16b x) |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 3 7 2 5 2 3 3 |a x + b +-+ 4 8 3 6 +--R (5a x + 25a b x + 36a b x + 16b x) |-------- \|b + a x + 14a b x +--R | 2 +--R \| x +--R + +--R 2 2 4 3 2 4 +--R 41a b x + 44a b x + 16b +--R / +--R +--------+ +--R | 2 +--------+ +--R 2 8 6 2 4 |a x + b +-+ | 2 +--R (5a x + 20a b x + 16b x ) |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 10 2 8 2 6 3 4 |a x + b +--R (- a x - 13a b x - 28a b x - 16b x ) |-------- +--R | 2 +--R \| x +--R Type: Expression Integer +--E 499 + +--S 500 of 554 +t0289:= (2+b/x^2)^(1/2)/(b+2*x^2) +--R +--R +--R +-------+ +--R | 2 +--R |2x + b +--R |------- +--R | 2 +--R \| x +--R (469) ---------- +--R 2 +--R 2x + b +--R Type: Expression Integer +--E 500 + +--S 501 of 554 +r0289:= -asinh(1/2*b^(1/2)*2^(1/2)/x)/b^(1/2) +--R +--R +--R +-+ +-+ +--R \|2 \|b +--R asinh(--------) +--R 2x +--R (470) - --------------- +--R +-+ +--R \|b +--R Type: Expression Integer +--E 501 + +--S 502 of 554 +a0289:= integrate(t0289,x) +--R +--R +--R +-------+ +--R | 2 +-+ +--R +-+ \|2x + b - \|b +--R \|b log(-----------------) +--R x +--R (471) -------------------------- +--R b +--R Type: Union(Expression Integer,...) +--E 502 + +--S 503 of 554 +m0289:= a0289-r0289 +--R +--R +--R +-------+ +--R | 2 +-+ +-+ +-+ +--R \|2x + b - \|b \|2 \|b +--R log(-----------------) + asinh(--------) +--R x 2x +--R (472) ---------------------------------------- +--R +-+ +--R \|b +--R Type: Expression Integer +--E 503 + +--S 504 of 554 +d0289:= D(m0289,x) +--R +--R +--R (473) +--R +-------+ +-------+ +--R | 2 +-------+ | 2 +--R +-+ +-+ |2x + b | 2 |2x + b +-+ 2 +-+ +--R (- \|2 \|b - 2x |------- )\|2x + b + 2x |------- \|b + (2x + b)\|2 +--R | 2 | 2 +--R \| 2x \| 2x +--R ------------------------------------------------------------------------ +--R +-------+ +-------+ +--R | 2 +-------+ | 2 +--R 2 |2x + b +-+ | 2 4 2 |2x + b +--R 2x |------- \|b \|2x + b + (- 4x - 2b x ) |------- +--R | 2 | 2 +--R \| 2x \| 2x +--R Type: Expression Integer +--E 504 + +--S 505 of 554 +t0290:= (2-b/x^2)^(1/2)/(-b+2*x^2) +--R +--R +--R +-------+ +--R | 2 +--R |2x - b +--R |------- +--R | 2 +--R \| x +--R (474) ---------- +--R 2 +--R 2x - b +--R Type: Expression Integer +--E 505 + +--S 506 of 554 +r0290:= -asin(1/2*b^(1/2)*2^(1/2)/x)/b^(1/2) +--R +--R +--R +-+ +-+ +--R \|2 \|b +--R asin(--------) +--R 2x +--R (475) - -------------- +--R +-+ +--R \|b +--R Type: Expression Integer +--E 506 + +--S 507 of 554 +a0290:= integrate(t0290,x) +--R +--R +--R +-------+ +--R | 2 +---+ +--R +---+ \|2x - b - \|- b +--R \|- b log(-------------------) +--R x +--R (476) - ------------------------------ +--R b +--R Type: Union(Expression Integer,...) +--E 507 + +--S 508 of 554 +m0290:= a0290-r0290 +--R +--R +--R +-------+ +--R | 2 +---+ +-+ +-+ +--R +---+ +-+ \|2x - b - \|- b \|2 \|b +--R - \|- b \|b log(-------------------) + b asin(--------) +--R x 2x +--R (477) ------------------------------------------------------- +--R +-+ +--R b\|b +--R Type: Expression Integer +--E 508 + +--S 509 of 554 +d0290:= D(m0290,x) +--R +--R +--R (478) +--R +-------+ +-------+ +--R | 2 +-------+ | 2 +--R |2x - b +-+ +---+ | 2 +---+ |2x - b 2 +-+ +--R (- 2x |------- - \|2 \|- b )\|2x - b + 2x\|- b |------- + (2x - b)\|2 +--R | 2 | 2 +--R \| 2x \| 2x +--R ---------------------------------------------------------------------------- +--R +-------+ +-------+ +--R | 2 +-------+ | 2 +--R 2 +---+ |2x - b | 2 4 2 |2x - b +--R 2x \|- b |------- \|2x - b + (- 4x + 2b x ) |------- +--R | 2 | 2 +--R \| 2x \| 2x +--R Type: Expression Integer +--E 509 + +--S 510 of 554 +t0291:= (-1+1/x^2)^(1/2)*(-1+x^2)/x +--R +--R +--R +--------+ +--R | 2 +--R 2 |- x + 1 +--R (x - 1) |-------- +--R | 2 +--R \| x +--R (479) ------------------- +--R x +--R Type: Expression Integer +--E 510 + +--S 511 of 554 +r0291:= (-1+1/x^2)^(1/2)+1/2*(-1+1/x^2)^(1/2)*x^2-3/2*atan((-1+1/x^2)^(1/2)) +--R +--R +--R +--------+ +--------+ +--R | 2 | 2 +--R |- x + 1 2 |- x + 1 +--R - 3atan( |-------- ) + (x + 2) |-------- +--R | 2 | 2 +--R \| x \| x +--R (480) ------------------------------------------ +--R 2 +--R Type: Expression Integer +--E 511 + +--S 512 of 554 +a0291:= integrate(t0291,x) +--R +--R +--R (481) +--R +--------+ +--R +--------+ | 2 +--R 3 | 2 3 \|- x + 1 - 1 +--R ((- 6x + 24x)\|- x + 1 + 18x - 24x)atan(---------------) +--R x +--R + +--R +--------+ +--R 4 2 | 2 6 4 2 +--R (- 3x - 2x + 8)\|- x + 1 - x + 3x + 6x - 8 +--R / +--R +--------+ +--R 3 | 2 3 +--R (2x - 8x)\|- x + 1 - 6x + 8x +--R Type: Union(Expression Integer,...) +--E 512 + +--S 513 of 554 +m0291:= a0291-r0291 +--R +--R +--R (482) +--R +--------+ +--R +--------+ | 2 +--R 3 | 2 3 |- x + 1 +--R ((3x - 12x)\|- x + 1 - 9x + 12x)atan( |-------- ) +--R | 2 +--R \| x +--R + +--R +--------+ +--R +--------+ | 2 +--R 3 | 2 3 \|- x + 1 - 1 +--R ((- 6x + 24x)\|- x + 1 + 18x - 24x)atan(---------------) +--R x +--R + +--R +--------+ +--R +--------+ | 2 +--R 5 3 | 2 5 3 |- x + 1 +--R ((- x + 2x + 8x)\|- x + 1 + 3x + 2x - 8x) |-------- +--R | 2 +--R \| x +--R + +--R +--------+ +--R 4 2 | 2 6 4 2 +--R (- 3x - 2x + 8)\|- x + 1 - x + 3x + 6x - 8 +--R / +--R +--------+ +--R 3 | 2 3 +--R (2x - 8x)\|- x + 1 - 6x + 8x +--R Type: Expression Integer +--E 513 + +--S 514 of 554 +d0291:= D(m0291,x) +--R +--R +--R (483) +--R +--------+ +--R 9 7 5 3 | 2 11 9 7 +--R (- 6x + 44x - 102x + 96x - 32x)\|- x + 1 - x + 20x - 85x +--R + +--R 5 3 +--R 146x - 112x + 32x +--R * +--R +--------+ +--R | 2 +--R |- x + 1 +--R |-------- +--R | 2 +--R \| x +--R + +--R +--------+ +--R 10 8 6 4 2 | 2 10 8 6 +--R (x - 20x + 85x - 146x + 112x - 32)\|- x + 1 - 6x + 50x - 146x +--R + +--R 4 2 +--R 198x - 128x + 32 +--R / +--R +--------+ +--R 9 7 5 3 | 2 9 7 5 3 +--R ((x - 18x + 48x - 32x )\|- x + 1 - 6x + 38x - 64x + 32x ) +--R * +--R +--------+ +--R | 2 +--R |- x + 1 +--R |-------- +--R | 2 +--R \| x +--R Type: Expression Integer +--E 514 + +--S 515 of 554 +t0292:= (-1+1/x^2)^(1/2)*(-1+x^2)^2/x +--R +--R +--R +--------+ +--R | 2 +--R 4 2 |- x + 1 +--R (x - 2x + 1) |-------- +--R | 2 +--R \| x +--R (484) ------------------------- +--R x +--R Type: Expression Integer +--E 515 + +--S 516 of 554 +r0292:= -(-1+1/x^2)^(1/2)-9/8*(-1+1/x^2)^(1/2)*x^2+1/4*(-1+1/x^2)^(1/2)*x^4+_ + 15/8*atan((-1+1/x^2)^(1/2)) +--R +--R +--R +--------+ +--------+ +--R | 2 | 2 +--R |- x + 1 4 2 |- x + 1 +--R 15atan( |-------- ) + (2x - 9x - 8) |-------- +--R | 2 | 2 +--R \| x \| x +--R (485) ------------------------------------------------ +--R 8 +--R Type: Expression Integer +--E 516 + +--S 517 of 554 +a0292:= integrate(t0292,x) +--R +--R +--R (486) +--R +--------+ +--R 5 3 | 2 5 3 +--R ((30x - 360x + 480x)\|- x + 1 - 150x + 600x - 480x) +--R * +--R +--------+ +--R | 2 +--R \|- x + 1 - 1 +--R atan(---------------) +--R x +--R + +--R +--------+ +--R 8 6 4 2 | 2 10 8 6 +--R (- 10x + 85x - 172x - 16x + 128)\|- x + 1 - 2x + 35x - 165x +--R + +--R 4 2 +--R 180x + 80x - 128 +--R / +--R +--------+ +--R 5 3 | 2 5 3 +--R (8x - 96x + 128x)\|- x + 1 - 40x + 160x - 128x +--R Type: Union(Expression Integer,...) +--E 517 + +--S 518 of 554 +m0292:= a0292-r0292 +--R +--R +--R (487) +--R +--------+ +--R 5 3 | 2 5 3 +--R ((- 15x + 180x - 240x)\|- x + 1 + 75x - 300x + 240x) +--R * +--R +--------+ +--R | 2 +--R |- x + 1 +--R atan( |-------- ) +--R | 2 +--R \| x +--R + +--R +--------+ +--R 5 3 | 2 5 3 +--R ((30x - 360x + 480x)\|- x + 1 - 150x + 600x - 480x) +--R * +--R +--------+ +--R | 2 +--R \|- x + 1 - 1 +--R atan(---------------) +--R x +--R + +--R +--------+ +--R 9 7 5 3 | 2 9 7 5 +--R (- 2x + 33x - 132x + 48x + 128x)\|- x + 1 + 10x - 85x + 172x +--R + +--R 3 +--R 16x - 128x +--R * +--R +--------+ +--R | 2 +--R |- x + 1 +--R |-------- +--R | 2 +--R \| x +--R + +--R +--------+ +--R 8 6 4 2 | 2 10 8 6 +--R (- 10x + 85x - 172x - 16x + 128)\|- x + 1 - 2x + 35x - 165x +--R + +--R 4 2 +--R 180x + 80x - 128 +--R / +--R +--------+ +--R 5 3 | 2 5 3 +--R (8x - 96x + 128x)\|- x + 1 - 40x + 160x - 128x +--R Type: Expression Integer +--E 518 + +--S 519 of 554 +d0292:= D(m0292,x) +--R +--R +--R (488) +--R 15 13 11 9 7 5 3 +--R - 10x + 190x - 1182x + 3530x - 5760x + 5280x - 2560x +--R + +--R 512x +--R * +--R +--------+ +--R | 2 +--R \|- x + 1 +--R + +--R 17 15 13 11 9 7 5 3 +--R - x + 53x - 553x + 2471x - 5890x + 8112x - 6496x + 2816x +--R + +--R - 512x +--R * +--R +--------+ +--R | 2 +--R |- x + 1 +--R |-------- +--R | 2 +--R \| x +--R + +--R 16 14 12 10 8 6 4 2 +--R x - 53x + 553x - 2471x + 5890x - 8112x + 6496x - 2816x +--R + +--R 512 +--R * +--R +--------+ +--R | 2 +--R \|- x + 1 +--R + +--R 16 14 12 10 8 6 4 2 +--R - 10x + 200x - 1372x + 4712x - 9290x + 11040x - 7840x + 3072x +--R + +--R - 512 +--R / +--R +--------+ +--R 13 11 9 7 5 3 | 2 13 +--R (x - 50x + 400x - 1120x + 1280x - 512x )\|- x + 1 - 10x +--R + +--R 11 9 7 5 3 +--R 170x - 832x + 1696x - 1536x + 512x +--R * +--R +--------+ +--R | 2 +--R |- x + 1 +--R |-------- +--R | 2 +--R \| x +--R Type: Expression Integer +--E 519 + +--S 520 of 554 +t0293:= (-1+1/x^2)^(1/2)*(-1+x^2)^3/x +--R +--R +--R +--------+ +--R | 2 +--R 6 4 2 |- x + 1 +--R (x - 3x + 3x - 1) |-------- +--R | 2 +--R \| x +--R (489) ------------------------------- +--R x +--R Type: Expression Integer +--E 520 + +--S 521 of 554 +r0293:= (-1+1/x^2)^(1/2)+29/16*(-1+1/x^2)^(1/2)*x^2-19/24*_ + (-1+1/x^2)^(1/2)*x^4+1/6*(-1+1/x^2)^(1/2)*x^6-_ + 35/16*atan((-1+1/x^2)^(1/2)) +--R +--R +--R +--------+ +--------+ +--R | 2 | 2 +--R |- x + 1 6 4 2 |- x + 1 +--R - 105atan( |-------- ) + (8x - 38x + 87x + 48) |-------- +--R | 2 | 2 +--R \| x \| x +--R (490) ------------------------------------------------------------ +--R 48 +--R Type: Expression Integer +--E 521 + +--S 522 of 554 +a0293:= integrate(t0293,x) +--R +--R +--R (491) +--R +--------+ +--R 7 5 3 | 2 7 5 +--R (- 210x + 5040x - 16800x + 13440x)\|- x + 1 + 1470x - 11760x +--R + +--R 3 +--R 23520x - 13440x +--R * +--R +--------+ +--R | 2 +--R \|- x + 1 - 1 +--R atan(---------------) +--R x +--R + +--R +--------+ +--R 12 10 8 6 4 2 | 2 +--R (- 56x + 714x - 3633x + 9304x - 9488x + 192x + 3072)\|- x + 1 +--R + +--R 14 12 10 8 6 4 2 +--R - 8x + 238x - 1869x + 7231x - 13832x + 9968x + 1344x - 3072 +--R / +--R +--------+ +--R 7 5 3 | 2 7 5 3 +--R (48x - 1152x + 3840x - 3072x)\|- x + 1 - 336x + 2688x - 5376x +--R + +--R 3072x +--R Type: Union(Expression Integer,...) +--E 522 + +--S 523 of 554 +m0293:= a0293-r0293 +--R +--R +--R (492) +--R +--------+ +--R 7 5 3 | 2 7 5 +--R (105x - 2520x + 8400x - 6720x)\|- x + 1 - 735x + 5880x +--R + +--R 3 +--R - 11760x + 6720x +--R * +--R +--------+ +--R | 2 +--R |- x + 1 +--R atan( |-------- ) +--R | 2 +--R \| x +--R + +--R +--------+ +--R 7 5 3 | 2 7 5 +--R (- 210x + 5040x - 16800x + 13440x)\|- x + 1 + 1470x - 11760x +--R + +--R 3 +--R 23520x - 13440x +--R * +--R +--------+ +--R | 2 +--R \|- x + 1 - 1 +--R atan(---------------) +--R x +--R + +--R 13 11 9 7 5 3 +--R (- 8x + 230x - 1639x + 5592x - 8240x + 1728x + 3072x) +--R * +--R +--------+ +--R | 2 +--R \|- x + 1 +--R + +--R 13 11 9 7 5 3 +--R 56x - 714x + 3633x - 9304x + 9488x - 192x - 3072x +--R * +--R +--------+ +--R | 2 +--R |- x + 1 +--R |-------- +--R | 2 +--R \| x +--R + +--R +--------+ +--R 12 10 8 6 4 2 | 2 +--R (- 56x + 714x - 3633x + 9304x - 9488x + 192x + 3072)\|- x + 1 +--R + +--R 14 12 10 8 6 4 2 +--R - 8x + 238x - 1869x + 7231x - 13832x + 9968x + 1344x - 3072 +--R / +--R +--------+ +--R 7 5 3 | 2 7 5 3 +--R (48x - 1152x + 3840x - 3072x)\|- x + 1 - 336x + 2688x - 5376x +--R + +--R 3072x +--R Type: Expression Integer +--E 523 + +--S 524 of 554 +d0293:= D(m0293,x) +--R +--R +--R (493) +--R 21 19 17 15 13 11 +--R - 14x + 504x - 5908x + 34232x - 115598x + 245952x +--R + +--R 9 7 5 3 +--R - 340928x + 308224x - 175616x + 57344x - 8192x +--R * +--R +--------+ +--R | 2 +--R \|- x + 1 +--R + +--R 23 21 19 17 15 13 +--R - x + 102x - 1966x + 16272x - 74313x + 209762x +--R + +--R 11 9 7 5 3 +--R - 386848x + 476352x - 389376x + 203264x - 61440x + 8192x +--R * +--R +--------+ +--R | 2 +--R |- x + 1 +--R |-------- +--R | 2 +--R \| x +--R + +--R 22 20 18 16 14 12 10 +--R x - 102x + 1966x - 16272x + 74313x - 209762x + 386848x +--R + +--R 8 6 4 2 +--R - 476352x + 389376x - 203264x + 61440x - 8192 +--R * +--R +--------+ +--R | 2 +--R \|- x + 1 +--R + +--R 22 20 18 16 14 12 10 +--R - 14x + 518x - 6412x + 40140x - 149830x + 361550x - 586880x +--R + +--R 8 6 4 2 +--R 649152x - 483840x + 232960x - 65536x + 8192 +--R / +--R 17 15 13 11 9 7 5 +--R x - 98x + 1568x - 9408x + 26880x - 39424x + 28672x +--R + +--R 3 +--R - 8192x +--R * +--R +--------+ +--R | 2 +--R \|- x + 1 +--R + +--R 17 15 13 11 9 7 5 +--R - 14x + 462x - 4480x + 19392x - 43520x + 52736x - 32768x +--R + +--R 3 +--R 8192x +--R * +--R +--------+ +--R | 2 +--R |- x + 1 +--R |-------- +--R | 2 +--R \| x +--R Type: Expression Integer +--E 524 + +--S 525 of 554 +t0294:= 1/x/(a+b/x^3)^(1/2) +--R +--R +--R 1 +--R (494) ------------ +--R +--------+ +--R | 3 +--R |a x + b +--R x |-------- +--R | 3 +--R \| x +--R Type: Expression Integer +--E 525 + +--S 526 of 554 +r0294:= 2/3*atanh((a+b/x^3)^(1/2)/a^(1/2))/a^(1/2) +--R +--R +--R +--------+ +--R | 3 +--R |a x + b +--R |-------- +--R | 3 +--R \| x +--R 2atanh(-----------) +--R +-+ +--R \|a +--R (495) ------------------- +--R +-+ +--R 3\|a +--R Type: Expression Integer +--E 526 + +--S 527 of 554 +a0294:= integrate(t0294,x) +--R +--R +--R +--------+ +--R +-+ +-+ | 3 +--R |1 2 |1 |a x + b 3 +--R |- log(2a x |- |-------- - 2a x - b) +--R \|a \|a \| x +--R (496) - ----------------------------------------- +--R 3 +--R Type: Union(Expression Integer,...) +--E 527 + +--S 528 of 554 +m0294:= a0294-r0294 +--R +--R +--R (497) +--R +--------+ +--R | 3 +--R |a x + b +--R +--------+ |-------- +--R +-+ +-+ | 3 | 3 +--R |1 +-+ 2 |1 |a x + b 3 \| x +--R - |- \|a log(2a x |- |-------- - 2a x - b) - 2atanh(-----------) +--R \|a \|a \| x +-+ +--R \|a +--R --------------------------------------------------------------------- +--R +-+ +--R 3\|a +--R Type: Expression Integer +--E 528 + +--S 529 of 554 +d0294:= D(m0294,x) +--R +--R +--R (498) +--R +--------+ +--------+ +--R +-+ | 3 | 3 +--R 3 |1 |a x + b 3 |a x + b +--R (- 2a x |- |-------- - 2a x - b) |-------- +--R \|a | 3 \| x +--R \| x +--R + +--R +--------+ +--R | 3 +-+ +--R 4 |a x + b 2 4 |1 +--R (2a x + b x) |-------- + (2a x + 2a b x) |- +--R | 3 \|a +--R \| x +--R / +--R +--------+ +--------+ +--------+ +--R | 3 | 3 +-+ | 3 +--R 4 |a x + b |a x + b 2 5 2 |1 |a x + b +--R (2a x + b x) |-------- |-------- + (- 2a x - 2a b x ) |- |-------- +--R | 3 \| x \|a | 3 +--R \| x \| x +--R Type: Expression Integer +--E 529 + +--S 530 of 554 +t0295:= 1/x/(-a+b/x^3)^(1/2) +--R +--R +--R 1 +--R (499) -------------- +--R +----------+ +--R | 3 +--R |- a x + b +--R x |---------- +--R | 3 +--R \| x +--R Type: Expression Integer +--E 530 + +--S 531 of 554 +r0295:= -2/3*atan((-a+b/x^3)^(1/2)/a^(1/2))/a^(1/2) +--R +--R +--R +----------+ +--R | 3 +--R |- a x + b +--R |---------- +--R | 3 +--R \| x +--R 2atan(-------------) +--R +-+ +--R \|a +--R (500) - -------------------- +--R +-+ +--R 3\|a +--R Type: Expression Integer +--E 531 + +--S 532 of 554 +a0295:= integrate(t0295,x) +--R +--R +--R +----------+ +--R +---+ | 3 +---+ +--R | 1 2 |- a x + b | 1 3 +--R |- - log(2a x |---------- |- - - 2a x + b) +--R \| a \| x \| a +--R (501) - ----------------------------------------------- +--R 3 +--R Type: Union(Expression Integer,...) +--E 532 + +--S 533 of 554 +m0295:= a0295-r0295 +--R +--R +--R (502) +--R +----------+ +--R | 3 +--R |- a x + b +--R +----------+ |---------- +--R +---+ | 3 +---+ | 3 +--R | 1 +-+ 2 |- a x + b | 1 3 \| x +--R - |- - \|a log(2a x |---------- |- - - 2a x + b) + 2atan(-------------) +--R \| a \| x \| a +-+ +--R \|a +--R ---------------------------------------------------------------------------- +--R +-+ +--R 3\|a +--R Type: Expression Integer +--E 533 + +--S 534 of 554 +d0295:= D(m0295,x) +--R +--R +--R (503) +--R +----------+ +----------+ +--R | 3 | 3 +---+ +--R 3 |- a x + b |- a x + b 2 4 | 1 +--R (- 2a x |---------- |---------- - 2a x + 2a b x) |- - +--R \| x | 3 \| a +--R \| x +--R + +--R +----------+ +----------+ +--R | 3 | 3 +--R 4 |- a x + b 3 |- a x + b +--R (2a x - b x) |---------- + (- 2a x + b) |---------- +--R | 3 \| x +--R \| x +--R / +--R +----------+ +--R | 3 +---+ +--R 2 5 2 |- a x + b | 1 +--R (2a x - 2a b x ) |---------- |- - +--R | 3 \| a +--R \| x +--R + +--R +----------+ +----------+ +--R | 3 | 3 +--R 4 |- a x + b |- a x + b +--R (2a x - b x) |---------- |---------- +--R \| x | 3 +--R \| x +--R Type: Expression Integer +--E 534 + +--S 535 of 554 +t0296:= x^2/(a+b/x^3)^(1/2) +--R +--R +--R 2 +--R x +--R (504) ----------- +--R +--------+ +--R | 3 +--R |a x + b +--R |-------- +--R | 3 +--R \| x +--R Type: Expression Integer +--E 535 + +--S 536 of 554 +r0296:= 1/3*(a+b/x^3)^(1/2)*x^3/a-1/3*b*atanh((a+b/x^3)^(1/2)/a^(1/2))/a^(3/2) +--R +--R +--R +--------+ +--R | 3 +--R |a x + b +--R |-------- +--------+ +--R | 3 | 3 +--R \| x 3 +-+ |a x + b +--R - b atanh(-----------) + x \|a |-------- +--R +-+ | 3 +--R \|a \| x +--R (505) ------------------------------------------ +--R +-+ +--R 3a\|a +--R Type: Expression Integer +--E 536 + +--S 537 of 554 +a0296:= integrate(t0296,x) +--R +--R +--R +--+ +--+ +--------+ +--------+ +--R | 2 | 2 | 3 | 3 +--R |b 2 2 |b |a x + b 3 2 2 |a x + b +--R - a |-- log(2a x |-- |-------- + 2a b x + b ) + 2x |-------- +--R | 3 | 3 \| x \| x +--R \|a \|a +--R (506) ------------------------------------------------------------------ +--R 6a +--R Type: Union(Expression Integer,...) +--E 537 + +--S 538 of 554 +m0296:= a0296-r0296 +--R +--R +--R (507) +--R +--+ +--+ +--------+ +--R | 2 | 2 | 3 +--R +-+ |b 2 2 |b |a x + b 3 2 +--R - a\|a |-- log(2a x |-- |-------- + 2a b x + b ) +--R | 3 | 3 \| x +--R \|a \|a +--R + +--R +--------+ +--R | 3 +--R |a x + b +--R |-------- +--------+ +--------+ +--R | 3 | 3 | 3 +--R \| x 2 +-+ |a x + b 3 +-+ |a x + b +--R 2b atanh(-----------) + 2x \|a |-------- - 2x \|a |-------- +--R +-+ \| x | 3 +--R \|a \| x +--R / +--R +-+ +--R 6a\|a +--R Type: Expression Integer +--E 538 + +--S 539 of 554 +d0296:= D(m0296,x) +--R +--R +--R (508) +--R +--+ +--------+ +--------+ +--R | 2 | 3 | 3 +--R 3 7 2 4 |b 7 2 4 |a x + b |a x + b +--R ((- 2a x - 2a b x ) |-- + (2a b x + b x ) |-------- ) |-------- +--R | 3 | 3 \| x +--R \|a \| x +--R + +--R +--------+ +--+ +--R | 3 | 2 +--R 3 8 2 5 |a x + b |b 2 8 2 5 3 2 +--R (2a x + 2a b x ) |-------- |-- - 2a b x - 3a b x - b x +--R | 3 | 3 +--R \| x \|a +--R / +--R +--------+ +--+ +--------+ +--R | 3 | 2 | 3 +--R 3 5 2 2 |a x + b |b |a x + b +--R (2a x + 2a b x ) |-------- |-- |-------- +--R | 3 | 3 \| x +--R \| x \|a +--R + +--R +--------+ +--R | 3 +--R 2 6 2 3 3 |a x + b +--R (2a b x + 3a b x + b ) |-------- +--R | 3 +--R \| x +--R Type: Expression Integer +--E 539 + +--S 540 of 554 +t0297:= (a+b/x^3)^(1/2)/x +--R +--R +--R +--------+ +--R | 3 +--R |a x + b +--R |-------- +--R | 3 +--R \| x +--R (509) ----------- +--R x +--R Type: Expression Integer +--E 540 + +--S 541 of 554 +r0297:= -2/3*(a+b/x^3)^(1/2)+2/3*a^(1/2)*atanh((a+b/x^3)^(1/2)/a^(1/2)) +--R +--R +--R +--------+ +--R | 3 +--R |a x + b +--R |-------- +--------+ +--R | 3 | 3 +--R +-+ \| x |a x + b +--R 2\|a atanh(-----------) - 2 |-------- +--R +-+ | 3 +--R \|a \| x +--R (510) -------------------------------------- +--R 3 +--R Type: Expression Integer +--E 541 + +--S 542 of 554 +a0297:= integrate(t0297,x) +--R +--R +--R +--------+ +--------+ +--R | 3 | 3 +--R +--+ 2 +--+ |a x + b 3 |a x + b +--R - x\|4a log(x \|4a |-------- - 2a x - b) - 4 |-------- +--R \| x \| x +--R (511) ---------------------------------------------------------- +--R 6x +--R Type: Union(Expression Integer,...) +--E 542 + +--S 543 of 554 +m0297:= a0297-r0297 +--R +--R +--R (512) +--R +--------+ +--R | 3 +--R |a x + b +--R +--------+ |-------- +--R | 3 | 3 +--R +--+ 2 +--+ |a x + b 3 +-+ \| x +--R - x\|4a log(x \|4a |-------- - 2a x - b) - 4x\|a atanh(-----------) +--R \| x +-+ +--R \|a +--R + +--R +--------+ +--------+ +--R | 3 | 3 +--R |a x + b |a x + b +--R - 4 |-------- + 4x |-------- +--R \| x | 3 +--R \| x +--R / +--R 6x +--R Type: Expression Integer +--E 543 + +--S 544 of 554 +d0297:= D(m0297,x) +--R +--R +--R (513) +--R +--------+ +--------+ +--R | 3 | 3 +--R 5 2 +--+ 5 2 |a x + b |a x + b +--R ((- a x - b x )\|4a + (- 2a x - b x ) |-------- ) |-------- +--R | 3 \| x +--R \| x +--R + +--R +--------+ +--R | 3 +--R 6 3 |a x + b +--+ 2 6 3 2 +--R (a x + b x ) |-------- \|4a + 2a x + 3a b x + b +--R | 3 +--R \| x +--R / +--R +--------+ +--------+ +--------+ +--R | 3 | 3 | 3 +--R 6 |a x + b +--+ |a x + b 7 4 |a x + b +--R x |-------- \|4a |-------- + (- 2a x - b x ) |-------- +--R | 3 \| x | 3 +--R \| x \| x +--R Type: Expression Integer +--E 544 + +--S 545 of 554 +t0298:= (-a+b/x^3)^(1/2)/x +--R +--R +--R +----------+ +--R | 3 +--R |- a x + b +--R |---------- +--R | 3 +--R \| x +--R (514) ------------- +--R x +--R Type: Expression Integer +--E 545 + +--S 546 of 554 +r0298:= -2/3*(-a+b/x^3)^(1/2)+2/3*a^(1/2)*atan((-a+b/x^3)^(1/2)/a^(1/2)) +--R +--R +--R +----------+ +--R | 3 +--R |- a x + b +--R |---------- +----------+ +--R | 3 | 3 +--R +-+ \| x |- a x + b +--R 2\|a atan(-------------) - 2 |---------- +--R +-+ | 3 +--R \|a \| x +--R (515) ----------------------------------------- +--R 3 +--R Type: Expression Integer +--E 546 + +--S 547 of 554 +a0298:= integrate(t0298,x) +--R +--R +--R +----------+ +----------+ +--R | 3 | 3 +--R +----+ 2 |- a x + b +----+ 3 |- a x + b +--R - x\|- 4a log(x |---------- \|- 4a + 2a x - b) - 4 |---------- +--R \| x \| x +--R (516) ------------------------------------------------------------------ +--R 6x +--R Type: Union(Expression Integer,...) +--E 547 + +--S 548 of 554 +m0298:= a0298-r0298 +--R +--R +--R (517) +--R +----------+ +--R | 3 +--R +----+ 2 |- a x + b +----+ 3 +--R - x\|- 4a log(x |---------- \|- 4a + 2a x - b) +--R \| x +--R + +--R +----------+ +--R | 3 +--R |- a x + b +--R |---------- +----------+ +----------+ +--R | 3 | 3 | 3 +--R +-+ \| x |- a x + b |- a x + b +--R - 4x\|a atan(-------------) + 4x |---------- - 4 |---------- +--R +-+ | 3 \| x +--R \|a \| x +--R / +--R 6x +--R Type: Expression Integer +--E 548 + +--S 549 of 554 +d0298:= D(m0298,x) +--R +--R +--R (518) +--R +----------+ +----------+ +--R | 3 | 3 +--R 6 3 +----+ 5 2 |- a x + b |- a x + b +--R ((- a x + b x )\|- 4a + (2a x - b x ) |---------- ) |---------- +--R \| x | 3 +--R \| x +--R + +--R +----------+ +--R | 3 +--R 5 2 |- a x + b +----+ 2 6 3 2 +--R (a x - b x ) |---------- \|- 4a + 2a x - 3a b x + b +--R \| x +--R / +--R +----------+ +----------+ +--R | 3 | 3 +--R 6 |- a x + b +----+ 7 4 |- a x + b +--R (x |---------- \|- 4a + 2a x - b x ) |---------- +--R \| x | 3 +--R \| x +--R Type: Expression Integer +--E 549 + +--S 550 of 554 +t0299:= x^2*(a+b/x^3)^(1/2) +--R +--R +--R +--------+ +--R | 3 +--R 2 |a x + b +--R (519) x |-------- +--R | 3 +--R \| x +--R Type: Expression Integer +--E 550 + +--S 551 of 554 +r0299:= 1/3*(a+b/x^3)^(1/2)*x^3+1/3*b*atanh((a+b/x^3)^(1/2)/a^(1/2))/a^(1/2) +--R +--R +--R +--------+ +--R | 3 +--R |a x + b +--R |-------- +--------+ +--R | 3 | 3 +--R \| x 3 +-+ |a x + b +--R b atanh(-----------) + x \|a |-------- +--R +-+ | 3 +--R \|a \| x +--R (520) ---------------------------------------- +--R +-+ +--R 3\|a +--R Type: Expression Integer +--E 551 + +--S 552 of 554 +a0299:= integrate(t0299,x) +--R +--R +--R +--+ +--+ +--------+ +--------+ +--R | 2 | 2 | 3 | 3 +--R |b 2 |b |a x + b 3 2 2 |a x + b +--R - |-- log(2a x |-- |-------- - 2a b x - b ) + 2x |-------- +--R \| a \| a \| x \| x +--R (521) ----------------------------------------------------------------- +--R 6 +--R Type: Union(Expression Integer,...) +--E 552 + +--S 553 of 554 +m0299:= a0299-r0299 +--R +--R +--R (522) +--R +--+ +--+ +--------+ +--R | 2 | 2 | 3 +--R +-+ |b 2 |b |a x + b 3 2 +--R - \|a |-- log(2a x |-- |-------- - 2a b x - b ) +--R \| a \| a \| x +--R + +--R +--------+ +--R | 3 +--R |a x + b +--R |-------- +--------+ +--------+ +--R | 3 | 3 | 3 +--R \| x 2 +-+ |a x + b 3 +-+ |a x + b +--R - 2b atanh(-----------) + 2x \|a |-------- - 2x \|a |-------- +--R +-+ \| x | 3 +--R \|a \| x +--R / +--R +-+ +--R 6\|a +--R Type: Expression Integer +--E 553 + +--S 554 of 554 +d0299:= D(m0299,x) +--R +--R +--R (523) +--R +--------+ +--+ +--------+ +--R | 3 | 2 | 3 +--R 4 |a x + b |b 4 2 |a x + b +--R (- 2a x |-------- |-- - 2a b x - b x) |-------- +--R | 3 \| a \| x +--R \| x +--R + +--R +--+ +--------+ +--R | 2 | 3 +--R 2 5 2 |b 5 2 2 |a x + b +--R (2a x + 2a b x ) |-- + (2a b x + b x ) |-------- +--R \| a | 3 +--R \| x +--R / +--R +--+ +--------+ +--R | 2 | 3 +--R 2 |b |a x + b 3 2 +--R 2a x |-- |-------- - 2a b x - b +--R \| a \| x +--R Type: Expression Integer +--E 554 + +)spool +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} +Rich, Albert D. ``Rule-based Mathematics'' \verb|www.apmaths.uwo.ca/~arich| +\end{thebibliography} +\end{document}