diff --git a/changelog b/changelog index 1f1c25a..1fc7f5d 100644 --- a/changelog +++ b/changelog @@ -1,3 +1,6 @@ +20100618 tpd src/axiom-website/patches.html 20100618.02.tpd.patch +20100618 tpd src/input/Makefile rule-based inverse trig integration +20100618 tpd src/input/richinvtrig000-092.input rule-based inverse trig int. 20100618 tpd src/axiom-website/patches.html 20100618.01.tpd.patch 20100618 tpd src/input/Makefile rule-based log integration 20100618 tpd src/input/richlog300-391.input rule-based log integration diff --git a/src/axiom-website/patches.html b/src/axiom-website/patches.html index 0a94193..95b377c 100644 --- a/src/axiom-website/patches.html +++ b/src/axiom-website/patches.html @@ -2916,6 +2916,8 @@ src/input/richlog100-199.input rule-based log integration
src/input/richlog200-299.input rule-based log integration
20100618.01.tpd.patch src/input/richlog300-391.input rule-based log integration
+20100618.02.tpd.patch +src/input/richinvtrig000-092.input rule-based inverse trig int.
diff --git a/src/input/Makefile.pamphlet b/src/input/Makefile.pamphlet index 0230dc3..0b9bcb6 100644 --- a/src/input/Makefile.pamphlet +++ b/src/input/Makefile.pamphlet @@ -386,6 +386,7 @@ REGRES= ackermann.regress \ richhyper800-899.regress \ richhyper900-999.regress \ richhyper1000-1098.regress \ + richinvtrig000-092.regress \ richlog000-099.regress \ richlog100-199.regress \ richlog200-299.regress \ @@ -730,6 +731,7 @@ FILES= ${OUT}/ackermann.input \ ${OUT}/richhyper800-899.input \ ${OUT}/richhyper900-999.input \ ${OUT}/richhyper1000-1098.input \ + ${OUT}/richinvtrig000-092.input \ ${OUT}/richlog000-099.input \ ${OUT}/richlog100-199.input \ ${OUT}/richlog200-299.input \ @@ -1103,6 +1105,7 @@ DOCFILES= \ ${DOC}/richhyper800-899.input.dvi \ ${DOC}/richhyper900-999.input.dvi \ ${DOC}/richhyper1000-1098.input.dvi \ + ${DOC}/richinvtrig000-092.input.dvi \ ${DOC}/richlog000-099.input.dvi \ ${DOC}/richlog100-199.input.dvi \ ${DOC}/richlog200-299.input.dvi \ diff --git a/src/input/richinvtrig000-092.input.pamphlet b/src/input/richinvtrig000-092.input.pamphlet new file mode 100644 index 0000000..064cf10 --- /dev/null +++ b/src/input/richinvtrig000-092.input.pamphlet @@ -0,0 +1,11669 @@ +\documentclass{article} +\usepackage{axiom} +\begin{document} +\title{\$SPAD/src/input richinvtrig000-092.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f richinvtrig000-092.output +)spool richinvtrig000-092.output +)set message auto off +)clear all + +--S 1 of 477 +t0000:= asin(a*x)/x +--R +--R +--R asin(a x) +--R (1) --------- +--R x +--R Type: Expression Integer +--E 1 + +--S 2 of 477 +r0000:= -1/2*%i*asin(a*x)^2+asin(a*x)*log(-2*%i*_ + (%i*a*x+(1-a^2*x^2)^(1/2))*a*x)-_ + 1/2*%i*polylog(2,(%i*a*x+(1-a^2*x^2)^(1/2))^2) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Complex Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 2 + +--S 3 of 477 +a0000:= integrate(t0000,x) +--R +--R +--R x +--R ++ asin(%Q a) +--R (2) | ---------- d%Q +--R ++ %Q +--R Type: Union(Expression Integer,...) +--E 3 + +--S 4 of 477 +--m0000:= a0000-r0000 +--E 4 + +--S 5 of 477 +--d0000:= D(m0000,x) +--E 5 + +--S 6 of 477 +t0001:= asin(x^(1/2))/x +--R +--R +--R +-+ +--R asin(\|x ) +--R (3) ---------- +--R x +--R Type: Expression Integer +--E 6 + +--S 7 of 477 +r0001:= -%i*asin(x^(1/2))^2+2*asin(x^(1/2))*_ + log(-2*%i*(%i*x+(1-x)^(1/2)*x^(1/2)))-_ + %i*polylog(2,((1-x)^(1/2)+%i*x^(1/2))^2) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Complex Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 7 + +--S 8 of 477 +a0001:= integrate(t0001,x) +--R +--R +--R x +--+ +--R ++ asin(\|%Q ) +--R (4) | ----------- d%Q +--R ++ %Q +--R Type: Union(Expression Integer,...) +--E 8 + +--S 9 of 477 +--m0001:= a0001-r0001 +--E 9 + +--S 10 of 477 +--d0001:= D(m0001,x) +--E 10 + +--S 11 of 477 +t0002:= atan(a*x)/x +--R +--R +--R atan(a x) +--R (5) --------- +--R x +--R Type: Expression Integer +--E 11 + +--S 12 of 477 +r0002:= 1/2*%i*polylog(2,-%i*a*x)-1/2*%i*polylog(2,%i*a*x) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Polynomial Complex Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 12 + +--S 13 of 477 +a0002:= integrate(t0002,x) +--R +--R +--R x +--R ++ atan(%Q a) +--R (6) | ---------- d%Q +--R ++ %Q +--R Type: Union(Expression Integer,...) +--E 13 + +--S 14 of 477 +--m0002:= a0002-r0002 +--E 14 + +--S 15 of 477 +--d0002:= D(m0002,x) +--E 15 + +--S 16 of 477 +t0003:= atan(1+x)/(2+2*x) +--R +--R +--R atan(x + 1) +--R (7) ----------- +--R 2x + 2 +--R Type: Expression Integer +--E 16 + +--S 17 of 477 +r0003:= 1/4*%i*polylog(2,-%i*(1+x))-1/4*%i*polylog(2,%i*(1+x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Polynomial Complex Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 17 + +--S 18 of 477 +a0003:= integrate(t0003,x) +--R +--R +--R x +--R ++ atan(%Q + 1) +--R (8) | ------------ d%Q +--R ++ 2%Q + 2 +--R Type: Union(Expression Integer,...) +--E 18 + +--S 19 of 477 +--m0003:= a0003-r0003 +--E 19 + +--S 20 of 477 +--d0003:= D(m0003,x) +--E 20 + +--S 21 of 477 +t0004:= atan(a+b*x)/(a+b*x) +--R +--R +--R atan(b x + a) +--R (9) ------------- +--R b x + a +--R Type: Expression Integer +--E 21 + +--S 22 of 477 +r0004:= 1/2*%i*(polylog(2,-%i*(a+b*x))-polylog(2,%i*(a+b*x)))/b +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Polynomial Complex Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 22 + +--S 23 of 477 +a0004:= integrate(t0004,x) +--R +--R +--R x +--R ++ atan(%Q b + a) +--R (10) | -------------- d%Q +--R ++ %Q b + a +--R Type: Union(Expression Integer,...) +--E 23 + +--S 24 of 477 +--m0004:= a0004-r0004 +--E 24 + +--S 25 of 477 +--d0004:= D(m0004,x) +--E 25 + +--S 26 of 477 +t0005:= atan(x)/(a+b*x^2)^(3/2) +--R +--R +--R atan(x) +--R (11) --------------------- +--R +--------+ +--R 2 | 2 +--R (b x + a)\|b x + a +--R Type: Expression Integer +--E 26 + +--S 27 of 477 +r0005:= x*atan(x)/a/(a+b*x^2)^(1/2)+atanh((a+b*x^2)^(1/2)/_ + (a-b)^(1/2))/a/(a-b)^(1/2) +--R +--R +--R +--------+ +--R +--------+ | 2 +--R | 2 \|b x + a +-------+ +--R \|b x + a atanh(-----------) + x atan(x)\|- b + a +--R +-------+ +--R \|- b + a +--R (12) --------------------------------------------------- +--R +--------+ +--R +-------+ | 2 +--R a\|- b + a \|b x + a +--R Type: Expression Integer +--E 27 + +--S 28 of 477 +a0005:= integrate(t0005,x) +--R +--R +--R (13) +--R [ +--R +--------+ +--R +-+ | 2 2 +--R (\|a \|b x + a - b x - a) +--R * +--R log +--R 2 2 4 2 2 +-+ +--R ((- 2b - 2a b + 4a )x + (- 8a b + 8a )x )\|a +--R + +--R 2 4 2 2 2 +-------+ +--R (4a x + (4a b + 8a )x + 8a )\|- b + a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 2 6 2 2 4 2 2 +--R (b - 2a b)x + (- b - 4a b - 4a )x + (- 8a b - 8a )x +--R + +--R 2 +--R - 8a +--R * +--R +-------+ +-+ +--R \|- b + a \|a +--R + +--R 2 2 6 2 2 3 4 2 3 2 +--R (2a b - 2a b)x + (6a b - 2a b - 4a )x + (8a b - 8a )x +--R / +--R +--------+ +--R 4 2 2 2 | 2 +--R (4a b x + (4a b + 8a )x + 8a )\|b x + a +--R + +--R 2 6 2 4 2 2 2 +-+ +--R (- b x + (- b - 8a b)x + (- 8a b - 8a )x - 8a )\|a +--R + +--R +--------+ +--R 2x +-------+ | 2 2x +-------+ +-+ +--R x atan(------)\|- b + a \|b x + a - x atan(------)\|- b + a \|a +--R 2 2 +--R x - 1 x - 1 +--R / +--R +--------+ +--R +-------+ +-+ | 2 2 2 +-------+ +--R 2a\|- b + a \|a \|b x + a + (- 2a b x - 2a )\|- b + a +--R , +--R +--R +--------+ +--R +-+ | 2 2 +--R (\|a \|b x + a - b x - a) +--R * +--R +--------+ +--R 2 +-----+ | 2 4 2 +-+ +-----+ +--R 2x \|b - a \|b x + a + (- 2x - 2x )\|a \|b - a +--R atan(---------------------------------------------------------) +--R +--------+ +--R 2 +-+ | 2 4 2 +--R (2x + 2)\|a \|b x + a + (b - 2a)x + (- b - 2a)x - 2a +--R + +--R +--------+ +--R 2x +-----+ | 2 2x +-+ +-----+ +--R x atan(------)\|b - a \|b x + a - x atan(------)\|a \|b - a +--R 2 2 +--R x - 1 x - 1 +--R / +--R +--------+ +--R +-+ +-----+ | 2 2 2 +-----+ +--R 2a\|a \|b - a \|b x + a + (- 2a b x - 2a )\|b - a +--R ] +--R Type: Union(List Expression Integer,...) +--E 28 + +--S 29 of 477 +m0005a:= a0005.1-r0005 +--R +--R +--R (14) +--R +--------+ +--R 2 | 2 2 +-+ +--R ((b x + a)\|b x + a + (- b x - a)\|a ) +--R * +--R log +--R 2 2 4 2 2 +-+ +--R ((- 2b - 2a b + 4a )x + (- 8a b + 8a )x )\|a +--R + +--R 2 4 2 2 2 +-------+ +--R (4a x + (4a b + 8a )x + 8a )\|- b + a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 2 6 2 2 4 2 2 +--R (b - 2a b)x + (- b - 4a b - 4a )x + (- 8a b - 8a )x +--R + +--R 2 +--R - 8a +--R * +--R +-------+ +-+ +--R \|- b + a \|a +--R + +--R 2 2 6 2 2 3 4 2 3 2 +--R (2a b - 2a b)x + (6a b - 2a b - 4a )x + (8a b - 8a )x +--R / +--R +--------+ +--R 4 2 2 2 | 2 +--R (4a b x + (4a b + 8a )x + 8a )\|b x + a +--R + +--R 2 6 2 4 2 2 2 +-+ +--R (- b x + (- b - 8a b)x + (- 8a b - 8a )x - 8a )\|a +--R + +--R +--------+ +--R +--------+ | 2 +--R 2 | 2 2 +-+ \|b x + a +--R ((- 2b x - 2a)\|b x + a + (2b x + 2a)\|a )atanh(-----------) +--R +-------+ +--R \|- b + a +--R + +--R +--------+ +--R 2x +-------+ +-+ | 2 +--R (2x atan(x) + x atan(------))\|- b + a \|a \|b x + a +--R 2 +--R x - 1 +--R + +--R 3 3 2x +-------+ +--R ((- 2b x - 2a x)atan(x) + (- b x - a x)atan(------))\|- b + a +--R 2 +--R x - 1 +--R / +--R +--------+ +--R 2 2 +-------+ | 2 2 2 +-------+ +-+ +--R (2a b x + 2a )\|- b + a \|b x + a + (- 2a b x - 2a )\|- b + a \|a +--R Type: Expression Integer +--E 29 + +--S 30 of 477 +d0005a:= D(m0005a,x) +--R +--R +--R 2x +--R - 2atan(x) - atan(------) +--R 2 +--R x - 1 +--R (15) ------------------------- +--R +--------+ +--R 2 | 2 +--R (2b x + 2a)\|b x + a +--R Type: Expression Integer +--E 30 + +--S 31 of 477 +m0005b:= a0005.2-r0005 +--R +--R +--R (16) +--R +--------+ +--R 2 +-----+ | 2 2 +-+ +-----+ +--R ((- 2b x - 2a)\|b - a \|b x + a + (2b x + 2a)\|a \|b - a ) +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R atanh(-----------) +--R +-------+ +--R \|- b + a +--R + +--R +--------+ +--R 2 +-------+ | 2 2 +-------+ +-+ +--R ((b x + a)\|- b + a \|b x + a + (- b x - a)\|- b + a \|a ) +--R * +--R +--------+ +--R 2 +-----+ | 2 4 2 +-+ +-----+ +--R 2x \|b - a \|b x + a + (- 2x - 2x )\|a \|b - a +--R atan(---------------------------------------------------------) +--R +--------+ +--R 2 +-+ | 2 4 2 +--R (2x + 2)\|a \|b x + a + (b - 2a)x + (- b - 2a)x - 2a +--R + +--R +--------+ +--R 2x +-------+ +-+ +-----+ | 2 +--R (2x atan(x) + x atan(------))\|- b + a \|a \|b - a \|b x + a +--R 2 +--R x - 1 +--R + +--R 3 3 2x +-------+ +-----+ +--R ((- 2b x - 2a x)atan(x) + (- b x - a x)atan(------))\|- b + a \|b - a +--R 2 +--R x - 1 +--R / +--R +--------+ +--R 2 2 +-------+ +-----+ | 2 +--R (2a b x + 2a )\|- b + a \|b - a \|b x + a +--R + +--R 2 2 +-------+ +-+ +-----+ +--R (- 2a b x - 2a )\|- b + a \|a \|b - a +--R Type: Expression Integer +--E 31 + +--S 32 of 477 +d0005b:= D(m0005b,x) +--R +--R +--R 2x +--R - 2atan(x) - atan(------) +--R 2 +--R x - 1 +--R (17) ------------------------- +--R +--------+ +--R 2 | 2 +--R (2b x + 2a)\|b x + a +--R Type: Expression Integer +--E 32 + +--S 33 of 477 +t0006:= atan(x)/(a+b*x^2)^(5/2) +--R +--R +--R atan(x) +--R (18) -------------------------------- +--R +--------+ +--R 2 4 2 2 | 2 +--R (b x + 2a b x + a )\|b x + a +--R Type: Expression Integer +--E 33 + +--S 34 of 477 +r0006:= -1/3/a/(a-b)/(a+b*x^2)^(1/2)+1/3*x*(3*a+2*b*x^2)*_ + atan(x)/a^2/(a+b*x^2)^(3/2)+1/3*(3*a-2*b)*_ + atanh((a+b*x^2)^(1/2)/(a-b)^(1/2))/a^2/(a-b)^(3/2) +--R +--R +--R (19) +--R +--------+ +--R +--------+ | 2 +--R 2 2 2 | 2 \|b x + a +--R ((2b - 3a b)x + 2a b - 3a )\|b x + a atanh(-----------) +--R +-------+ +--R \|- b + a +--R + +--R 2 3 2 2 2 +-------+ +--R (((2b - 2a b)x + (3a b - 3a )x)atan(x) + a b x + a )\|- b + a +--R / +--R +--------+ +--R 2 2 3 2 3 4 +-------+ | 2 +--R ((3a b - 3a b)x + 3a b - 3a )\|- b + a \|b x + a +--R Type: Expression Integer +--E 34 + +--S 35 of 477 +a0006:= integrate(t0006,x) +--R +--R +--R (20) +--R [ +--R 4 3 6 3 2 2 4 2 2 3 2 +--R (8b - 12a b )x + (32a b - 48a b )x + (40a b - 60a b)x +--R + +--R 3 4 +--R 16a b - 24a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 5 4 8 4 2 3 6 2 3 3 2 4 +--R (- 2b + 3a b )x + (- 20a b + 30a b )x + (- 50a b + 75a b )x +--R + +--R 3 2 4 2 4 5 +--R (- 48a b + 72a b)x - 16a b + 24a +--R * +--R log +--R 2 2 4 2 2 +-+ +--R ((- 2b - 2a b + 4a )x + (- 8a b + 8a )x )\|a +--R + +--R 2 4 2 2 2 +-------+ +--R (4a x + (4a b + 8a )x + 8a )\|- b + a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 2 6 2 2 4 2 2 +--R (b - 2a b)x + (- b - 4a b - 4a )x + (- 8a b - 8a )x +--R + +--R 2 +--R - 8a +--R * +--R +-------+ +-+ +--R \|- b + a \|a +--R + +--R 2 2 6 2 2 3 4 2 3 2 +--R (2a b - 2a b)x + (6a b - 2a b - 4a )x + (8a b - 8a )x +--R / +--R +--------+ +--R 4 2 2 2 | 2 +--R (4a b x + (4a b + 8a )x + 8a )\|b x + a +--R + +--R 2 6 2 4 2 2 2 +-+ +--R (- b x + (- b - 8a b)x + (- 8a b - 8a )x - 8a )\|a +--R + +--R 4 3 7 3 2 2 5 2 2 3 3 +--R (2b - 2a b )x + (19a b - 19a b )x + (40a b - 40a b)x +--R + +--R 3 4 +--R (24a b - 24a )x +--R * +--R 2x +--R atan(------) +--R 2 +--R x - 1 +--R + +--R 3 6 2 2 4 3 2 +--R 6a b x + 14a b x + 8a b x +--R * +--R +--------+ +--R +-------+ | 2 +--R \|- b + a \|b x + a +--R + +--R 4 3 7 3 2 2 5 +--R (- 8b + 8a b )x + (- 36a b + 36a b )x +--R + +--R 2 2 3 3 3 4 +--R (- 52a b + 52a b)x + (- 24a b + 24a )x +--R * +--R 2x +--R atan(------) +--R 2 +--R x - 1 +--R + +--R 4 8 3 6 2 2 4 3 2 +--R - 2b x - 12a b x - 18a b x - 8a b x +--R * +--R +-------+ +-+ +--R \|- b + a \|a +--R / +--R 2 4 3 3 6 3 3 4 2 4 4 2 5 2 +--R (24a b - 24a b )x + (96a b - 96a b )x + (120a b - 120a b)x +--R + +--R 5 6 +--R 48a b - 48a +--R * +--R +--------+ +--R +-------+ +-+ | 2 +--R \|- b + a \|a \|b x + a +--R + +--R 2 5 3 4 8 3 4 4 3 6 +--R (- 6a b + 6a b )x + (- 60a b + 60a b )x +--R + +--R 4 3 5 2 4 5 2 6 2 6 7 +--R (- 150a b + 150a b )x + (- 144a b + 144a b)x - 48a b + 48a +--R * +--R +-------+ +--R \|- b + a +--R , +--R +--R 4 3 6 3 2 2 4 2 2 3 2 +--R (8b - 12a b )x + (32a b - 48a b )x + (40a b - 60a b)x +--R + +--R 3 4 +--R 16a b - 24a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 5 4 8 4 2 3 6 2 3 3 2 4 +--R (- 2b + 3a b )x + (- 20a b + 30a b )x + (- 50a b + 75a b )x +--R + +--R 3 2 4 2 4 5 +--R (- 48a b + 72a b)x - 16a b + 24a +--R * +--R +--------+ +--R 2 +-----+ | 2 4 2 +-+ +-----+ +--R 2x \|b - a \|b x + a + (- 2x - 2x )\|a \|b - a +--R atan(---------------------------------------------------------) +--R +--------+ +--R 2 +-+ | 2 4 2 +--R (2x + 2)\|a \|b x + a + (b - 2a)x + (- b - 2a)x - 2a +--R + +--R 4 3 7 3 2 2 5 2 2 3 3 +--R (2b - 2a b )x + (19a b - 19a b )x + (40a b - 40a b)x +--R + +--R 3 4 +--R (24a b - 24a )x +--R * +--R 2x +--R atan(------) +--R 2 +--R x - 1 +--R + +--R 3 6 2 2 4 3 2 +--R 6a b x + 14a b x + 8a b x +--R * +--R +--------+ +--R +-----+ | 2 +--R \|b - a \|b x + a +--R + +--R 4 3 7 3 2 2 5 +--R (- 8b + 8a b )x + (- 36a b + 36a b )x +--R + +--R 2 2 3 3 3 4 +--R (- 52a b + 52a b)x + (- 24a b + 24a )x +--R * +--R 2x +--R atan(------) +--R 2 +--R x - 1 +--R + +--R 4 8 3 6 2 2 4 3 2 +--R - 2b x - 12a b x - 18a b x - 8a b x +--R * +--R +-+ +-----+ +--R \|a \|b - a +--R / +--R 2 4 3 3 6 3 3 4 2 4 4 2 5 2 +--R (24a b - 24a b )x + (96a b - 96a b )x + (120a b - 120a b)x +--R + +--R 5 6 +--R 48a b - 48a +--R * +--R +--------+ +--R +-+ +-----+ | 2 +--R \|a \|b - a \|b x + a +--R + +--R 2 5 3 4 8 3 4 4 3 6 +--R (- 6a b + 6a b )x + (- 60a b + 60a b )x +--R + +--R 4 3 5 2 4 5 2 6 2 6 7 +--R (- 150a b + 150a b )x + (- 144a b + 144a b)x - 48a b + 48a +--R * +--R +-----+ +--R \|b - a +--R ] +--R Type: Union(List Expression Integer,...) +--E 35 + +--S 36 of 477 +m0006a:= a0006.1-r0006 +--R +--R +--R (21) +--R 4 3 6 3 2 2 4 2 2 3 2 +--R (2b - 3a b )x + (18a b - 27a b )x + (32a b - 48a b)x +--R + +--R 3 4 +--R 16a b - 24a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 4 3 6 3 2 2 4 2 2 3 2 +--R (- 8b + 12a b )x + (- 32a b + 48a b )x + (- 40a b + 60a b)x +--R + +--R 3 4 +--R - 16a b + 24a +--R * +--R +-+ +--R \|a +--R * +--R log +--R 2 2 4 2 2 +-+ +--R ((- 2b - 2a b + 4a )x + (- 8a b + 8a )x )\|a +--R + +--R 2 4 2 2 2 +-------+ +--R (4a x + (4a b + 8a )x + 8a )\|- b + a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 2 6 2 2 4 2 2 +--R (b - 2a b)x + (- b - 4a b - 4a )x + (- 8a b - 8a )x +--R + +--R 2 +--R - 8a +--R * +--R +-------+ +-+ +--R \|- b + a \|a +--R + +--R 2 2 6 2 2 3 4 2 3 2 +--R (2a b - 2a b)x + (6a b - 2a b - 4a )x + (8a b - 8a )x +--R / +--R +--------+ +--R 4 2 2 2 | 2 +--R (4a b x + (4a b + 8a )x + 8a )\|b x + a +--R + +--R 2 6 2 4 2 2 2 +-+ +--R (- b x + (- b - 8a b)x + (- 8a b - 8a )x - 8a )\|a +--R + +--R 4 3 6 3 2 2 4 2 2 3 2 +--R (- 4b + 6a b )x + (- 36a b + 54a b )x + (- 64a b + 96a b)x +--R + +--R 3 4 +--R - 32a b + 48a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 4 3 6 3 2 2 4 2 2 3 2 +--R (16b - 24a b )x + (64a b - 96a b )x + (80a b - 120a b)x +--R + +--R 3 4 +--R 32a b - 48a +--R * +--R +-+ +--R \|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R atanh(-----------) +--R +-------+ +--R \|- b + a +--R + +--R 3 2 5 2 2 3 2 3 +--R ((16b - 16a b )x + (56a b - 56a b)x + (48a b - 48a )x)atan(x) +--R + +--R 3 2 5 2 2 3 2 3 2x +--R ((8b - 8a b )x + (28a b - 28a b)x + (24a b - 24a )x)atan(------) +--R 2 +--R x - 1 +--R + +--R 3 6 2 4 2 2 3 +--R 2b x + 18a b x + 32a b x + 16a +--R * +--R +--------+ +--R +-------+ +-+ | 2 +--R \|- b + a \|a \|b x + a +--R + +--R 4 3 7 3 2 2 5 2 2 3 3 +--R (- 4b + 4a b )x + (- 38a b + 38a b )x + (- 80a b + 80a b)x +--R + +--R 3 4 +--R (- 48a b + 48a )x +--R * +--R atan(x) +--R + +--R 4 3 7 3 2 2 5 2 2 3 3 +--R (- 2b + 2a b )x + (- 19a b + 19a b )x + (- 40a b + 40a b)x +--R + +--R 3 4 +--R (- 24a b + 24a )x +--R * +--R 2x +--R atan(------) +--R 2 +--R x - 1 +--R + +--R 3 6 2 2 4 3 2 4 +--R - 8a b x - 32a b x - 40a b x - 16a +--R * +--R +-------+ +--R \|- b + a +--R / +--R 2 4 3 3 6 3 3 4 2 4 4 2 5 2 5 +--R (6a b - 6a b )x + (54a b - 54a b )x + (96a b - 96a b)x + 48a b +--R + +--R 6 +--R - 48a +--R * +--R +--------+ +--R +-------+ | 2 +--R \|- b + a \|b x + a +--R + +--R 2 4 3 3 6 3 3 4 2 4 +--R (- 24a b + 24a b )x + (- 96a b + 96a b )x +--R + +--R 4 2 5 2 5 6 +--R (- 120a b + 120a b)x - 48a b + 48a +--R * +--R +-------+ +-+ +--R \|- b + a \|a +--R Type: Expression Integer +--E 36 + +--S 37 of 477 +d0006a:= D(m0006a,x) +--R +--R +--R 2x +--R - 2atan(x) - atan(------) +--R 2 +--R x - 1 +--R (22) ---------------------------------- +--R +--------+ +--R 2 4 2 2 | 2 +--R (2b x + 4a b x + 2a )\|b x + a +--R Type: Expression Integer +--E 37 + +--S 38 of 477 +m0006b:= a0006.2-r0006 +--R +--R +--R (23) +--R 4 3 6 3 2 2 4 2 2 3 2 +--R (- 4b + 6a b )x + (- 36a b + 54a b )x + (- 64a b + 96a b)x +--R + +--R 3 4 +--R - 32a b + 48a +--R * +--R +--------+ +--R +-----+ | 2 +--R \|b - a \|b x + a +--R + +--R 4 3 6 3 2 2 4 2 2 3 2 +--R (16b - 24a b )x + (64a b - 96a b )x + (80a b - 120a b)x +--R + +--R 3 4 +--R 32a b - 48a +--R * +--R +-+ +-----+ +--R \|a \|b - a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R atanh(-----------) +--R +-------+ +--R \|- b + a +--R + +--R 4 3 6 3 2 2 4 2 2 3 2 +--R (2b - 3a b )x + (18a b - 27a b )x + (32a b - 48a b)x +--R + +--R 3 4 +--R 16a b - 24a +--R * +--R +--------+ +--R +-------+ | 2 +--R \|- b + a \|b x + a +--R + +--R 4 3 6 3 2 2 4 2 2 3 2 +--R (- 8b + 12a b )x + (- 32a b + 48a b )x + (- 40a b + 60a b)x +--R + +--R 3 4 +--R - 16a b + 24a +--R * +--R +-------+ +-+ +--R \|- b + a \|a +--R * +--R +--------+ +--R 2 +-----+ | 2 4 2 +-+ +-----+ +--R 2x \|b - a \|b x + a + (- 2x - 2x )\|a \|b - a +--R atan(---------------------------------------------------------) +--R +--------+ +--R 2 +-+ | 2 4 2 +--R (2x + 2)\|a \|b x + a + (b - 2a)x + (- b - 2a)x - 2a +--R + +--R 3 2 5 2 2 3 2 3 +--R ((16b - 16a b )x + (56a b - 56a b)x + (48a b - 48a )x)atan(x) +--R + +--R 3 2 5 2 2 3 2 3 2x +--R ((8b - 8a b )x + (28a b - 28a b)x + (24a b - 24a )x)atan(------) +--R 2 +--R x - 1 +--R + +--R 3 6 2 4 2 2 3 +--R 2b x + 18a b x + 32a b x + 16a +--R * +--R +--------+ +--R +-------+ +-+ +-----+ | 2 +--R \|- b + a \|a \|b - a \|b x + a +--R + +--R 4 3 7 3 2 2 5 2 2 3 3 +--R (- 4b + 4a b )x + (- 38a b + 38a b )x + (- 80a b + 80a b)x +--R + +--R 3 4 +--R (- 48a b + 48a )x +--R * +--R atan(x) +--R + +--R 4 3 7 3 2 2 5 2 2 3 3 +--R (- 2b + 2a b )x + (- 19a b + 19a b )x + (- 40a b + 40a b)x +--R + +--R 3 4 +--R (- 24a b + 24a )x +--R * +--R 2x +--R atan(------) +--R 2 +--R x - 1 +--R + +--R 3 6 2 2 4 3 2 4 +--R - 8a b x - 32a b x - 40a b x - 16a +--R * +--R +-------+ +-----+ +--R \|- b + a \|b - a +--R / +--R 2 4 3 3 6 3 3 4 2 4 4 2 5 2 5 +--R (6a b - 6a b )x + (54a b - 54a b )x + (96a b - 96a b)x + 48a b +--R + +--R 6 +--R - 48a +--R * +--R +--------+ +--R +-------+ +-----+ | 2 +--R \|- b + a \|b - a \|b x + a +--R + +--R 2 4 3 3 6 3 3 4 2 4 +--R (- 24a b + 24a b )x + (- 96a b + 96a b )x +--R + +--R 4 2 5 2 5 6 +--R (- 120a b + 120a b)x - 48a b + 48a +--R * +--R +-------+ +-+ +-----+ +--R \|- b + a \|a \|b - a +--R Type: Expression Integer +--E 38 + +--S 39 of 477 +d0006b:= D(m0006b,x) +--R +--R +--R 2x +--R - 2atan(x) - atan(------) +--R 2 +--R x - 1 +--R (24) ---------------------------------- +--R +--------+ +--R 2 4 2 2 | 2 +--R (2b x + 4a b x + 2a )\|b x + a +--R Type: Expression Integer +--E 39 + +--S 40 of 477 +t0007:= atan(x)/(a+b*x^2)^(7/2) +--R +--R +--R atan(x) +--R (25) ------------------------------------------ +--R +--------+ +--R 3 6 2 4 2 2 3 | 2 +--R (b x + 3a b x + 3a b x + a )\|b x + a +--R Type: Expression Integer +--E 40 + +--S 41 of 477 +r0007:= -1/15/a/(a-b)/(a+b*x^2)^(3/2)-1/15*(7*a-4*b)/a^2/(a-b)^2/_ + (a+b*x^2)^(1/2)+1/15*x*(8*(a+b*x^2)^2+a*(7*a+4*b*x^2))*_ + atan(x)/a^3/(a+b*x^2)^(5/2)+1/15*(15*a^2-20*a*b+8*b^2)*_ + atanh((a+b*x^2)^(1/2)/(a-b)^(1/2))/a^3/(a-b)^(5/2) +--R +--R +--R (26) +--R 4 3 2 2 4 3 2 2 3 2 2 2 +--R (8b - 20a b + 15a b )x + (16a b - 40a b + 30a b)x + 8a b +--R + +--R 3 4 +--R - 20a b + 15a +--R * +--R +--------+ +--R +--------+ | 2 +--R | 2 \|b x + a +--R \|b x + a atanh(-----------) +--R +-------+ +--R \|- b + a +--R + +--R 4 3 2 2 5 3 2 2 3 3 +--R (8b - 16a b + 8a b )x + (20a b - 40a b + 20a b)x +--R + +--R 2 2 3 4 +--R (15a b - 30a b + 15a )x +--R * +--R atan(x) +--R + +--R 3 2 2 4 2 2 3 2 3 4 +--R (4a b - 7a b )x + (9a b - 15a b)x + 5a b - 8a +--R * +--R +-------+ +--R \|- b + a +--R / +--R 3 4 4 3 5 2 4 4 3 5 2 6 2 5 2 +--R (15a b - 30a b + 15a b )x + (30a b - 60a b + 30a b)x + 15a b +--R + +--R 6 7 +--R - 30a b + 15a +--R * +--R +--------+ +--R +-------+ | 2 +--R \|- b + a \|b x + a +--R Type: Expression Integer +--E 41 + +--S 42 of 477 +a0007:= integrate(t0007,x) +--R +--R +--R (27) +--R [ +--R 8 7 2 6 12 +--R (64b - 160a b + 120a b )x +--R + +--R 7 2 6 3 5 10 +--R (832a b - 2080a b + 1560a b )x +--R + +--R 2 6 3 5 4 4 8 +--R (3648a b - 9120a b + 6840a b )x +--R + +--R 3 5 4 4 5 3 6 +--R (7616a b - 19040a b + 14280a b )x +--R + +--R 4 4 5 3 6 2 4 +--R (8320a b - 20800a b + 15600a b )x +--R + +--R 5 3 6 2 7 2 6 2 7 8 +--R (4608a b - 11520a b + 8640a b)x + 1024a b - 2560a b + 1920a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 9 8 2 7 14 8 2 7 3 6 12 +--R (- 8b + 20a b - 15a b )x + (- 280a b + 700a b - 525a b )x +--R + +--R 2 7 3 6 4 5 10 +--R (- 2072a b + 5180a b - 3885a b )x +--R + +--R 3 6 4 5 5 4 8 +--R (- 6664a b + 16660a b - 12495a b )x +--R + +--R 4 5 5 4 6 3 6 +--R (- 11264a b + 28160a b - 21120a b )x +--R + +--R 5 4 6 3 7 2 4 +--R (- 10496a b + 26240a b - 19680a b )x +--R + +--R 6 3 7 2 8 2 7 2 8 9 +--R (- 5120a b + 12800a b - 9600a b)x - 1024a b + 2560a b - 1920a +--R * +--R log +--R 2 2 4 2 2 +-+ +--R ((- 2b - 2a b + 4a )x + (- 8a b + 8a )x )\|a +--R + +--R 2 4 2 2 2 +-------+ +--R (4a x + (4a b + 8a )x + 8a )\|- b + a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 2 6 2 2 4 2 2 +--R (b - 2a b)x + (- b - 4a b - 4a )x + (- 8a b - 8a )x +--R + +--R 2 +--R - 8a +--R * +--R +-------+ +-+ +--R \|- b + a \|a +--R + +--R 2 2 6 2 2 3 4 2 3 2 +--R (2a b - 2a b)x + (6a b - 2a b - 4a )x + (8a b - 8a )x +--R / +--R +--------+ +--R 4 2 2 2 | 2 +--R (4a b x + (4a b + 8a )x + 8a )\|b x + a +--R + +--R 2 6 2 4 2 2 2 +-+ +--R (- b x + (- b - 8a b)x + (- 8a b - 8a )x - 8a )\|a +--R + +--R 8 7 2 6 13 7 2 6 3 5 11 +--R (8b - 16a b + 8a b )x + (276a b - 552a b + 276a b )x +--R + +--R 2 6 3 5 4 4 9 +--R (1935a b - 3870a b + 1935a b )x +--R + +--R 3 5 4 4 5 3 7 +--R (5728a b - 11456a b + 5728a b )x +--R + +--R 4 4 5 3 6 2 5 +--R (8544a b - 17088a b + 8544a b )x +--R + +--R 5 3 6 2 7 3 +--R (6400a b - 12800a b + 6400a b)x +--R + +--R 6 2 7 8 +--R (1920a b - 3840a b + 1920a )x +--R * +--R 2x +--R atan(------) +--R 2 +--R x - 1 +--R + +--R 7 2 6 12 2 6 3 5 10 +--R (72a b - 114a b )x + (766a b - 1186a b )x +--R + +--R 3 5 4 4 8 4 4 5 3 6 +--R (2694a b - 4080a b )x + (4272a b - 6336a b )x +--R + +--R 5 3 6 2 4 6 2 7 2 +--R (3168a b - 4608a b )x + (896a b - 1280a b)x +--R * +--R +--------+ +--R +-------+ | 2 +--R \|- b + a \|b x + a +--R + +--R 8 7 2 6 13 +--R (- 64b + 128a b - 64a b )x +--R + +--R 7 2 6 3 5 11 +--R (- 864a b + 1728a b - 864a b )x +--R + +--R 2 6 3 5 4 4 9 +--R (- 4056a b + 8112a b - 4056a b )x +--R + +--R 3 5 4 4 5 3 7 +--R (- 9320a b + 18640a b - 9320a b )x +--R + +--R 4 4 5 3 6 2 5 +--R (- 11504a b + 23008a b - 11504a b )x +--R + +--R 5 3 6 2 7 3 +--R (- 7360a b + 14720a b - 7360a b)x +--R + +--R 6 2 7 8 +--R (- 1920a b + 3840a b - 1920a )x +--R * +--R 2x +--R atan(------) +--R 2 +--R x - 1 +--R + +--R 8 7 14 7 2 6 12 +--R (- 10b + 16a b )x + (- 286a b + 448a b )x +--R + +--R 2 6 3 5 10 3 5 4 4 8 +--R (- 1742a b + 2672a b )x + (- 4490a b + 6752a b )x +--R + +--R 4 4 5 3 6 5 3 6 2 4 +--R (- 5744a b + 8480a b )x + (- 3616a b + 5248a b )x +--R + +--R 6 2 7 2 +--R (- 896a b + 1280a b)x +--R * +--R +-------+ +-+ +--R \|- b + a \|a +--R / +--R 3 8 4 7 5 6 12 +--R (240a b - 480a b + 240a b )x +--R + +--R 4 7 5 6 6 5 10 +--R (3120a b - 6240a b + 3120a b )x +--R + +--R 5 6 6 5 7 4 8 +--R (13680a b - 27360a b + 13680a b )x +--R + +--R 6 5 7 4 8 3 6 +--R (28560a b - 57120a b + 28560a b )x +--R + +--R 7 4 8 3 9 2 4 +--R (31200a b - 62400a b + 31200a b )x +--R + +--R 8 3 9 2 10 2 9 2 10 11 +--R (17280a b - 34560a b + 17280a b)x + 3840a b - 7680a b + 3840a +--R * +--R +--------+ +--R +-------+ +-+ | 2 +--R \|- b + a \|a \|b x + a +--R + +--R 3 9 4 8 5 7 14 +--R (- 30a b + 60a b - 30a b )x +--R + +--R 4 8 5 7 6 6 12 +--R (- 1050a b + 2100a b - 1050a b )x +--R + +--R 5 7 6 6 7 5 10 +--R (- 7770a b + 15540a b - 7770a b )x +--R + +--R 6 6 7 5 8 4 8 +--R (- 24990a b + 49980a b - 24990a b )x +--R + +--R 7 5 8 4 9 3 6 +--R (- 42240a b + 84480a b - 42240a b )x +--R + +--R 8 4 9 3 10 2 4 +--R (- 39360a b + 78720a b - 39360a b )x +--R + +--R 9 3 10 2 11 2 10 2 11 +--R (- 19200a b + 38400a b - 19200a b)x - 3840a b + 7680a b +--R + +--R 12 +--R - 3840a +--R * +--R +-------+ +--R \|- b + a +--R , +--R +--R 8 7 2 6 12 +--R (64b - 160a b + 120a b )x +--R + +--R 7 2 6 3 5 10 +--R (832a b - 2080a b + 1560a b )x +--R + +--R 2 6 3 5 4 4 8 +--R (3648a b - 9120a b + 6840a b )x +--R + +--R 3 5 4 4 5 3 6 +--R (7616a b - 19040a b + 14280a b )x +--R + +--R 4 4 5 3 6 2 4 +--R (8320a b - 20800a b + 15600a b )x +--R + +--R 5 3 6 2 7 2 6 2 7 8 +--R (4608a b - 11520a b + 8640a b)x + 1024a b - 2560a b + 1920a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 9 8 2 7 14 8 2 7 3 6 12 +--R (- 8b + 20a b - 15a b )x + (- 280a b + 700a b - 525a b )x +--R + +--R 2 7 3 6 4 5 10 +--R (- 2072a b + 5180a b - 3885a b )x +--R + +--R 3 6 4 5 5 4 8 +--R (- 6664a b + 16660a b - 12495a b )x +--R + +--R 4 5 5 4 6 3 6 +--R (- 11264a b + 28160a b - 21120a b )x +--R + +--R 5 4 6 3 7 2 4 +--R (- 10496a b + 26240a b - 19680a b )x +--R + +--R 6 3 7 2 8 2 7 2 8 9 +--R (- 5120a b + 12800a b - 9600a b)x - 1024a b + 2560a b - 1920a +--R * +--R +--------+ +--R 2 +-----+ | 2 4 2 +-+ +-----+ +--R 2x \|b - a \|b x + a + (- 2x - 2x )\|a \|b - a +--R atan(---------------------------------------------------------) +--R +--------+ +--R 2 +-+ | 2 4 2 +--R (2x + 2)\|a \|b x + a + (b - 2a)x + (- b - 2a)x - 2a +--R + +--R 8 7 2 6 13 7 2 6 3 5 11 +--R (8b - 16a b + 8a b )x + (276a b - 552a b + 276a b )x +--R + +--R 2 6 3 5 4 4 9 +--R (1935a b - 3870a b + 1935a b )x +--R + +--R 3 5 4 4 5 3 7 +--R (5728a b - 11456a b + 5728a b )x +--R + +--R 4 4 5 3 6 2 5 +--R (8544a b - 17088a b + 8544a b )x +--R + +--R 5 3 6 2 7 3 +--R (6400a b - 12800a b + 6400a b)x +--R + +--R 6 2 7 8 +--R (1920a b - 3840a b + 1920a )x +--R * +--R 2x +--R atan(------) +--R 2 +--R x - 1 +--R + +--R 7 2 6 12 2 6 3 5 10 +--R (72a b - 114a b )x + (766a b - 1186a b )x +--R + +--R 3 5 4 4 8 4 4 5 3 6 +--R (2694a b - 4080a b )x + (4272a b - 6336a b )x +--R + +--R 5 3 6 2 4 6 2 7 2 +--R (3168a b - 4608a b )x + (896a b - 1280a b)x +--R * +--R +--------+ +--R +-----+ | 2 +--R \|b - a \|b x + a +--R + +--R 8 7 2 6 13 +--R (- 64b + 128a b - 64a b )x +--R + +--R 7 2 6 3 5 11 +--R (- 864a b + 1728a b - 864a b )x +--R + +--R 2 6 3 5 4 4 9 +--R (- 4056a b + 8112a b - 4056a b )x +--R + +--R 3 5 4 4 5 3 7 +--R (- 9320a b + 18640a b - 9320a b )x +--R + +--R 4 4 5 3 6 2 5 +--R (- 11504a b + 23008a b - 11504a b )x +--R + +--R 5 3 6 2 7 3 +--R (- 7360a b + 14720a b - 7360a b)x +--R + +--R 6 2 7 8 +--R (- 1920a b + 3840a b - 1920a )x +--R * +--R 2x +--R atan(------) +--R 2 +--R x - 1 +--R + +--R 8 7 14 7 2 6 12 +--R (- 10b + 16a b )x + (- 286a b + 448a b )x +--R + +--R 2 6 3 5 10 3 5 4 4 8 +--R (- 1742a b + 2672a b )x + (- 4490a b + 6752a b )x +--R + +--R 4 4 5 3 6 5 3 6 2 4 +--R (- 5744a b + 8480a b )x + (- 3616a b + 5248a b )x +--R + +--R 6 2 7 2 +--R (- 896a b + 1280a b)x +--R * +--R +-+ +-----+ +--R \|a \|b - a +--R / +--R 3 8 4 7 5 6 12 +--R (240a b - 480a b + 240a b )x +--R + +--R 4 7 5 6 6 5 10 +--R (3120a b - 6240a b + 3120a b )x +--R + +--R 5 6 6 5 7 4 8 +--R (13680a b - 27360a b + 13680a b )x +--R + +--R 6 5 7 4 8 3 6 +--R (28560a b - 57120a b + 28560a b )x +--R + +--R 7 4 8 3 9 2 4 +--R (31200a b - 62400a b + 31200a b )x +--R + +--R 8 3 9 2 10 2 9 2 10 11 +--R (17280a b - 34560a b + 17280a b)x + 3840a b - 7680a b + 3840a +--R * +--R +--------+ +--R +-+ +-----+ | 2 +--R \|a \|b - a \|b x + a +--R + +--R 3 9 4 8 5 7 14 +--R (- 30a b + 60a b - 30a b )x +--R + +--R 4 8 5 7 6 6 12 +--R (- 1050a b + 2100a b - 1050a b )x +--R + +--R 5 7 6 6 7 5 10 +--R (- 7770a b + 15540a b - 7770a b )x +--R + +--R 6 6 7 5 8 4 8 +--R (- 24990a b + 49980a b - 24990a b )x +--R + +--R 7 5 8 4 9 3 6 +--R (- 42240a b + 84480a b - 42240a b )x +--R + +--R 8 4 9 3 10 2 4 +--R (- 39360a b + 78720a b - 39360a b )x +--R + +--R 9 3 10 2 11 2 10 2 11 +--R (- 19200a b + 38400a b - 19200a b)x - 3840a b + 7680a b +--R + +--R 12 +--R - 3840a +--R * +--R +-----+ +--R \|b - a +--R ] +--R Type: Union(List Expression Integer,...) +--E 42 + +--S 43 of 477 +m0007a:= a0007.1-r0007 +--R +--R +--R (28) +--R 8 7 2 6 12 7 2 6 3 5 10 +--R (8b - 20a b + 15a b )x + (272a b - 680a b + 510a b )x +--R + +--R 2 6 3 5 4 4 8 +--R (1800a b - 4500a b + 3375a b )x +--R + +--R 3 5 4 4 5 3 6 +--R (4864a b - 12160a b + 9120a b )x +--R + +--R 4 4 5 3 6 2 4 +--R (6400a b - 16000a b + 12000a b )x +--R + +--R 5 3 6 2 7 2 6 2 7 8 +--R (4096a b - 10240a b + 7680a b)x + 1024a b - 2560a b + 1920a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 8 7 2 6 12 +--R (- 64b + 160a b - 120a b )x +--R + +--R 7 2 6 3 5 10 +--R (- 832a b + 2080a b - 1560a b )x +--R + +--R 2 6 3 5 4 4 8 +--R (- 3648a b + 9120a b - 6840a b )x +--R + +--R 3 5 4 4 5 3 6 +--R (- 7616a b + 19040a b - 14280a b )x +--R + +--R 4 4 5 3 6 2 4 +--R (- 8320a b + 20800a b - 15600a b )x +--R + +--R 5 3 6 2 7 2 6 2 7 8 +--R (- 4608a b + 11520a b - 8640a b)x - 1024a b + 2560a b - 1920a +--R * +--R +-+ +--R \|a +--R * +--R log +--R 2 2 4 2 2 +-+ +--R ((- 2b - 2a b + 4a )x + (- 8a b + 8a )x )\|a +--R + +--R 2 4 2 2 2 +-------+ +--R (4a x + (4a b + 8a )x + 8a )\|- b + a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 2 6 2 2 4 2 2 +--R (b - 2a b)x + (- b - 4a b - 4a )x + (- 8a b - 8a )x +--R + +--R 2 +--R - 8a +--R * +--R +-------+ +-+ +--R \|- b + a \|a +--R + +--R 2 2 6 2 2 3 4 2 3 2 +--R (2a b - 2a b)x + (6a b - 2a b - 4a )x + (8a b - 8a )x +--R / +--R +--------+ +--R 4 2 2 2 | 2 +--R (4a b x + (4a b + 8a )x + 8a )\|b x + a +--R + +--R 2 6 2 4 2 2 2 +-+ +--R (- b x + (- b - 8a b)x + (- 8a b - 8a )x - 8a )\|a +--R + +--R 8 7 2 6 12 +--R (- 16b + 40a b - 30a b )x +--R + +--R 7 2 6 3 5 10 +--R (- 544a b + 1360a b - 1020a b )x +--R + +--R 2 6 3 5 4 4 8 +--R (- 3600a b + 9000a b - 6750a b )x +--R + +--R 3 5 4 4 5 3 6 +--R (- 9728a b + 24320a b - 18240a b )x +--R + +--R 4 4 5 3 6 2 4 +--R (- 12800a b + 32000a b - 24000a b )x +--R + +--R 5 3 6 2 7 2 6 2 7 8 +--R (- 8192a b + 20480a b - 15360a b)x - 2048a b + 5120a b - 3840a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 8 7 2 6 12 +--R (128b - 320a b + 240a b )x +--R + +--R 7 2 6 3 5 10 +--R (1664a b - 4160a b + 3120a b )x +--R + +--R 2 6 3 5 4 4 8 +--R (7296a b - 18240a b + 13680a b )x +--R + +--R 3 5 4 4 5 3 6 +--R (15232a b - 38080a b + 28560a b )x +--R + +--R 4 4 5 3 6 2 4 +--R (16640a b - 41600a b + 31200a b )x +--R + +--R 5 3 6 2 7 2 6 2 7 8 +--R (9216a b - 23040a b + 17280a b)x + 2048a b - 5120a b + 3840a +--R * +--R +-+ +--R \|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R atanh(-----------) +--R +-------+ +--R \|- b + a +--R + +--R 7 6 2 5 11 +--R (128b - 256a b + 128a b )x +--R + +--R 6 2 5 3 4 9 +--R (1600a b - 3200a b + 1600a b )x +--R + +--R 2 5 3 4 4 3 7 +--R (6512a b - 13024a b + 6512a b )x +--R + +--R 3 4 4 3 5 2 5 +--R (12128a b - 24256a b + 12128a b )x +--R + +--R 4 3 5 2 6 3 +--R (10880a b - 21760a b + 10880a b)x +--R + +--R 5 2 6 7 +--R (3840a b - 7680a b + 3840a )x +--R * +--R atan(x) +--R + +--R 7 6 2 5 11 6 2 5 3 4 9 +--R (64b - 128a b + 64a b )x + (800a b - 1600a b + 800a b )x +--R + +--R 2 5 3 4 4 3 7 +--R (3256a b - 6512a b + 3256a b )x +--R + +--R 3 4 4 3 5 2 5 +--R (6064a b - 12128a b + 6064a b )x +--R + +--R 4 3 5 2 6 3 5 2 6 7 +--R (5440a b - 10880a b + 5440a b)x + (1920a b - 3840a b + 1920a )x +--R * +--R 2x +--R atan(------) +--R 2 +--R x - 1 +--R + +--R 7 6 12 6 2 5 10 2 5 3 4 8 +--R (10b - 16a b )x + (340a b - 544a b )x + (2250a b - 3600a b )x +--R + +--R 3 4 4 3 6 4 3 5 2 4 +--R (6080a b - 9728a b )x + (8000a b - 12800a b )x +--R + +--R 5 2 6 2 6 7 +--R (5120a b - 8192a b)x + 1280a b - 2048a +--R * +--R +--------+ +--R +-------+ +-+ | 2 +--R \|- b + a \|a \|b x + a +--R + +--R 8 7 2 6 13 +--R (- 16b + 32a b - 16a b )x +--R + +--R 7 2 6 3 5 11 +--R (- 552a b + 1104a b - 552a b )x +--R + +--R 2 6 3 5 4 4 9 +--R (- 3870a b + 7740a b - 3870a b )x +--R + +--R 3 5 4 4 5 3 7 +--R (- 11456a b + 22912a b - 11456a b )x +--R + +--R 4 4 5 3 6 2 5 +--R (- 17088a b + 34176a b - 17088a b )x +--R + +--R 5 3 6 2 7 3 +--R (- 12800a b + 25600a b - 12800a b)x +--R + +--R 6 2 7 8 +--R (- 3840a b + 7680a b - 3840a )x +--R * +--R atan(x) +--R + +--R 8 7 2 6 13 7 2 6 3 5 11 +--R (- 8b + 16a b - 8a b )x + (- 276a b + 552a b - 276a b )x +--R + +--R 2 6 3 5 4 4 9 +--R (- 1935a b + 3870a b - 1935a b )x +--R + +--R 3 5 4 4 5 3 7 +--R (- 5728a b + 11456a b - 5728a b )x +--R + +--R 4 4 5 3 6 2 5 +--R (- 8544a b + 17088a b - 8544a b )x +--R + +--R 5 3 6 2 7 3 +--R (- 6400a b + 12800a b - 6400a b)x +--R + +--R 6 2 7 8 +--R (- 1920a b + 3840a b - 1920a )x +--R * +--R 2x +--R atan(------) +--R 2 +--R x - 1 +--R + +--R 7 2 6 12 2 6 3 5 10 +--R (- 80a b + 128a b )x + (- 1040a b + 1664a b )x +--R + +--R 3 5 4 4 8 4 4 5 3 6 +--R (- 4560a b + 7296a b )x + (- 9520a b + 15232a b )x +--R + +--R 5 3 6 2 4 6 2 7 2 7 +--R (- 10400a b + 16640a b )x + (- 5760a b + 9216a b)x - 1280a b +--R + +--R 8 +--R 2048a +--R * +--R +-------+ +--R \|- b + a +--R / +--R 3 8 4 7 5 6 12 4 7 5 6 6 5 10 +--R (30a b - 60a b + 30a b )x + (1020a b - 2040a b + 1020a b )x +--R + +--R 5 6 6 5 7 4 8 +--R (6750a b - 13500a b + 6750a b )x +--R + +--R 6 5 7 4 8 3 6 +--R (18240a b - 36480a b + 18240a b )x +--R + +--R 7 4 8 3 9 2 4 +--R (24000a b - 48000a b + 24000a b )x +--R + +--R 8 3 9 2 10 2 9 2 10 11 +--R (15360a b - 30720a b + 15360a b)x + 3840a b - 7680a b + 3840a +--R * +--R +--------+ +--R +-------+ | 2 +--R \|- b + a \|b x + a +--R + +--R 3 8 4 7 5 6 12 +--R (- 240a b + 480a b - 240a b )x +--R + +--R 4 7 5 6 6 5 10 +--R (- 3120a b + 6240a b - 3120a b )x +--R + +--R 5 6 6 5 7 4 8 +--R (- 13680a b + 27360a b - 13680a b )x +--R + +--R 6 5 7 4 8 3 6 +--R (- 28560a b + 57120a b - 28560a b )x +--R + +--R 7 4 8 3 9 2 4 +--R (- 31200a b + 62400a b - 31200a b )x +--R + +--R 8 3 9 2 10 2 9 2 10 11 +--R (- 17280a b + 34560a b - 17280a b)x - 3840a b + 7680a b - 3840a +--R * +--R +-------+ +-+ +--R \|- b + a \|a +--R Type: Expression Integer +--E 43 + +--S 44 of 477 +d0007a:= D(m0007a,x) +--R +--R +--R 2x +--R - 2atan(x) - atan(------) +--R 2 +--R x - 1 +--R (29) -------------------------------------------- +--R +--------+ +--R 3 6 2 4 2 2 3 | 2 +--R (2b x + 6a b x + 6a b x + 2a )\|b x + a +--R Type: Expression Integer +--E 44 + +--S 45 of 477 +m0007b:= a0007.2-r0007 +--R +--R +--R (30) +--R 8 7 2 6 12 +--R (- 16b + 40a b - 30a b )x +--R + +--R 7 2 6 3 5 10 +--R (- 544a b + 1360a b - 1020a b )x +--R + +--R 2 6 3 5 4 4 8 +--R (- 3600a b + 9000a b - 6750a b )x +--R + +--R 3 5 4 4 5 3 6 +--R (- 9728a b + 24320a b - 18240a b )x +--R + +--R 4 4 5 3 6 2 4 +--R (- 12800a b + 32000a b - 24000a b )x +--R + +--R 5 3 6 2 7 2 6 2 7 8 +--R (- 8192a b + 20480a b - 15360a b)x - 2048a b + 5120a b - 3840a +--R * +--R +--------+ +--R +-----+ | 2 +--R \|b - a \|b x + a +--R + +--R 8 7 2 6 12 +--R (128b - 320a b + 240a b )x +--R + +--R 7 2 6 3 5 10 +--R (1664a b - 4160a b + 3120a b )x +--R + +--R 2 6 3 5 4 4 8 +--R (7296a b - 18240a b + 13680a b )x +--R + +--R 3 5 4 4 5 3 6 +--R (15232a b - 38080a b + 28560a b )x +--R + +--R 4 4 5 3 6 2 4 +--R (16640a b - 41600a b + 31200a b )x +--R + +--R 5 3 6 2 7 2 6 2 7 8 +--R (9216a b - 23040a b + 17280a b)x + 2048a b - 5120a b + 3840a +--R * +--R +-+ +-----+ +--R \|a \|b - a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R atanh(-----------) +--R +-------+ +--R \|- b + a +--R + +--R 8 7 2 6 12 7 2 6 3 5 10 +--R (8b - 20a b + 15a b )x + (272a b - 680a b + 510a b )x +--R + +--R 2 6 3 5 4 4 8 +--R (1800a b - 4500a b + 3375a b )x +--R + +--R 3 5 4 4 5 3 6 +--R (4864a b - 12160a b + 9120a b )x +--R + +--R 4 4 5 3 6 2 4 +--R (6400a b - 16000a b + 12000a b )x +--R + +--R 5 3 6 2 7 2 6 2 7 8 +--R (4096a b - 10240a b + 7680a b)x + 1024a b - 2560a b + 1920a +--R * +--R +--------+ +--R +-------+ | 2 +--R \|- b + a \|b x + a +--R + +--R 8 7 2 6 12 +--R (- 64b + 160a b - 120a b )x +--R + +--R 7 2 6 3 5 10 +--R (- 832a b + 2080a b - 1560a b )x +--R + +--R 2 6 3 5 4 4 8 +--R (- 3648a b + 9120a b - 6840a b )x +--R + +--R 3 5 4 4 5 3 6 +--R (- 7616a b + 19040a b - 14280a b )x +--R + +--R 4 4 5 3 6 2 4 +--R (- 8320a b + 20800a b - 15600a b )x +--R + +--R 5 3 6 2 7 2 6 2 7 8 +--R (- 4608a b + 11520a b - 8640a b)x - 1024a b + 2560a b - 1920a +--R * +--R +-------+ +-+ +--R \|- b + a \|a +--R * +--R +--------+ +--R 2 +-----+ | 2 4 2 +-+ +-----+ +--R 2x \|b - a \|b x + a + (- 2x - 2x )\|a \|b - a +--R atan(---------------------------------------------------------) +--R +--------+ +--R 2 +-+ | 2 4 2 +--R (2x + 2)\|a \|b x + a + (b - 2a)x + (- b - 2a)x - 2a +--R + +--R 7 6 2 5 11 +--R (128b - 256a b + 128a b )x +--R + +--R 6 2 5 3 4 9 +--R (1600a b - 3200a b + 1600a b )x +--R + +--R 2 5 3 4 4 3 7 +--R (6512a b - 13024a b + 6512a b )x +--R + +--R 3 4 4 3 5 2 5 +--R (12128a b - 24256a b + 12128a b )x +--R + +--R 4 3 5 2 6 3 +--R (10880a b - 21760a b + 10880a b)x +--R + +--R 5 2 6 7 +--R (3840a b - 7680a b + 3840a )x +--R * +--R atan(x) +--R + +--R 7 6 2 5 11 6 2 5 3 4 9 +--R (64b - 128a b + 64a b )x + (800a b - 1600a b + 800a b )x +--R + +--R 2 5 3 4 4 3 7 +--R (3256a b - 6512a b + 3256a b )x +--R + +--R 3 4 4 3 5 2 5 +--R (6064a b - 12128a b + 6064a b )x +--R + +--R 4 3 5 2 6 3 5 2 6 7 +--R (5440a b - 10880a b + 5440a b)x + (1920a b - 3840a b + 1920a )x +--R * +--R 2x +--R atan(------) +--R 2 +--R x - 1 +--R + +--R 7 6 12 6 2 5 10 2 5 3 4 8 +--R (10b - 16a b )x + (340a b - 544a b )x + (2250a b - 3600a b )x +--R + +--R 3 4 4 3 6 4 3 5 2 4 +--R (6080a b - 9728a b )x + (8000a b - 12800a b )x +--R + +--R 5 2 6 2 6 7 +--R (5120a b - 8192a b)x + 1280a b - 2048a +--R * +--R +--------+ +--R +-------+ +-+ +-----+ | 2 +--R \|- b + a \|a \|b - a \|b x + a +--R + +--R 8 7 2 6 13 +--R (- 16b + 32a b - 16a b )x +--R + +--R 7 2 6 3 5 11 +--R (- 552a b + 1104a b - 552a b )x +--R + +--R 2 6 3 5 4 4 9 +--R (- 3870a b + 7740a b - 3870a b )x +--R + +--R 3 5 4 4 5 3 7 +--R (- 11456a b + 22912a b - 11456a b )x +--R + +--R 4 4 5 3 6 2 5 +--R (- 17088a b + 34176a b - 17088a b )x +--R + +--R 5 3 6 2 7 3 +--R (- 12800a b + 25600a b - 12800a b)x +--R + +--R 6 2 7 8 +--R (- 3840a b + 7680a b - 3840a )x +--R * +--R atan(x) +--R + +--R 8 7 2 6 13 7 2 6 3 5 11 +--R (- 8b + 16a b - 8a b )x + (- 276a b + 552a b - 276a b )x +--R + +--R 2 6 3 5 4 4 9 +--R (- 1935a b + 3870a b - 1935a b )x +--R + +--R 3 5 4 4 5 3 7 +--R (- 5728a b + 11456a b - 5728a b )x +--R + +--R 4 4 5 3 6 2 5 +--R (- 8544a b + 17088a b - 8544a b )x +--R + +--R 5 3 6 2 7 3 +--R (- 6400a b + 12800a b - 6400a b)x +--R + +--R 6 2 7 8 +--R (- 1920a b + 3840a b - 1920a )x +--R * +--R 2x +--R atan(------) +--R 2 +--R x - 1 +--R + +--R 7 2 6 12 2 6 3 5 10 +--R (- 80a b + 128a b )x + (- 1040a b + 1664a b )x +--R + +--R 3 5 4 4 8 4 4 5 3 6 +--R (- 4560a b + 7296a b )x + (- 9520a b + 15232a b )x +--R + +--R 5 3 6 2 4 6 2 7 2 7 +--R (- 10400a b + 16640a b )x + (- 5760a b + 9216a b)x - 1280a b +--R + +--R 8 +--R 2048a +--R * +--R +-------+ +-----+ +--R \|- b + a \|b - a +--R / +--R 3 8 4 7 5 6 12 4 7 5 6 6 5 10 +--R (30a b - 60a b + 30a b )x + (1020a b - 2040a b + 1020a b )x +--R + +--R 5 6 6 5 7 4 8 +--R (6750a b - 13500a b + 6750a b )x +--R + +--R 6 5 7 4 8 3 6 +--R (18240a b - 36480a b + 18240a b )x +--R + +--R 7 4 8 3 9 2 4 +--R (24000a b - 48000a b + 24000a b )x +--R + +--R 8 3 9 2 10 2 9 2 10 11 +--R (15360a b - 30720a b + 15360a b)x + 3840a b - 7680a b + 3840a +--R * +--R +--------+ +--R +-------+ +-----+ | 2 +--R \|- b + a \|b - a \|b x + a +--R + +--R 3 8 4 7 5 6 12 +--R (- 240a b + 480a b - 240a b )x +--R + +--R 4 7 5 6 6 5 10 +--R (- 3120a b + 6240a b - 3120a b )x +--R + +--R 5 6 6 5 7 4 8 +--R (- 13680a b + 27360a b - 13680a b )x +--R + +--R 6 5 7 4 8 3 6 +--R (- 28560a b + 57120a b - 28560a b )x +--R + +--R 7 4 8 3 9 2 4 +--R (- 31200a b + 62400a b - 31200a b )x +--R + +--R 8 3 9 2 10 2 9 2 10 11 +--R (- 17280a b + 34560a b - 17280a b)x - 3840a b + 7680a b - 3840a +--R * +--R +-------+ +-+ +-----+ +--R \|- b + a \|a \|b - a +--R Type: Expression Integer +--E 45 + +--S 46 of 477 +d0007b:= D(m0007b,x) +--R +--R +--R 2x +--R - 2atan(x) - atan(------) +--R 2 +--R x - 1 +--R (31) -------------------------------------------- +--R +--------+ +--R 3 6 2 4 2 2 3 | 2 +--R (2b x + 6a b x + 6a b x + 2a )\|b x + a +--R Type: Expression Integer +--E 46 + +--S 47 of 477 +t0008:= atan(x)*(a+a*x^2)^(1/2) +--R +--R +--R +--------+ +--R | 2 +--R (32) atan(x)\|a x + a +--R Type: Expression Integer +--E 47 + +--S 48 of 477 +r0008:= -1/2/(1+x^2)^(1/2)*(a*(1+x^2))^(1/2)*((1+x^2)^(1/2)-_ + x*(1+x^2)^(1/2)*atan(x)+2*%i*atan(exp(1)^(%i*atan(x)))*_ + atan(x)-%i*polylog(2,-%i*exp(1)^(%i*atan(x)))+_ + %i*polylog(2,%i*exp(1)^(%i*atan(x)))) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Complex Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 48 + +--S 49 of 477 +a0008:= integrate(t0008,x) +--R +--R +--R x +----------+ +--R ++ | 2 +--R (33) | atan(%Q)\|(%Q + 1)a d%Q +--R ++ +--R Type: Union(Expression Integer,...) +--E 49 + +--S 50 of 477 +--m0008:= a0008-r0008 +--E 50 + +--S 51 of 477 +--d0008:= D(m0008,x) +--E 51 + +--S 52 of 477 +t0009:= atan(x)/(a+a*x^2)^(1/2) +--R +--R +--R atan(x) +--R (34) ----------- +--R +--------+ +--R | 2 +--R \|a x + a +--R Type: Expression Integer +--E 52 + +--S 53 of 477 +r0009:= -%i*(1+x^2)^(1/2)*(2*atan(exp(1)^(%i*atan(x)))*atan(x)-_ + polylog(2,-%i*exp(1)^(%i*atan(x)))+_ + polylog(2,%i*exp(1)^(%i*atan(x))))/(a*(1+x^2))^(1/2) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Complex Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 53 + +--S 54 of 477 +a0009:= integrate(t0009,x) +--R +--R +--R x +--R ++ atan(%Q) +--R (35) | ------------- d%Q +--R ++ +----------+ +--R | 2 +--R \|(%Q + 1)a +--R Type: Union(Expression Integer,...) +--E 54 + +--S 55 of 477 +--m0009:= a0009-r0009 +--E 55 + +--S 56 of 477 +--d0009:= D(m0009,x) +--E 56 + +--S 57 of 477 +t0010:= atan(x)/(a+a*x^2)^(3/2) +--R +--R +--R atan(x) +--R (36) --------------------- +--R +--------+ +--R 2 | 2 +--R (a x + a)\|a x + a +--R Type: Expression Integer +--E 57 + +--S 58 of 477 +r0010:= (1+atan(x)*x)/a/(a*(1+x^2))^(1/2) +--R +--R +--R x atan(x) + 1 +--R (37) ------------- +--R +--------+ +--R | 2 +--R a\|a x + a +--R Type: Expression Integer +--E 58 + +--S 59 of 477 +a0010:= integrate(t0010,x) +--R +--R +--R +--------+ +--R 2x | 2 2x 2 +-+ +--R x atan(------)\|a x + a + (- x atan(------) - 2x )\|a +--R 2 2 +--R x - 1 x - 1 +--R (38) -------------------------------------------------------- +--R +--------+ +--R +-+ | 2 2 2 2 +--R 2a\|a \|a x + a - 2a x - 2a +--R Type: Union(Expression Integer,...) +--E 59 + +--S 60 of 477 +m0010:= a0010-r0010 +--R +--R +--R (39) +--R +--------+ +--R 2x 2 +-+ | 2 +--R (2x atan(x) + x atan(------) + 2x + 2)\|a \|a x + a +--R 2 +--R x - 1 +--R + +--R 3 3 2x 2 +--R (- 2a x - 2a x)atan(x) + (- a x - a x)atan(------) - 2a x - 2a +--R 2 +--R x - 1 +--R / +--R +--------+ +--R 2 2 2 | 2 2 2 2 +-+ +--R (2a x + 2a )\|a x + a + (- 2a x - 2a )\|a +--R Type: Expression Integer +--E 60 + +--S 61 of 477 +d0010:= D(m0010,x) +--R +--R +--R 2x +--R - 2atan(x) - atan(------) +--R 2 +--R x - 1 +--R (40) ------------------------- +--R +--------+ +--R 2 | 2 +--R (2a x + 2a)\|a x + a +--R Type: Expression Integer +--E 61 + +--S 62 of 477 +t0011:= atan(x)/(a+a*x^2)^(5/2) +--R +--R +--R atan(x) +--R (41) ------------------------------ +--R +--------+ +--R 2 4 2 2 2 | 2 +--R (a x + 2a x + a )\|a x + a +--R Type: Expression Integer +--E 62 + +--S 63 of 477 +r0011:= 1/9*(6+1/(1+x^2)+6*atan(x)*x+3*x*atan(x)/(1+x^2))/a^2/(a*(1+x^2))^(1/2) +--R +--R +--R 3 2 +--R (6x + 9x)atan(x) + 6x + 7 +--R (42) --------------------------- +--R +--------+ +--R 2 2 2 | 2 +--R (9a x + 9a )\|a x + a +--R Type: Expression Integer +--E 63 + +--S 64 of 477 +a0011:= integrate(t0011,x) +--R +--R +--R (43) +--R +--------+ +--R 5 3 2x 4 2 | 2 +--R ((6x + 33x + 36x)atan(------) + 30x + 36x )\|a x + a +--R 2 +--R x - 1 +--R + +--R 5 3 2x 6 4 2 +-+ +--R ((- 18x - 51x - 36x)atan(------) - 14x - 48x - 36x )\|a +--R 2 +--R x - 1 +--R / +--R +--------+ +--R 2 4 2 2 2 +-+ | 2 3 6 3 4 3 2 +--R (54a x + 126a x + 72a )\|a \|a x + a - 18a x - 108a x - 162a x +--R + +--R 3 +--R - 72a +--R Type: Union(Expression Integer,...) +--E 64 + +--S 65 of 477 +m0011:= a0011-r0011 +--R +--R +--R (44) +--R 5 3 5 3 2x 6 +--R (36x + 102x + 72x)atan(x) + (18x + 51x + 36x)atan(------) + 14x +--R 2 +--R x - 1 +--R + +--R 4 2 +--R 84x + 126x + 56 +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|a x + a +--R + +--R 7 5 3 +--R (- 12a x - 78a x - 138a x - 72a x)atan(x) +--R + +--R 7 5 3 2x 6 4 +--R (- 6a x - 39a x - 69a x - 36a x)atan(------) - 42a x - 140a x +--R 2 +--R x - 1 +--R + +--R 2 +--R - 154a x - 56a +--R / +--R +--------+ +--R 3 6 3 4 3 2 3 | 2 +--R (18a x + 108a x + 162a x + 72a )\|a x + a +--R + +--R 3 6 3 4 3 2 3 +-+ +--R (- 54a x - 180a x - 198a x - 72a )\|a +--R Type: Expression Integer +--E 65 + +--S 66 of 477 +d0011:= D(m0011,x) +--R +--R +--R 2x +--R - 2atan(x) - atan(------) +--R 2 +--R x - 1 +--R (45) -------------------------------- +--R +--------+ +--R 2 4 2 2 2 | 2 +--R (2a x + 4a x + 2a )\|a x + a +--R Type: Expression Integer +--E 66 + +--S 67 of 477 +t0012:= atan(x)/(a+a*x^2)^(7/2) +--R +--R +--R atan(x) +--R (46) -------------------------------------- +--R +--------+ +--R 3 6 3 4 3 2 3 | 2 +--R (a x + 3a x + 3a x + a )\|a x + a +--R Type: Expression Integer +--E 67 + +--S 68 of 477 +r0012:= 1/225*(149+120*x^4+260*x^2+225*atan(x)*x+120*atan(x)*x^5+_ + 300*atan(x)*x^3)/(1+x^2)^2/a^3/(a*(1+x^2))^(1/2) +--R +--R +--R 5 3 4 2 +--R (120x + 300x + 225x)atan(x) + 120x + 260x + 149 +--R (47) --------------------------------------------------- +--R +--------+ +--R 3 4 3 2 3 | 2 +--R (225a x + 450a x + 225a )\|a x + a +--R Type: Expression Integer +--E 68 + +--S 69 of 477 +a0012:= integrate(t0012,x) +--R +--R +--R (48) +--R 9 7 5 3 2x 8 +--R (120x + 1740x + 5745x + 7500x + 3600x)atan(------) + 1250x +--R 2 +--R x - 1 +--R + +--R 6 4 2 +--R 5540x + 7800x + 3600x +--R * +--R +--------+ +--R | 2 +--R \|a x + a +--R + +--R 9 7 5 3 2x 10 +--R (- 600x - 3900x - 9045x - 9300x - 3600x)atan(------) - 298x +--R 2 +--R x - 1 +--R + +--R 8 6 4 2 +--R - 3270x - 8990x - 9600x - 3600x +--R * +--R +-+ +--R \|a +--R / +--R +--------+ +--R 3 8 3 6 3 4 3 2 3 +-+ | 2 +--R (2250a x + 13500a x + 27450a x + 23400a x + 7200a )\|a \|a x + a +--R + +--R 4 10 4 8 4 6 4 4 4 2 4 +--R - 450a x - 6750a x - 24750a x - 38250a x - 27000a x - 7200a +--R Type: Union(Expression Integer,...) +--E 69 + +--S 70 of 477 +m0012:= a0012-r0012 +--R +--R +--R (49) +--R 9 7 5 3 +--R (1200x + 7800x + 18090x + 18600x + 7200x)atan(x) +--R + +--R 9 7 5 3 2x 10 +--R (600x + 3900x + 9045x + 9300x + 3600x)atan(------) + 298x +--R 2 +--R x - 1 +--R + +--R 8 6 4 2 +--R 4470x + 16390x + 25330x + 17880x + 4768 +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|a x + a +--R + +--R 11 9 7 5 3 +--R (- 240a x - 3720a x - 14970a x - 26490a x - 22200a x - 7200a x) +--R * +--R atan(x) +--R + +--R 11 9 7 5 3 +--R (- 120a x - 1860a x - 7485a x - 13245a x - 11100a x - 3600a x) +--R * +--R 2x +--R atan(------) +--R 2 +--R x - 1 +--R + +--R 10 8 6 4 2 +--R - 1490a x - 10430a x - 27118a x - 33674a x - 20264a x - 4768a +--R / +--R 4 10 4 8 4 6 4 4 4 2 4 +--R (450a x + 6750a x + 24750a x + 38250a x + 27000a x + 7200a ) +--R * +--R +--------+ +--R | 2 +--R \|a x + a +--R + +--R 4 10 4 8 4 6 4 4 4 2 4 +-+ +--R (- 2250a x - 15750a x - 40950a x - 50850a x - 30600a x - 7200a )\|a +--R Type: Expression Integer +--E 70 + +--S 71 of 477 +d0012:= D(m0012,x) +--R +--R +--R 2x +--R - 2atan(x) - atan(------) +--R 2 +--R x - 1 +--R (50) ---------------------------------------- +--R +--------+ +--R 3 6 3 4 3 2 3 | 2 +--R (2a x + 6a x + 6a x + 2a )\|a x + a +--R Type: Expression Integer +--E 71 + +--S 72 of 477 +t0013:= atan(x^(1/2))/x +--R +--R +--R +-+ +--R atan(\|x ) +--R (51) ---------- +--R x +--R Type: Expression Integer +--E 72 + +--S 73 of 477 +r0013:= %i*polylog(2,-%i*x^(1/2))-%i*polylog(2,%i*x^(1/2)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Complex Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 73 + +--S 74 of 477 +a0013:= integrate(t0013,x) +--R +--R +--R x +--+ +--R ++ atan(\|%Q ) +--R (52) | ----------- d%Q +--R ++ %Q +--R Type: Union(Expression Integer,...) +--E 74 + +--S 75 of 477 +--m0013:= a0013-r0013 +--E 75 + +--S 76 of 477 +--d0013:= D(m0013,x) +--E 76 + +--S 77 of 477 +t0014:= acot(a*x)/x +--R +--R +--R acot(a x) +--R (53) --------- +--R x +--R Type: Expression Integer +--E 77 + +--S 78 of 477 +r0014:= -1/2*%i*polylog(2,-%i/a/x)+1/2*%i*polylog(2,%i/a/x) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction Polynomial Complex Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 78 + +--S 79 of 477 +a0014:= integrate(t0014,x) +--R +--R +--R x +--R ++ acot(%Q a) +--R (54) | ---------- d%Q +--R ++ %Q +--R Type: Union(Expression Integer,...) +--E 79 + +--S 80 of 477 +--m0014:= a0014-r0014 +--E 80 + +--S 81 of 477 +--d0014:= D(m0014,x) +--E 81 + +--S 82 of 477 +t0015:= acot(1+x)/(2+2*x) +--R +--R +--R acot(x + 1) +--R (55) ----------- +--R 2x + 2 +--R Type: Expression Integer +--E 82 + +--S 83 of 477 +r0015:= -1/4*%i*polylog(2,-%i/(1+x))+1/4*%i*polylog(2,%i/(1+x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction Polynomial Complex Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 83 + +--S 84 of 477 +a0015:= integrate(t0015,x) +--R +--R +--R x +--R ++ acot(%Q + 1) +--R (56) | ------------ d%Q +--R ++ 2%Q + 2 +--R Type: Union(Expression Integer,...) +--E 84 + +--S 85 of 477 +--m0015:= a0015-r0015 +--E 85 + +--S 86 of 477 +--d0015:= D(m0015,x) +--E 86 + +--S 87 of 477 +t0016:= acot(a+b*x)/(a+b*x) +--R +--R +--R acot(b x + a) +--R (57) ------------- +--R b x + a +--R Type: Expression Integer +--E 87 + +--S 88 of 477 +r0016:= -1/2*%i*(polylog(2,-%i/(a+b*x))-polylog(2,%i/(a+b*x)))/b +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction Polynomial Complex Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 88 + +--S 89 of 477 +a0016:= integrate(t0016,x) +--R +--R +--R x +--R ++ acot(%Q b + a) +--R (58) | -------------- d%Q +--R ++ %Q b + a +--R Type: Union(Expression Integer,...) +--E 89 + +--S 90 of 477 +--m0016:= a0016-r0016 +--E 90 + +--S 91 of 477 +--d0016:= D(m0016,x) +--E 91 + +--S 92 of 477 +t0017:= acot(x)/(1+x^2)^2 +--R +--R +--R acot(x) +--R (59) ------------ +--R 4 2 +--R x + 2x + 1 +--R Type: Expression Integer +--E 92 + +--S 93 of 477 +r0017:= -1/(4+4*x^2)+x*acot(x)/(2+2*x^2)-1/4*acot(x)^2 +--R +--R +--R 2 2 +--R (- x - 1)acot(x) + 2x acot(x) - 1 +--R (60) ----------------------------------- +--R 2 +--R 4x + 4 +--R Type: Expression Integer +--E 93 + +--S 94 of 477 +a0017:= integrate(t0017,x) +--R +--R +--R 2 2x 2 2x +--R (- x - 1)atan(------) + 4x atan(------) - 4 +--R 2 2 +--R x - 1 x - 1 +--R (61) --------------------------------------------- +--R 2 +--R 16x + 16 +--R Type: Union(Expression Integer,...) +--E 94 + +--S 95 of 477 +m0017:= a0017-r0017 +--R +--R +--R (62) +--R 2 2x 2 2x 2 2 +--R (- x - 1)atan(------) + 4x atan(------) + (4x + 4)acot(x) - 8x acot(x) +--R 2 2 +--R x - 1 x - 1 +--R -------------------------------------------------------------------------- +--R 2 +--R 16x + 16 +--R Type: Expression Integer +--E 95 + +--S 96 of 477 +d0017:= D(m0017,x) +--R +--R +--R 2x +--R atan(------) - 2acot(x) +--R 2 +--R x - 1 +--R (63) ----------------------- +--R 4 2 +--R 2x + 4x + 2 +--R Type: Expression Integer +--E 96 + +--S 97 of 477 +t0018:= x*acot(x)/(1+x^2) +--R +--R +--R x acot(x) +--R (64) --------- +--R 2 +--R x + 1 +--R Type: Expression Integer +--E 97 + +--S 98 of 477 +r0018:= 1/2*%i*acot(x)^2-acot(x)*log(1-exp(1)^(2*%i*acot(x)))+_ + 1/2*%i*polylog(2,exp(1)^(2*%i*acot(x))) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Complex Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 98 + +--S 99 of 477 +a0018:= integrate(t0018,x) +--R +--R +--R x +--R ++ %Q acot(%Q) +--R (65) | ----------- d%Q +--R ++ 2 +--R %Q + 1 +--R Type: Union(Expression Integer,...) +--E 99 + +--S 100 of 477 +--m0018:= a0018-r0018 +--E 100 + +--S 101 of 477 +--d0018:= D(m0018,x) +--E 101 + +--S 102 of 477 +t0019:= acot(x)/(a+b*x^2)^(3/2) +--R +--R +--R acot(x) +--R (66) --------------------- +--R +--------+ +--R 2 | 2 +--R (b x + a)\|b x + a +--R Type: Expression Integer +--E 102 + +--S 103 of 477 +r0019:= x*acot(x)/a/(a+b*x^2)^(1/2)-atanh((a+b*x^2)^(1/2)/(a-b)^(1/2))/_ + a/(a-b)^(1/2) +--R +--R +--R +--------+ +--R +--------+ | 2 +--R | 2 \|b x + a +-------+ +--R - \|b x + a atanh(-----------) + x acot(x)\|- b + a +--R +-------+ +--R \|- b + a +--R (67) ----------------------------------------------------- +--R +--------+ +--R +-------+ | 2 +--R a\|- b + a \|b x + a +--R Type: Expression Integer +--E 103 + +--S 104 of 477 +a0019:= integrate(t0019,x) +--R +--R +--R (68) +--R [ +--R +--------+ +--R +-+ | 2 2 +--R (\|a \|b x + a - b x - a) +--R * +--R log +--R 2 2 4 2 2 +-+ +--R ((2b + 2a b - 4a )x + (8a b - 8a )x )\|a +--R + +--R 2 4 2 2 2 +-------+ +--R (4a x + (4a b + 8a )x + 8a )\|- b + a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 2 6 2 2 4 2 2 +--R (b - 2a b)x + (- b - 4a b - 4a )x + (- 8a b - 8a )x +--R + +--R 2 +--R - 8a +--R * +--R +-------+ +-+ +--R \|- b + a \|a +--R + +--R 2 2 6 2 2 3 4 2 3 2 +--R (- 2a b + 2a b)x + (- 6a b + 2a b + 4a )x + (- 8a b + 8a )x +--R / +--R +--------+ +--R 4 2 2 2 | 2 +--R (4a b x + (4a b + 8a )x + 8a )\|b x + a +--R + +--R 2 6 2 4 2 2 2 +-+ +--R (- b x + (- b - 8a b)x + (- 8a b - 8a )x - 8a )\|a +--R + +--R +--------+ +--R 2x +-------+ | 2 2x +-------+ +-+ +--R - x atan(------)\|- b + a \|b x + a + x atan(------)\|- b + a \|a +--R 2 2 +--R x - 1 x - 1 +--R / +--R +--------+ +--R +-------+ +-+ | 2 2 2 +-------+ +--R 2a\|- b + a \|a \|b x + a + (- 2a b x - 2a )\|- b + a +--R , +--R +--R +--------+ +--R +-+ | 2 2 +--R (- \|a \|b x + a + b x + a) +--R * +--R +--------+ +--R 2 +-----+ | 2 4 2 +-+ +-----+ +--R 2x \|b - a \|b x + a + (- 2x - 2x )\|a \|b - a +--R atan(---------------------------------------------------------) +--R +--------+ +--R 2 +-+ | 2 4 2 +--R (2x + 2)\|a \|b x + a + (b - 2a)x + (- b - 2a)x - 2a +--R + +--R +--------+ +--R 2x +-----+ | 2 2x +-+ +-----+ +--R - x atan(------)\|b - a \|b x + a + x atan(------)\|a \|b - a +--R 2 2 +--R x - 1 x - 1 +--R / +--R +--------+ +--R +-+ +-----+ | 2 2 2 +-----+ +--R 2a\|a \|b - a \|b x + a + (- 2a b x - 2a )\|b - a +--R ] +--R Type: Union(List Expression Integer,...) +--E 104 + +--S 105 of 477 +m0019a:= a0019.1-r0019 +--R +--R +--R (69) +--R +--------+ +--R 2 | 2 2 +-+ +--R ((b x + a)\|b x + a + (- b x - a)\|a ) +--R * +--R log +--R 2 2 4 2 2 +-+ +--R ((2b + 2a b - 4a )x + (8a b - 8a )x )\|a +--R + +--R 2 4 2 2 2 +-------+ +--R (4a x + (4a b + 8a )x + 8a )\|- b + a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 2 6 2 2 4 2 2 +--R (b - 2a b)x + (- b - 4a b - 4a )x + (- 8a b - 8a )x +--R + +--R 2 +--R - 8a +--R * +--R +-------+ +-+ +--R \|- b + a \|a +--R + +--R 2 2 6 2 2 3 4 2 3 2 +--R (- 2a b + 2a b)x + (- 6a b + 2a b + 4a )x + (- 8a b + 8a )x +--R / +--R +--------+ +--R 4 2 2 2 | 2 +--R (4a b x + (4a b + 8a )x + 8a )\|b x + a +--R + +--R 2 6 2 4 2 2 2 +-+ +--R (- b x + (- b - 8a b)x + (- 8a b - 8a )x - 8a )\|a +--R + +--R +--------+ +--R +--------+ | 2 +--R 2 | 2 2 +-+ \|b x + a +--R ((2b x + 2a)\|b x + a + (- 2b x - 2a)\|a )atanh(-----------) +--R +-------+ +--R \|- b + a +--R + +--R +--------+ +--R 2x +-------+ +-+ | 2 +--R (- x atan(------) + 2x acot(x))\|- b + a \|a \|b x + a +--R 2 +--R x - 1 +--R + +--R 3 2x 3 +-------+ +--R ((b x + a x)atan(------) + (- 2b x - 2a x)acot(x))\|- b + a +--R 2 +--R x - 1 +--R / +--R +--------+ +--R 2 2 +-------+ | 2 2 2 +-------+ +-+ +--R (2a b x + 2a )\|- b + a \|b x + a + (- 2a b x - 2a )\|- b + a \|a +--R Type: Expression Integer +--E 105 + +--S 106 of 477 +d0019a:= D(m0019a,x) +--R +--R +--R 2x +--R atan(------) - 2acot(x) +--R 2 +--R x - 1 +--R (70) ----------------------- +--R +--------+ +--R 2 | 2 +--R (2b x + 2a)\|b x + a +--R Type: Expression Integer +--E 106 + +--S 107 of 477 +m0019b:= a0019.2-r0019 +--R +--R +--R (71) +--R +--------+ +--R 2 +-----+ | 2 2 +-+ +-----+ +--R ((2b x + 2a)\|b - a \|b x + a + (- 2b x - 2a)\|a \|b - a ) +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R atanh(-----------) +--R +-------+ +--R \|- b + a +--R + +--R +--------+ +--R 2 +-------+ | 2 2 +-------+ +-+ +--R ((- b x - a)\|- b + a \|b x + a + (b x + a)\|- b + a \|a ) +--R * +--R +--------+ +--R 2 +-----+ | 2 4 2 +-+ +-----+ +--R 2x \|b - a \|b x + a + (- 2x - 2x )\|a \|b - a +--R atan(---------------------------------------------------------) +--R +--------+ +--R 2 +-+ | 2 4 2 +--R (2x + 2)\|a \|b x + a + (b - 2a)x + (- b - 2a)x - 2a +--R + +--R +--------+ +--R 2x +-------+ +-+ +-----+ | 2 +--R (- x atan(------) + 2x acot(x))\|- b + a \|a \|b - a \|b x + a +--R 2 +--R x - 1 +--R + +--R 3 2x 3 +-------+ +-----+ +--R ((b x + a x)atan(------) + (- 2b x - 2a x)acot(x))\|- b + a \|b - a +--R 2 +--R x - 1 +--R / +--R +--------+ +--R 2 2 +-------+ +-----+ | 2 +--R (2a b x + 2a )\|- b + a \|b - a \|b x + a +--R + +--R 2 2 +-------+ +-+ +-----+ +--R (- 2a b x - 2a )\|- b + a \|a \|b - a +--R Type: Expression Integer +--E 107 + +--S 108 of 477 +d0019b:= D(m0019b,x) +--R +--R +--R 2x +--R atan(------) - 2acot(x) +--R 2 +--R x - 1 +--R (72) ----------------------- +--R +--------+ +--R 2 | 2 +--R (2b x + 2a)\|b x + a +--R Type: Expression Integer +--E 108 + +--S 109 of 477 +t0020:= acot(x)/(a+b*x^2)^(5/2) +--R +--R +--R acot(x) +--R (73) -------------------------------- +--R +--------+ +--R 2 4 2 2 | 2 +--R (b x + 2a b x + a )\|b x + a +--R Type: Expression Integer +--E 109 + +--S 110 of 477 +r0020:= 1/3/a/(a-b)/(a+b*x^2)^(1/2)+1/3*x*(3*a+2*b*x^2)*_ + acot(x)/a^2/(a+b*x^2)^(3/2)-1/3*(3*a-2*b)*_ + atanh((a+b*x^2)^(1/2)/(a-b)^(1/2))/a^2/(a-b)^(3/2) +--R +--R +--R (74) +--R +--------+ +--R +--------+ | 2 +--R 2 2 2 | 2 \|b x + a +--R ((- 2b + 3a b)x - 2a b + 3a )\|b x + a atanh(-----------) +--R +-------+ +--R \|- b + a +--R + +--R 2 3 2 2 2 +-------+ +--R (((2b - 2a b)x + (3a b - 3a )x)acot(x) - a b x - a )\|- b + a +--R / +--R +--------+ +--R 2 2 3 2 3 4 +-------+ | 2 +--R ((3a b - 3a b)x + 3a b - 3a )\|- b + a \|b x + a +--R Type: Expression Integer +--E 110 + +--S 111 of 477 +a0020:= integrate(t0020,x) +--R +--R +--R (75) +--R [ +--R 4 3 6 3 2 2 4 2 2 3 2 +--R (8b - 12a b )x + (32a b - 48a b )x + (40a b - 60a b)x +--R + +--R 3 4 +--R 16a b - 24a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 5 4 8 4 2 3 6 2 3 3 2 4 +--R (- 2b + 3a b )x + (- 20a b + 30a b )x + (- 50a b + 75a b )x +--R + +--R 3 2 4 2 4 5 +--R (- 48a b + 72a b)x - 16a b + 24a +--R * +--R log +--R 2 2 4 2 2 +-+ +--R ((2b + 2a b - 4a )x + (8a b - 8a )x )\|a +--R + +--R 2 4 2 2 2 +-------+ +--R (4a x + (4a b + 8a )x + 8a )\|- b + a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 2 6 2 2 4 2 2 +--R (b - 2a b)x + (- b - 4a b - 4a )x + (- 8a b - 8a )x +--R + +--R 2 +--R - 8a +--R * +--R +-------+ +-+ +--R \|- b + a \|a +--R + +--R 2 2 6 2 2 3 4 2 3 2 +--R (- 2a b + 2a b)x + (- 6a b + 2a b + 4a )x + (- 8a b + 8a )x +--R / +--R +--------+ +--R 4 2 2 2 | 2 +--R (4a b x + (4a b + 8a )x + 8a )\|b x + a +--R + +--R 2 6 2 4 2 2 2 +-+ +--R (- b x + (- b - 8a b)x + (- 8a b - 8a )x - 8a )\|a +--R + +--R 4 3 7 3 2 2 5 +--R (- 2b + 2a b )x + (- 19a b + 19a b )x +--R + +--R 2 2 3 3 3 4 +--R (- 40a b + 40a b)x + (- 24a b + 24a )x +--R * +--R 2x +--R atan(------) +--R 2 +--R x - 1 +--R + +--R 3 6 2 2 4 3 2 +--R - 6a b x - 14a b x - 8a b x +--R * +--R +--------+ +--R +-------+ | 2 +--R \|- b + a \|b x + a +--R + +--R 4 3 7 3 2 2 5 2 2 3 3 +--R (8b - 8a b )x + (36a b - 36a b )x + (52a b - 52a b)x +--R + +--R 3 4 +--R (24a b - 24a )x +--R * +--R 2x +--R atan(------) +--R 2 +--R x - 1 +--R + +--R 4 8 3 6 2 2 4 3 2 +--R 2b x + 12a b x + 18a b x + 8a b x +--R * +--R +-------+ +-+ +--R \|- b + a \|a +--R / +--R 2 4 3 3 6 3 3 4 2 4 4 2 5 2 +--R (24a b - 24a b )x + (96a b - 96a b )x + (120a b - 120a b)x +--R + +--R 5 6 +--R 48a b - 48a +--R * +--R +--------+ +--R +-------+ +-+ | 2 +--R \|- b + a \|a \|b x + a +--R + +--R 2 5 3 4 8 3 4 4 3 6 +--R (- 6a b + 6a b )x + (- 60a b + 60a b )x +--R + +--R 4 3 5 2 4 5 2 6 2 6 7 +--R (- 150a b + 150a b )x + (- 144a b + 144a b)x - 48a b + 48a +--R * +--R +-------+ +--R \|- b + a +--R , +--R +--R 4 3 6 3 2 2 4 +--R (- 8b + 12a b )x + (- 32a b + 48a b )x +--R + +--R 2 2 3 2 3 4 +--R (- 40a b + 60a b)x - 16a b + 24a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 5 4 8 4 2 3 6 2 3 3 2 4 +--R (2b - 3a b )x + (20a b - 30a b )x + (50a b - 75a b )x +--R + +--R 3 2 4 2 4 5 +--R (48a b - 72a b)x + 16a b - 24a +--R * +--R +--------+ +--R 2 +-----+ | 2 4 2 +-+ +-----+ +--R 2x \|b - a \|b x + a + (- 2x - 2x )\|a \|b - a +--R atan(---------------------------------------------------------) +--R +--------+ +--R 2 +-+ | 2 4 2 +--R (2x + 2)\|a \|b x + a + (b - 2a)x + (- b - 2a)x - 2a +--R + +--R 4 3 7 3 2 2 5 +--R (- 2b + 2a b )x + (- 19a b + 19a b )x +--R + +--R 2 2 3 3 3 4 +--R (- 40a b + 40a b)x + (- 24a b + 24a )x +--R * +--R 2x +--R atan(------) +--R 2 +--R x - 1 +--R + +--R 3 6 2 2 4 3 2 +--R - 6a b x - 14a b x - 8a b x +--R * +--R +--------+ +--R +-----+ | 2 +--R \|b - a \|b x + a +--R + +--R 4 3 7 3 2 2 5 2 2 3 3 +--R (8b - 8a b )x + (36a b - 36a b )x + (52a b - 52a b)x +--R + +--R 3 4 +--R (24a b - 24a )x +--R * +--R 2x +--R atan(------) +--R 2 +--R x - 1 +--R + +--R 4 8 3 6 2 2 4 3 2 +--R 2b x + 12a b x + 18a b x + 8a b x +--R * +--R +-+ +-----+ +--R \|a \|b - a +--R / +--R 2 4 3 3 6 3 3 4 2 4 4 2 5 2 +--R (24a b - 24a b )x + (96a b - 96a b )x + (120a b - 120a b)x +--R + +--R 5 6 +--R 48a b - 48a +--R * +--R +--------+ +--R +-+ +-----+ | 2 +--R \|a \|b - a \|b x + a +--R + +--R 2 5 3 4 8 3 4 4 3 6 +--R (- 6a b + 6a b )x + (- 60a b + 60a b )x +--R + +--R 4 3 5 2 4 5 2 6 2 6 7 +--R (- 150a b + 150a b )x + (- 144a b + 144a b)x - 48a b + 48a +--R * +--R +-----+ +--R \|b - a +--R ] +--R Type: Union(List Expression Integer,...) +--E 111 + +--S 112 of 477 +m0020a:= a0020.1-r0020 +--R +--R +--R (76) +--R 4 3 6 3 2 2 4 2 2 3 2 +--R (2b - 3a b )x + (18a b - 27a b )x + (32a b - 48a b)x +--R + +--R 3 4 +--R 16a b - 24a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 4 3 6 3 2 2 4 2 2 3 2 +--R (- 8b + 12a b )x + (- 32a b + 48a b )x + (- 40a b + 60a b)x +--R + +--R 3 4 +--R - 16a b + 24a +--R * +--R +-+ +--R \|a +--R * +--R log +--R 2 2 4 2 2 +-+ +--R ((2b + 2a b - 4a )x + (8a b - 8a )x )\|a +--R + +--R 2 4 2 2 2 +-------+ +--R (4a x + (4a b + 8a )x + 8a )\|- b + a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 2 6 2 2 4 2 2 +--R (b - 2a b)x + (- b - 4a b - 4a )x + (- 8a b - 8a )x +--R + +--R 2 +--R - 8a +--R * +--R +-------+ +-+ +--R \|- b + a \|a +--R + +--R 2 2 6 2 2 3 4 2 3 2 +--R (- 2a b + 2a b)x + (- 6a b + 2a b + 4a )x + (- 8a b + 8a )x +--R / +--R +--------+ +--R 4 2 2 2 | 2 +--R (4a b x + (4a b + 8a )x + 8a )\|b x + a +--R + +--R 2 6 2 4 2 2 2 +-+ +--R (- b x + (- b - 8a b)x + (- 8a b - 8a )x - 8a )\|a +--R + +--R 4 3 6 3 2 2 4 2 2 3 2 +--R (4b - 6a b )x + (36a b - 54a b )x + (64a b - 96a b)x +--R + +--R 3 4 +--R 32a b - 48a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 4 3 6 3 2 2 4 +--R (- 16b + 24a b )x + (- 64a b + 96a b )x +--R + +--R 2 2 3 2 3 4 +--R (- 80a b + 120a b)x - 32a b + 48a +--R * +--R +-+ +--R \|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R atanh(-----------) +--R +-------+ +--R \|- b + a +--R + +--R 3 2 5 2 2 3 2 3 +--R ((- 8b + 8a b )x + (- 28a b + 28a b)x + (- 24a b + 24a )x) +--R * +--R 2x +--R atan(------) +--R 2 +--R x - 1 +--R + +--R 3 2 5 2 2 3 2 3 +--R ((16b - 16a b )x + (56a b - 56a b)x + (48a b - 48a )x)acot(x) +--R + +--R 3 6 2 4 2 2 3 +--R - 2b x - 18a b x - 32a b x - 16a +--R * +--R +--------+ +--R +-------+ +-+ | 2 +--R \|- b + a \|a \|b x + a +--R + +--R 4 3 7 3 2 2 5 2 2 3 3 +--R (2b - 2a b )x + (19a b - 19a b )x + (40a b - 40a b)x +--R + +--R 3 4 +--R (24a b - 24a )x +--R * +--R 2x +--R atan(------) +--R 2 +--R x - 1 +--R + +--R 4 3 7 3 2 2 5 2 2 3 3 +--R (- 4b + 4a b )x + (- 38a b + 38a b )x + (- 80a b + 80a b)x +--R + +--R 3 4 +--R (- 48a b + 48a )x +--R * +--R acot(x) +--R + +--R 3 6 2 2 4 3 2 4 +--R 8a b x + 32a b x + 40a b x + 16a +--R * +--R +-------+ +--R \|- b + a +--R / +--R 2 4 3 3 6 3 3 4 2 4 4 2 5 2 5 +--R (6a b - 6a b )x + (54a b - 54a b )x + (96a b - 96a b)x + 48a b +--R + +--R 6 +--R - 48a +--R * +--R +--------+ +--R +-------+ | 2 +--R \|- b + a \|b x + a +--R + +--R 2 4 3 3 6 3 3 4 2 4 +--R (- 24a b + 24a b )x + (- 96a b + 96a b )x +--R + +--R 4 2 5 2 5 6 +--R (- 120a b + 120a b)x - 48a b + 48a +--R * +--R +-------+ +-+ +--R \|- b + a \|a +--R Type: Expression Integer +--E 112 + +--S 113 of 477 +d0020a:= D(m0020a,x) +--R +--R +--R 2x +--R atan(------) - 2acot(x) +--R 2 +--R x - 1 +--R (77) ---------------------------------- +--R +--------+ +--R 2 4 2 2 | 2 +--R (2b x + 4a b x + 2a )\|b x + a +--R Type: Expression Integer +--E 113 + +--S 114 of 477 +m0020b:= a0020.2-r0020 +--R +--R +--R (78) +--R 4 3 6 3 2 2 4 2 2 3 2 +--R (4b - 6a b )x + (36a b - 54a b )x + (64a b - 96a b)x +--R + +--R 3 4 +--R 32a b - 48a +--R * +--R +--------+ +--R +-----+ | 2 +--R \|b - a \|b x + a +--R + +--R 4 3 6 3 2 2 4 +--R (- 16b + 24a b )x + (- 64a b + 96a b )x +--R + +--R 2 2 3 2 3 4 +--R (- 80a b + 120a b)x - 32a b + 48a +--R * +--R +-+ +-----+ +--R \|a \|b - a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R atanh(-----------) +--R +-------+ +--R \|- b + a +--R + +--R 4 3 6 3 2 2 4 2 2 3 2 +--R (- 2b + 3a b )x + (- 18a b + 27a b )x + (- 32a b + 48a b)x +--R + +--R 3 4 +--R - 16a b + 24a +--R * +--R +--------+ +--R +-------+ | 2 +--R \|- b + a \|b x + a +--R + +--R 4 3 6 3 2 2 4 2 2 3 2 +--R (8b - 12a b )x + (32a b - 48a b )x + (40a b - 60a b)x +--R + +--R 3 4 +--R 16a b - 24a +--R * +--R +-------+ +-+ +--R \|- b + a \|a +--R * +--R +--------+ +--R 2 +-----+ | 2 4 2 +-+ +-----+ +--R 2x \|b - a \|b x + a + (- 2x - 2x )\|a \|b - a +--R atan(---------------------------------------------------------) +--R +--------+ +--R 2 +-+ | 2 4 2 +--R (2x + 2)\|a \|b x + a + (b - 2a)x + (- b - 2a)x - 2a +--R + +--R 3 2 5 2 2 3 2 3 +--R ((- 8b + 8a b )x + (- 28a b + 28a b)x + (- 24a b + 24a )x) +--R * +--R 2x +--R atan(------) +--R 2 +--R x - 1 +--R + +--R 3 2 5 2 2 3 2 3 +--R ((16b - 16a b )x + (56a b - 56a b)x + (48a b - 48a )x)acot(x) +--R + +--R 3 6 2 4 2 2 3 +--R - 2b x - 18a b x - 32a b x - 16a +--R * +--R +--------+ +--R +-------+ +-+ +-----+ | 2 +--R \|- b + a \|a \|b - a \|b x + a +--R + +--R 4 3 7 3 2 2 5 2 2 3 3 +--R (2b - 2a b )x + (19a b - 19a b )x + (40a b - 40a b)x +--R + +--R 3 4 +--R (24a b - 24a )x +--R * +--R 2x +--R atan(------) +--R 2 +--R x - 1 +--R + +--R 4 3 7 3 2 2 5 2 2 3 3 +--R (- 4b + 4a b )x + (- 38a b + 38a b )x + (- 80a b + 80a b)x +--R + +--R 3 4 +--R (- 48a b + 48a )x +--R * +--R acot(x) +--R + +--R 3 6 2 2 4 3 2 4 +--R 8a b x + 32a b x + 40a b x + 16a +--R * +--R +-------+ +-----+ +--R \|- b + a \|b - a +--R / +--R 2 4 3 3 6 3 3 4 2 4 4 2 5 2 5 +--R (6a b - 6a b )x + (54a b - 54a b )x + (96a b - 96a b)x + 48a b +--R + +--R 6 +--R - 48a +--R * +--R +--------+ +--R +-------+ +-----+ | 2 +--R \|- b + a \|b - a \|b x + a +--R + +--R 2 4 3 3 6 3 3 4 2 4 +--R (- 24a b + 24a b )x + (- 96a b + 96a b )x +--R + +--R 4 2 5 2 5 6 +--R (- 120a b + 120a b)x - 48a b + 48a +--R * +--R +-------+ +-+ +-----+ +--R \|- b + a \|a \|b - a +--R Type: Expression Integer +--E 114 + +--S 115 of 477 +d0020b:= D(m0020b,x) +--R +--R +--R 2x +--R atan(------) - 2acot(x) +--R 2 +--R x - 1 +--R (79) ---------------------------------- +--R +--------+ +--R 2 4 2 2 | 2 +--R (2b x + 4a b x + 2a )\|b x + a +--R Type: Expression Integer +--E 115 + +--S 116 of 477 +t0021:= acot(x)/(a+b*x^2)^(7/2) +--R +--R +--R acot(x) +--R (80) ------------------------------------------ +--R +--------+ +--R 3 6 2 4 2 2 3 | 2 +--R (b x + 3a b x + 3a b x + a )\|b x + a +--R Type: Expression Integer +--E 116 + +--S 117 of 477 +r0021:= 1/15/a/(a-b)/(a+b*x^2)^(3/2)+1/15*(7*a-4*b)/a^2/(a-b)^2/_ + (a+b*x^2)^(1/2)+1/15*x*(8*(a+b*x^2)^2+a*(7*a+4*b*x^2))*_ + acot(x)/a^3/(a+b*x^2)^(5/2)-1/15*(15*a^2-20*a*b+8*b^2)*_ + atanh((a+b*x^2)^(1/2)/(a-b)^(1/2))/a^3/(a-b)^(5/2) +--R +--R +--R (81) +--R 4 3 2 2 4 3 2 2 3 2 2 2 +--R (- 8b + 20a b - 15a b )x + (- 16a b + 40a b - 30a b)x - 8a b +--R + +--R 3 4 +--R 20a b - 15a +--R * +--R +--------+ +--R +--------+ | 2 +--R | 2 \|b x + a +--R \|b x + a atanh(-----------) +--R +-------+ +--R \|- b + a +--R + +--R 4 3 2 2 5 3 2 2 3 3 +--R (8b - 16a b + 8a b )x + (20a b - 40a b + 20a b)x +--R + +--R 2 2 3 4 +--R (15a b - 30a b + 15a )x +--R * +--R acot(x) +--R + +--R 3 2 2 4 2 2 3 2 3 4 +--R (- 4a b + 7a b )x + (- 9a b + 15a b)x - 5a b + 8a +--R * +--R +-------+ +--R \|- b + a +--R / +--R 3 4 4 3 5 2 4 4 3 5 2 6 2 5 2 +--R (15a b - 30a b + 15a b )x + (30a b - 60a b + 30a b)x + 15a b +--R + +--R 6 7 +--R - 30a b + 15a +--R * +--R +--------+ +--R +-------+ | 2 +--R \|- b + a \|b x + a +--R Type: Expression Integer +--E 117 + +--S 118 of 477 +a0021:= integrate(t0021,x) +--R +--R +--R (82) +--R [ +--R 8 7 2 6 12 +--R (64b - 160a b + 120a b )x +--R + +--R 7 2 6 3 5 10 +--R (832a b - 2080a b + 1560a b )x +--R + +--R 2 6 3 5 4 4 8 +--R (3648a b - 9120a b + 6840a b )x +--R + +--R 3 5 4 4 5 3 6 +--R (7616a b - 19040a b + 14280a b )x +--R + +--R 4 4 5 3 6 2 4 +--R (8320a b - 20800a b + 15600a b )x +--R + +--R 5 3 6 2 7 2 6 2 7 8 +--R (4608a b - 11520a b + 8640a b)x + 1024a b - 2560a b + 1920a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 9 8 2 7 14 8 2 7 3 6 12 +--R (- 8b + 20a b - 15a b )x + (- 280a b + 700a b - 525a b )x +--R + +--R 2 7 3 6 4 5 10 +--R (- 2072a b + 5180a b - 3885a b )x +--R + +--R 3 6 4 5 5 4 8 +--R (- 6664a b + 16660a b - 12495a b )x +--R + +--R 4 5 5 4 6 3 6 +--R (- 11264a b + 28160a b - 21120a b )x +--R + +--R 5 4 6 3 7 2 4 +--R (- 10496a b + 26240a b - 19680a b )x +--R + +--R 6 3 7 2 8 2 7 2 8 9 +--R (- 5120a b + 12800a b - 9600a b)x - 1024a b + 2560a b - 1920a +--R * +--R log +--R 2 2 4 2 2 +-+ +--R ((2b + 2a b - 4a )x + (8a b - 8a )x )\|a +--R + +--R 2 4 2 2 2 +-------+ +--R (4a x + (4a b + 8a )x + 8a )\|- b + a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 2 6 2 2 4 2 2 +--R (b - 2a b)x + (- b - 4a b - 4a )x + (- 8a b - 8a )x +--R + +--R 2 +--R - 8a +--R * +--R +-------+ +-+ +--R \|- b + a \|a +--R + +--R 2 2 6 2 2 3 4 2 3 2 +--R (- 2a b + 2a b)x + (- 6a b + 2a b + 4a )x + (- 8a b + 8a )x +--R / +--R +--------+ +--R 4 2 2 2 | 2 +--R (4a b x + (4a b + 8a )x + 8a )\|b x + a +--R + +--R 2 6 2 4 2 2 2 +-+ +--R (- b x + (- b - 8a b)x + (- 8a b - 8a )x - 8a )\|a +--R + +--R 8 7 2 6 13 +--R (- 8b + 16a b - 8a b )x +--R + +--R 7 2 6 3 5 11 +--R (- 276a b + 552a b - 276a b )x +--R + +--R 2 6 3 5 4 4 9 +--R (- 1935a b + 3870a b - 1935a b )x +--R + +--R 3 5 4 4 5 3 7 +--R (- 5728a b + 11456a b - 5728a b )x +--R + +--R 4 4 5 3 6 2 5 +--R (- 8544a b + 17088a b - 8544a b )x +--R + +--R 5 3 6 2 7 3 +--R (- 6400a b + 12800a b - 6400a b)x +--R + +--R 6 2 7 8 +--R (- 1920a b + 3840a b - 1920a )x +--R * +--R 2x +--R atan(------) +--R 2 +--R x - 1 +--R + +--R 7 2 6 12 2 6 3 5 10 +--R (- 72a b + 114a b )x + (- 766a b + 1186a b )x +--R + +--R 3 5 4 4 8 4 4 5 3 6 +--R (- 2694a b + 4080a b )x + (- 4272a b + 6336a b )x +--R + +--R 5 3 6 2 4 6 2 7 2 +--R (- 3168a b + 4608a b )x + (- 896a b + 1280a b)x +--R * +--R +--------+ +--R +-------+ | 2 +--R \|- b + a \|b x + a +--R + +--R 8 7 2 6 13 +--R (64b - 128a b + 64a b )x +--R + +--R 7 2 6 3 5 11 +--R (864a b - 1728a b + 864a b )x +--R + +--R 2 6 3 5 4 4 9 +--R (4056a b - 8112a b + 4056a b )x +--R + +--R 3 5 4 4 5 3 7 +--R (9320a b - 18640a b + 9320a b )x +--R + +--R 4 4 5 3 6 2 5 +--R (11504a b - 23008a b + 11504a b )x +--R + +--R 5 3 6 2 7 3 +--R (7360a b - 14720a b + 7360a b)x +--R + +--R 6 2 7 8 +--R (1920a b - 3840a b + 1920a )x +--R * +--R 2x +--R atan(------) +--R 2 +--R x - 1 +--R + +--R 8 7 14 7 2 6 12 +--R (10b - 16a b )x + (286a b - 448a b )x +--R + +--R 2 6 3 5 10 3 5 4 4 8 +--R (1742a b - 2672a b )x + (4490a b - 6752a b )x +--R + +--R 4 4 5 3 6 5 3 6 2 4 +--R (5744a b - 8480a b )x + (3616a b - 5248a b )x +--R + +--R 6 2 7 2 +--R (896a b - 1280a b)x +--R * +--R +-------+ +-+ +--R \|- b + a \|a +--R / +--R 3 8 4 7 5 6 12 +--R (240a b - 480a b + 240a b )x +--R + +--R 4 7 5 6 6 5 10 +--R (3120a b - 6240a b + 3120a b )x +--R + +--R 5 6 6 5 7 4 8 +--R (13680a b - 27360a b + 13680a b )x +--R + +--R 6 5 7 4 8 3 6 +--R (28560a b - 57120a b + 28560a b )x +--R + +--R 7 4 8 3 9 2 4 +--R (31200a b - 62400a b + 31200a b )x +--R + +--R 8 3 9 2 10 2 9 2 10 11 +--R (17280a b - 34560a b + 17280a b)x + 3840a b - 7680a b + 3840a +--R * +--R +--------+ +--R +-------+ +-+ | 2 +--R \|- b + a \|a \|b x + a +--R + +--R 3 9 4 8 5 7 14 +--R (- 30a b + 60a b - 30a b )x +--R + +--R 4 8 5 7 6 6 12 +--R (- 1050a b + 2100a b - 1050a b )x +--R + +--R 5 7 6 6 7 5 10 +--R (- 7770a b + 15540a b - 7770a b )x +--R + +--R 6 6 7 5 8 4 8 +--R (- 24990a b + 49980a b - 24990a b )x +--R + +--R 7 5 8 4 9 3 6 +--R (- 42240a b + 84480a b - 42240a b )x +--R + +--R 8 4 9 3 10 2 4 +--R (- 39360a b + 78720a b - 39360a b )x +--R + +--R 9 3 10 2 11 2 10 2 11 +--R (- 19200a b + 38400a b - 19200a b)x - 3840a b + 7680a b +--R + +--R 12 +--R - 3840a +--R * +--R +-------+ +--R \|- b + a +--R , +--R +--R 8 7 2 6 12 +--R (- 64b + 160a b - 120a b )x +--R + +--R 7 2 6 3 5 10 +--R (- 832a b + 2080a b - 1560a b )x +--R + +--R 2 6 3 5 4 4 8 +--R (- 3648a b + 9120a b - 6840a b )x +--R + +--R 3 5 4 4 5 3 6 +--R (- 7616a b + 19040a b - 14280a b )x +--R + +--R 4 4 5 3 6 2 4 +--R (- 8320a b + 20800a b - 15600a b )x +--R + +--R 5 3 6 2 7 2 6 2 7 +--R (- 4608a b + 11520a b - 8640a b)x - 1024a b + 2560a b +--R + +--R 8 +--R - 1920a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 9 8 2 7 14 8 2 7 3 6 12 +--R (8b - 20a b + 15a b )x + (280a b - 700a b + 525a b )x +--R + +--R 2 7 3 6 4 5 10 +--R (2072a b - 5180a b + 3885a b )x +--R + +--R 3 6 4 5 5 4 8 +--R (6664a b - 16660a b + 12495a b )x +--R + +--R 4 5 5 4 6 3 6 +--R (11264a b - 28160a b + 21120a b )x +--R + +--R 5 4 6 3 7 2 4 +--R (10496a b - 26240a b + 19680a b )x +--R + +--R 6 3 7 2 8 2 7 2 8 9 +--R (5120a b - 12800a b + 9600a b)x + 1024a b - 2560a b + 1920a +--R * +--R +--------+ +--R 2 +-----+ | 2 4 2 +-+ +-----+ +--R 2x \|b - a \|b x + a + (- 2x - 2x )\|a \|b - a +--R atan(---------------------------------------------------------) +--R +--------+ +--R 2 +-+ | 2 4 2 +--R (2x + 2)\|a \|b x + a + (b - 2a)x + (- b - 2a)x - 2a +--R + +--R 8 7 2 6 13 +--R (- 8b + 16a b - 8a b )x +--R + +--R 7 2 6 3 5 11 +--R (- 276a b + 552a b - 276a b )x +--R + +--R 2 6 3 5 4 4 9 +--R (- 1935a b + 3870a b - 1935a b )x +--R + +--R 3 5 4 4 5 3 7 +--R (- 5728a b + 11456a b - 5728a b )x +--R + +--R 4 4 5 3 6 2 5 +--R (- 8544a b + 17088a b - 8544a b )x +--R + +--R 5 3 6 2 7 3 +--R (- 6400a b + 12800a b - 6400a b)x +--R + +--R 6 2 7 8 +--R (- 1920a b + 3840a b - 1920a )x +--R * +--R 2x +--R atan(------) +--R 2 +--R x - 1 +--R + +--R 7 2 6 12 2 6 3 5 10 +--R (- 72a b + 114a b )x + (- 766a b + 1186a b )x +--R + +--R 3 5 4 4 8 4 4 5 3 6 +--R (- 2694a b + 4080a b )x + (- 4272a b + 6336a b )x +--R + +--R 5 3 6 2 4 6 2 7 2 +--R (- 3168a b + 4608a b )x + (- 896a b + 1280a b)x +--R * +--R +--------+ +--R +-----+ | 2 +--R \|b - a \|b x + a +--R + +--R 8 7 2 6 13 +--R (64b - 128a b + 64a b )x +--R + +--R 7 2 6 3 5 11 +--R (864a b - 1728a b + 864a b )x +--R + +--R 2 6 3 5 4 4 9 +--R (4056a b - 8112a b + 4056a b )x +--R + +--R 3 5 4 4 5 3 7 +--R (9320a b - 18640a b + 9320a b )x +--R + +--R 4 4 5 3 6 2 5 +--R (11504a b - 23008a b + 11504a b )x +--R + +--R 5 3 6 2 7 3 +--R (7360a b - 14720a b + 7360a b)x +--R + +--R 6 2 7 8 +--R (1920a b - 3840a b + 1920a )x +--R * +--R 2x +--R atan(------) +--R 2 +--R x - 1 +--R + +--R 8 7 14 7 2 6 12 +--R (10b - 16a b )x + (286a b - 448a b )x +--R + +--R 2 6 3 5 10 3 5 4 4 8 +--R (1742a b - 2672a b )x + (4490a b - 6752a b )x +--R + +--R 4 4 5 3 6 5 3 6 2 4 +--R (5744a b - 8480a b )x + (3616a b - 5248a b )x +--R + +--R 6 2 7 2 +--R (896a b - 1280a b)x +--R * +--R +-+ +-----+ +--R \|a \|b - a +--R / +--R 3 8 4 7 5 6 12 +--R (240a b - 480a b + 240a b )x +--R + +--R 4 7 5 6 6 5 10 +--R (3120a b - 6240a b + 3120a b )x +--R + +--R 5 6 6 5 7 4 8 +--R (13680a b - 27360a b + 13680a b )x +--R + +--R 6 5 7 4 8 3 6 +--R (28560a b - 57120a b + 28560a b )x +--R + +--R 7 4 8 3 9 2 4 +--R (31200a b - 62400a b + 31200a b )x +--R + +--R 8 3 9 2 10 2 9 2 10 11 +--R (17280a b - 34560a b + 17280a b)x + 3840a b - 7680a b + 3840a +--R * +--R +--------+ +--R +-+ +-----+ | 2 +--R \|a \|b - a \|b x + a +--R + +--R 3 9 4 8 5 7 14 +--R (- 30a b + 60a b - 30a b )x +--R + +--R 4 8 5 7 6 6 12 +--R (- 1050a b + 2100a b - 1050a b )x +--R + +--R 5 7 6 6 7 5 10 +--R (- 7770a b + 15540a b - 7770a b )x +--R + +--R 6 6 7 5 8 4 8 +--R (- 24990a b + 49980a b - 24990a b )x +--R + +--R 7 5 8 4 9 3 6 +--R (- 42240a b + 84480a b - 42240a b )x +--R + +--R 8 4 9 3 10 2 4 +--R (- 39360a b + 78720a b - 39360a b )x +--R + +--R 9 3 10 2 11 2 10 2 11 +--R (- 19200a b + 38400a b - 19200a b)x - 3840a b + 7680a b +--R + +--R 12 +--R - 3840a +--R * +--R +-----+ +--R \|b - a +--R ] +--R Type: Union(List Expression Integer,...) +--E 118 + +--S 119 of 477 +m0021a:= a0021.1-r0021 +--R +--R +--R (83) +--R 8 7 2 6 12 7 2 6 3 5 10 +--R (8b - 20a b + 15a b )x + (272a b - 680a b + 510a b )x +--R + +--R 2 6 3 5 4 4 8 +--R (1800a b - 4500a b + 3375a b )x +--R + +--R 3 5 4 4 5 3 6 +--R (4864a b - 12160a b + 9120a b )x +--R + +--R 4 4 5 3 6 2 4 +--R (6400a b - 16000a b + 12000a b )x +--R + +--R 5 3 6 2 7 2 6 2 7 8 +--R (4096a b - 10240a b + 7680a b)x + 1024a b - 2560a b + 1920a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 8 7 2 6 12 +--R (- 64b + 160a b - 120a b )x +--R + +--R 7 2 6 3 5 10 +--R (- 832a b + 2080a b - 1560a b )x +--R + +--R 2 6 3 5 4 4 8 +--R (- 3648a b + 9120a b - 6840a b )x +--R + +--R 3 5 4 4 5 3 6 +--R (- 7616a b + 19040a b - 14280a b )x +--R + +--R 4 4 5 3 6 2 4 +--R (- 8320a b + 20800a b - 15600a b )x +--R + +--R 5 3 6 2 7 2 6 2 7 8 +--R (- 4608a b + 11520a b - 8640a b)x - 1024a b + 2560a b - 1920a +--R * +--R +-+ +--R \|a +--R * +--R log +--R 2 2 4 2 2 +-+ +--R ((2b + 2a b - 4a )x + (8a b - 8a )x )\|a +--R + +--R 2 4 2 2 2 +-------+ +--R (4a x + (4a b + 8a )x + 8a )\|- b + a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 2 6 2 2 4 2 2 +--R (b - 2a b)x + (- b - 4a b - 4a )x + (- 8a b - 8a )x +--R + +--R 2 +--R - 8a +--R * +--R +-------+ +-+ +--R \|- b + a \|a +--R + +--R 2 2 6 2 2 3 4 2 3 2 +--R (- 2a b + 2a b)x + (- 6a b + 2a b + 4a )x + (- 8a b + 8a )x +--R / +--R +--------+ +--R 4 2 2 2 | 2 +--R (4a b x + (4a b + 8a )x + 8a )\|b x + a +--R + +--R 2 6 2 4 2 2 2 +-+ +--R (- b x + (- b - 8a b)x + (- 8a b - 8a )x - 8a )\|a +--R + +--R 8 7 2 6 12 7 2 6 3 5 10 +--R (16b - 40a b + 30a b )x + (544a b - 1360a b + 1020a b )x +--R + +--R 2 6 3 5 4 4 8 +--R (3600a b - 9000a b + 6750a b )x +--R + +--R 3 5 4 4 5 3 6 +--R (9728a b - 24320a b + 18240a b )x +--R + +--R 4 4 5 3 6 2 4 +--R (12800a b - 32000a b + 24000a b )x +--R + +--R 5 3 6 2 7 2 6 2 7 8 +--R (8192a b - 20480a b + 15360a b)x + 2048a b - 5120a b + 3840a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 8 7 2 6 12 +--R (- 128b + 320a b - 240a b )x +--R + +--R 7 2 6 3 5 10 +--R (- 1664a b + 4160a b - 3120a b )x +--R + +--R 2 6 3 5 4 4 8 +--R (- 7296a b + 18240a b - 13680a b )x +--R + +--R 3 5 4 4 5 3 6 +--R (- 15232a b + 38080a b - 28560a b )x +--R + +--R 4 4 5 3 6 2 4 +--R (- 16640a b + 41600a b - 31200a b )x +--R + +--R 5 3 6 2 7 2 6 2 7 8 +--R (- 9216a b + 23040a b - 17280a b)x - 2048a b + 5120a b - 3840a +--R * +--R +-+ +--R \|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R atanh(-----------) +--R +-------+ +--R \|- b + a +--R + +--R 7 6 2 5 11 +--R (- 64b + 128a b - 64a b )x +--R + +--R 6 2 5 3 4 9 +--R (- 800a b + 1600a b - 800a b )x +--R + +--R 2 5 3 4 4 3 7 +--R (- 3256a b + 6512a b - 3256a b )x +--R + +--R 3 4 4 3 5 2 5 +--R (- 6064a b + 12128a b - 6064a b )x +--R + +--R 4 3 5 2 6 3 +--R (- 5440a b + 10880a b - 5440a b)x +--R + +--R 5 2 6 7 +--R (- 1920a b + 3840a b - 1920a )x +--R * +--R 2x +--R atan(------) +--R 2 +--R x - 1 +--R + +--R 7 6 2 5 11 +--R (128b - 256a b + 128a b )x +--R + +--R 6 2 5 3 4 9 +--R (1600a b - 3200a b + 1600a b )x +--R + +--R 2 5 3 4 4 3 7 +--R (6512a b - 13024a b + 6512a b )x +--R + +--R 3 4 4 3 5 2 5 +--R (12128a b - 24256a b + 12128a b )x +--R + +--R 4 3 5 2 6 3 +--R (10880a b - 21760a b + 10880a b)x +--R + +--R 5 2 6 7 +--R (3840a b - 7680a b + 3840a )x +--R * +--R acot(x) +--R + +--R 7 6 12 6 2 5 10 +--R (- 10b + 16a b )x + (- 340a b + 544a b )x +--R + +--R 2 5 3 4 8 3 4 4 3 6 +--R (- 2250a b + 3600a b )x + (- 6080a b + 9728a b )x +--R + +--R 4 3 5 2 4 5 2 6 2 6 +--R (- 8000a b + 12800a b )x + (- 5120a b + 8192a b)x - 1280a b +--R + +--R 7 +--R 2048a +--R * +--R +--------+ +--R +-------+ +-+ | 2 +--R \|- b + a \|a \|b x + a +--R + +--R 8 7 2 6 13 7 2 6 3 5 11 +--R (8b - 16a b + 8a b )x + (276a b - 552a b + 276a b )x +--R + +--R 2 6 3 5 4 4 9 +--R (1935a b - 3870a b + 1935a b )x +--R + +--R 3 5 4 4 5 3 7 +--R (5728a b - 11456a b + 5728a b )x +--R + +--R 4 4 5 3 6 2 5 +--R (8544a b - 17088a b + 8544a b )x +--R + +--R 5 3 6 2 7 3 6 2 7 8 +--R (6400a b - 12800a b + 6400a b)x + (1920a b - 3840a b + 1920a )x +--R * +--R 2x +--R atan(------) +--R 2 +--R x - 1 +--R + +--R 8 7 2 6 13 +--R (- 16b + 32a b - 16a b )x +--R + +--R 7 2 6 3 5 11 +--R (- 552a b + 1104a b - 552a b )x +--R + +--R 2 6 3 5 4 4 9 +--R (- 3870a b + 7740a b - 3870a b )x +--R + +--R 3 5 4 4 5 3 7 +--R (- 11456a b + 22912a b - 11456a b )x +--R + +--R 4 4 5 3 6 2 5 +--R (- 17088a b + 34176a b - 17088a b )x +--R + +--R 5 3 6 2 7 3 +--R (- 12800a b + 25600a b - 12800a b)x +--R + +--R 6 2 7 8 +--R (- 3840a b + 7680a b - 3840a )x +--R * +--R acot(x) +--R + +--R 7 2 6 12 2 6 3 5 10 +--R (80a b - 128a b )x + (1040a b - 1664a b )x +--R + +--R 3 5 4 4 8 4 4 5 3 6 +--R (4560a b - 7296a b )x + (9520a b - 15232a b )x +--R + +--R 5 3 6 2 4 6 2 7 2 7 8 +--R (10400a b - 16640a b )x + (5760a b - 9216a b)x + 1280a b - 2048a +--R * +--R +-------+ +--R \|- b + a +--R / +--R 3 8 4 7 5 6 12 4 7 5 6 6 5 10 +--R (30a b - 60a b + 30a b )x + (1020a b - 2040a b + 1020a b )x +--R + +--R 5 6 6 5 7 4 8 +--R (6750a b - 13500a b + 6750a b )x +--R + +--R 6 5 7 4 8 3 6 +--R (18240a b - 36480a b + 18240a b )x +--R + +--R 7 4 8 3 9 2 4 +--R (24000a b - 48000a b + 24000a b )x +--R + +--R 8 3 9 2 10 2 9 2 10 11 +--R (15360a b - 30720a b + 15360a b)x + 3840a b - 7680a b + 3840a +--R * +--R +--------+ +--R +-------+ | 2 +--R \|- b + a \|b x + a +--R + +--R 3 8 4 7 5 6 12 +--R (- 240a b + 480a b - 240a b )x +--R + +--R 4 7 5 6 6 5 10 +--R (- 3120a b + 6240a b - 3120a b )x +--R + +--R 5 6 6 5 7 4 8 +--R (- 13680a b + 27360a b - 13680a b )x +--R + +--R 6 5 7 4 8 3 6 +--R (- 28560a b + 57120a b - 28560a b )x +--R + +--R 7 4 8 3 9 2 4 +--R (- 31200a b + 62400a b - 31200a b )x +--R + +--R 8 3 9 2 10 2 9 2 10 11 +--R (- 17280a b + 34560a b - 17280a b)x - 3840a b + 7680a b - 3840a +--R * +--R +-------+ +-+ +--R \|- b + a \|a +--R Type: Expression Integer +--E 119 + +--S 120 of 477 +d0021a:= D(m0021a,x) +--R +--R +--R 2x +--R atan(------) - 2acot(x) +--R 2 +--R x - 1 +--R (84) -------------------------------------------- +--R +--------+ +--R 3 6 2 4 2 2 3 | 2 +--R (2b x + 6a b x + 6a b x + 2a )\|b x + a +--R Type: Expression Integer +--E 120 + +--S 121 of 477 +m0021b:= a0021.2-r0021 +--R +--R +--R (85) +--R 8 7 2 6 12 7 2 6 3 5 10 +--R (16b - 40a b + 30a b )x + (544a b - 1360a b + 1020a b )x +--R + +--R 2 6 3 5 4 4 8 +--R (3600a b - 9000a b + 6750a b )x +--R + +--R 3 5 4 4 5 3 6 +--R (9728a b - 24320a b + 18240a b )x +--R + +--R 4 4 5 3 6 2 4 +--R (12800a b - 32000a b + 24000a b )x +--R + +--R 5 3 6 2 7 2 6 2 7 8 +--R (8192a b - 20480a b + 15360a b)x + 2048a b - 5120a b + 3840a +--R * +--R +--------+ +--R +-----+ | 2 +--R \|b - a \|b x + a +--R + +--R 8 7 2 6 12 +--R (- 128b + 320a b - 240a b )x +--R + +--R 7 2 6 3 5 10 +--R (- 1664a b + 4160a b - 3120a b )x +--R + +--R 2 6 3 5 4 4 8 +--R (- 7296a b + 18240a b - 13680a b )x +--R + +--R 3 5 4 4 5 3 6 +--R (- 15232a b + 38080a b - 28560a b )x +--R + +--R 4 4 5 3 6 2 4 +--R (- 16640a b + 41600a b - 31200a b )x +--R + +--R 5 3 6 2 7 2 6 2 7 8 +--R (- 9216a b + 23040a b - 17280a b)x - 2048a b + 5120a b - 3840a +--R * +--R +-+ +-----+ +--R \|a \|b - a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R atanh(-----------) +--R +-------+ +--R \|- b + a +--R + +--R 8 7 2 6 12 7 2 6 3 5 10 +--R (- 8b + 20a b - 15a b )x + (- 272a b + 680a b - 510a b )x +--R + +--R 2 6 3 5 4 4 8 +--R (- 1800a b + 4500a b - 3375a b )x +--R + +--R 3 5 4 4 5 3 6 +--R (- 4864a b + 12160a b - 9120a b )x +--R + +--R 4 4 5 3 6 2 4 +--R (- 6400a b + 16000a b - 12000a b )x +--R + +--R 5 3 6 2 7 2 6 2 7 8 +--R (- 4096a b + 10240a b - 7680a b)x - 1024a b + 2560a b - 1920a +--R * +--R +--------+ +--R +-------+ | 2 +--R \|- b + a \|b x + a +--R + +--R 8 7 2 6 12 +--R (64b - 160a b + 120a b )x +--R + +--R 7 2 6 3 5 10 +--R (832a b - 2080a b + 1560a b )x +--R + +--R 2 6 3 5 4 4 8 +--R (3648a b - 9120a b + 6840a b )x +--R + +--R 3 5 4 4 5 3 6 +--R (7616a b - 19040a b + 14280a b )x +--R + +--R 4 4 5 3 6 2 4 +--R (8320a b - 20800a b + 15600a b )x +--R + +--R 5 3 6 2 7 2 6 2 7 8 +--R (4608a b - 11520a b + 8640a b)x + 1024a b - 2560a b + 1920a +--R * +--R +-------+ +-+ +--R \|- b + a \|a +--R * +--R +--------+ +--R 2 +-----+ | 2 4 2 +-+ +-----+ +--R 2x \|b - a \|b x + a + (- 2x - 2x )\|a \|b - a +--R atan(---------------------------------------------------------) +--R +--------+ +--R 2 +-+ | 2 4 2 +--R (2x + 2)\|a \|b x + a + (b - 2a)x + (- b - 2a)x - 2a +--R + +--R 7 6 2 5 11 +--R (- 64b + 128a b - 64a b )x +--R + +--R 6 2 5 3 4 9 +--R (- 800a b + 1600a b - 800a b )x +--R + +--R 2 5 3 4 4 3 7 +--R (- 3256a b + 6512a b - 3256a b )x +--R + +--R 3 4 4 3 5 2 5 +--R (- 6064a b + 12128a b - 6064a b )x +--R + +--R 4 3 5 2 6 3 +--R (- 5440a b + 10880a b - 5440a b)x +--R + +--R 5 2 6 7 +--R (- 1920a b + 3840a b - 1920a )x +--R * +--R 2x +--R atan(------) +--R 2 +--R x - 1 +--R + +--R 7 6 2 5 11 +--R (128b - 256a b + 128a b )x +--R + +--R 6 2 5 3 4 9 +--R (1600a b - 3200a b + 1600a b )x +--R + +--R 2 5 3 4 4 3 7 +--R (6512a b - 13024a b + 6512a b )x +--R + +--R 3 4 4 3 5 2 5 +--R (12128a b - 24256a b + 12128a b )x +--R + +--R 4 3 5 2 6 3 +--R (10880a b - 21760a b + 10880a b)x +--R + +--R 5 2 6 7 +--R (3840a b - 7680a b + 3840a )x +--R * +--R acot(x) +--R + +--R 7 6 12 6 2 5 10 +--R (- 10b + 16a b )x + (- 340a b + 544a b )x +--R + +--R 2 5 3 4 8 3 4 4 3 6 +--R (- 2250a b + 3600a b )x + (- 6080a b + 9728a b )x +--R + +--R 4 3 5 2 4 5 2 6 2 6 +--R (- 8000a b + 12800a b )x + (- 5120a b + 8192a b)x - 1280a b +--R + +--R 7 +--R 2048a +--R * +--R +--------+ +--R +-------+ +-+ +-----+ | 2 +--R \|- b + a \|a \|b - a \|b x + a +--R + +--R 8 7 2 6 13 7 2 6 3 5 11 +--R (8b - 16a b + 8a b )x + (276a b - 552a b + 276a b )x +--R + +--R 2 6 3 5 4 4 9 +--R (1935a b - 3870a b + 1935a b )x +--R + +--R 3 5 4 4 5 3 7 +--R (5728a b - 11456a b + 5728a b )x +--R + +--R 4 4 5 3 6 2 5 +--R (8544a b - 17088a b + 8544a b )x +--R + +--R 5 3 6 2 7 3 6 2 7 8 +--R (6400a b - 12800a b + 6400a b)x + (1920a b - 3840a b + 1920a )x +--R * +--R 2x +--R atan(------) +--R 2 +--R x - 1 +--R + +--R 8 7 2 6 13 +--R (- 16b + 32a b - 16a b )x +--R + +--R 7 2 6 3 5 11 +--R (- 552a b + 1104a b - 552a b )x +--R + +--R 2 6 3 5 4 4 9 +--R (- 3870a b + 7740a b - 3870a b )x +--R + +--R 3 5 4 4 5 3 7 +--R (- 11456a b + 22912a b - 11456a b )x +--R + +--R 4 4 5 3 6 2 5 +--R (- 17088a b + 34176a b - 17088a b )x +--R + +--R 5 3 6 2 7 3 +--R (- 12800a b + 25600a b - 12800a b)x +--R + +--R 6 2 7 8 +--R (- 3840a b + 7680a b - 3840a )x +--R * +--R acot(x) +--R + +--R 7 2 6 12 2 6 3 5 10 +--R (80a b - 128a b )x + (1040a b - 1664a b )x +--R + +--R 3 5 4 4 8 4 4 5 3 6 +--R (4560a b - 7296a b )x + (9520a b - 15232a b )x +--R + +--R 5 3 6 2 4 6 2 7 2 7 8 +--R (10400a b - 16640a b )x + (5760a b - 9216a b)x + 1280a b - 2048a +--R * +--R +-------+ +-----+ +--R \|- b + a \|b - a +--R / +--R 3 8 4 7 5 6 12 4 7 5 6 6 5 10 +--R (30a b - 60a b + 30a b )x + (1020a b - 2040a b + 1020a b )x +--R + +--R 5 6 6 5 7 4 8 +--R (6750a b - 13500a b + 6750a b )x +--R + +--R 6 5 7 4 8 3 6 +--R (18240a b - 36480a b + 18240a b )x +--R + +--R 7 4 8 3 9 2 4 +--R (24000a b - 48000a b + 24000a b )x +--R + +--R 8 3 9 2 10 2 9 2 10 11 +--R (15360a b - 30720a b + 15360a b)x + 3840a b - 7680a b + 3840a +--R * +--R +--------+ +--R +-------+ +-----+ | 2 +--R \|- b + a \|b - a \|b x + a +--R + +--R 3 8 4 7 5 6 12 +--R (- 240a b + 480a b - 240a b )x +--R + +--R 4 7 5 6 6 5 10 +--R (- 3120a b + 6240a b - 3120a b )x +--R + +--R 5 6 6 5 7 4 8 +--R (- 13680a b + 27360a b - 13680a b )x +--R + +--R 6 5 7 4 8 3 6 +--R (- 28560a b + 57120a b - 28560a b )x +--R + +--R 7 4 8 3 9 2 4 +--R (- 31200a b + 62400a b - 31200a b )x +--R + +--R 8 3 9 2 10 2 9 2 10 11 +--R (- 17280a b + 34560a b - 17280a b)x - 3840a b + 7680a b - 3840a +--R * +--R +-------+ +-+ +-----+ +--R \|- b + a \|a \|b - a +--R Type: Expression Integer +--E 121 + +--S 122 of 477 +d0021b:= D(m0021b,x) +--R +--R +--R 2x +--R atan(------) - 2acot(x) +--R 2 +--R x - 1 +--R (86) -------------------------------------------- +--R +--------+ +--R 3 6 2 4 2 2 3 | 2 +--R (2b x + 6a b x + 6a b x + 2a )\|b x + a +--R Type: Expression Integer +--E 122 + +--S 123 of 477 +t0022:= acot(x)*(a+a*x^2)^(1/2) +--R +--R +--R +--------+ +--R | 2 +--R (87) acot(x)\|a x + a +--R Type: Expression Integer +--E 123 + +--S 124 of 477 +r0022:= 1/2/(1+1/x^2)^(1/2)/x*(a*(1+x^2))^(1/2)*((1+1/x^2)^(1/2)*x+_ + (1+1/x^2)^(1/2)*x^2*acot(x)+2*acot(x)*atanh(exp(1)^(%i*acot(x)))-_ + %i*polylog(2,-exp(1)^(%i*acot(x)))+%i*polylog(2,exp(1)^(%i*acot(x)))) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Complex Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 124 + +--S 125 of 477 +a0022:= integrate(t0022,x) +--R +--R +--R x +----------+ +--R ++ | 2 +--R (88) | acot(%Q)\|(%Q + 1)a d%Q +--R ++ +--R Type: Union(Expression Integer,...) +--E 125 + +--S 126 of 477 +--m0022:= a0022-r0022 +--E 126 + +--S 127 of 477 +--d0022:= D(m0022,x) +--E 127 + +--S 128 of 477 +t0023:= acot(x)/(a+a*x^2)^(1/2) +--R +--R +--R acot(x) +--R (89) ----------- +--R +--------+ +--R | 2 +--R \|a x + a +--R Type: Expression Integer +--E 128 + +--S 129 of 477 +r0023:= (1+1/x^2)^(1/2)*x*(2*acot(x)*atanh(exp(1)^(%i*acot(x)))-_ + %i*polylog(2,-exp(1)^(%i*acot(x)))+_ + %i*polylog(2,exp(1)^(%i*acot(x))))/(a*(1+x^2))^(1/2) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Complex Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 129 + +--S 130 of 477 +a0023:= integrate(t0023,x) +--R +--R +--R x +--R ++ acot(%Q) +--R (90) | ------------- d%Q +--R ++ +----------+ +--R | 2 +--R \|(%Q + 1)a +--R Type: Union(Expression Integer,...) +--E 130 + +--S 131 of 477 +--m0023:= a0023-r0023 +--E 131 + +--S 132 of 477 +--d0023:= D(m0023,x) +--E 132 + +--S 133 of 477 +t0024:= acot(x)/(a+a*x^2)^(3/2) +--R +--R +--R acot(x) +--R (91) --------------------- +--R +--------+ +--R 2 | 2 +--R (a x + a)\|a x + a +--R Type: Expression Integer +--E 133 + +--S 134 of 477 +r0024:= -(1-x*acot(x))/a/(a*(1+x^2))^(1/2) +--R +--R +--R x acot(x) - 1 +--R (92) ------------- +--R +--------+ +--R | 2 +--R a\|a x + a +--R Type: Expression Integer +--E 134 + +--S 135 of 477 +a0024:= integrate(t0024,x) +--R +--R +--R +--------+ +--R 2x | 2 2x 2 +-+ +--R - x atan(------)\|a x + a + (x atan(------) + 2x )\|a +--R 2 2 +--R x - 1 x - 1 +--R (93) -------------------------------------------------------- +--R +--------+ +--R +-+ | 2 2 2 2 +--R 2a\|a \|a x + a - 2a x - 2a +--R Type: Union(Expression Integer,...) +--E 135 + +--S 136 of 477 +m0024:= a0024-r0024 +--R +--R +--R (94) +--R +--------+ +--R 2x 2 +-+ | 2 +--R (- x atan(------) + 2x acot(x) - 2x - 2)\|a \|a x + a +--R 2 +--R x - 1 +--R + +--R 3 2x 3 2 +--R (a x + a x)atan(------) + (- 2a x - 2a x)acot(x) + 2a x + 2a +--R 2 +--R x - 1 +--R / +--R +--------+ +--R 2 2 2 | 2 2 2 2 +-+ +--R (2a x + 2a )\|a x + a + (- 2a x - 2a )\|a +--R Type: Expression Integer +--E 136 + +--S 137 of 477 +d0024:= D(m0024,x) +--R +--R +--R 2x +--R atan(------) - 2acot(x) +--R 2 +--R x - 1 +--R (95) ----------------------- +--R +--------+ +--R 2 | 2 +--R (2a x + 2a)\|a x + a +--R Type: Expression Integer +--E 137 + +--S 138 of 477 +t0025:= acot(x)/(a+a*x^2)^(5/2) +--R +--R +--R acot(x) +--R (96) ------------------------------ +--R +--------+ +--R 2 4 2 2 2 | 2 +--R (a x + 2a x + a )\|a x + a +--R Type: Expression Integer +--E 138 + +--S 139 of 477 +r0025:= -1/9*(6+1/(1+x^2)-3*x*(2+1/(1+x^2))*acot(x))/a^2/(a*(1+x^2))^(1/2) +--R +--R +--R 3 2 +--R (6x + 9x)acot(x) - 6x - 7 +--R (97) --------------------------- +--R +--------+ +--R 2 2 2 | 2 +--R (9a x + 9a )\|a x + a +--R Type: Expression Integer +--E 139 + +--S 140 of 477 +a0025:= integrate(t0025,x) +--R +--R +--R (98) +--R +--------+ +--R 5 3 2x 4 2 | 2 +--R ((- 6x - 33x - 36x)atan(------) - 30x - 36x )\|a x + a +--R 2 +--R x - 1 +--R + +--R 5 3 2x 6 4 2 +-+ +--R ((18x + 51x + 36x)atan(------) + 14x + 48x + 36x )\|a +--R 2 +--R x - 1 +--R / +--R +--------+ +--R 2 4 2 2 2 +-+ | 2 3 6 3 4 3 2 +--R (54a x + 126a x + 72a )\|a \|a x + a - 18a x - 108a x - 162a x +--R + +--R 3 +--R - 72a +--R Type: Union(Expression Integer,...) +--E 140 + +--S 141 of 477 +m0025:= a0025-r0025 +--R +--R +--R (99) +--R 5 3 2x 5 3 +--R (- 18x - 51x - 36x)atan(------) + (36x + 102x + 72x)acot(x) +--R 2 +--R x - 1 +--R + +--R 6 4 2 +--R - 14x - 84x - 126x - 56 +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|a x + a +--R + +--R 7 5 3 2x +--R (6a x + 39a x + 69a x + 36a x)atan(------) +--R 2 +--R x - 1 +--R + +--R 7 5 3 6 4 2 +--R (- 12a x - 78a x - 138a x - 72a x)acot(x) + 42a x + 140a x + 154a x +--R + +--R 56a +--R / +--R +--------+ +--R 3 6 3 4 3 2 3 | 2 +--R (18a x + 108a x + 162a x + 72a )\|a x + a +--R + +--R 3 6 3 4 3 2 3 +-+ +--R (- 54a x - 180a x - 198a x - 72a )\|a +--R Type: Expression Integer +--E 141 + +--S 142 of 477 +d0025:= D(m0025,x) +--R +--R +--R 2x +--R atan(------) - 2acot(x) +--R 2 +--R x - 1 +--R (100) -------------------------------- +--R +--------+ +--R 2 4 2 2 2 | 2 +--R (2a x + 4a x + 2a )\|a x + a +--R Type: Expression Integer +--E 142 + +--S 143 of 477 +t0026:= acot(x)/(a+a*x^2)^(7/2) +--R +--R +--R acot(x) +--R (101) -------------------------------------- +--R +--------+ +--R 3 6 3 4 3 2 3 | 2 +--R (a x + 3a x + 3a x + a )\|a x + a +--R Type: Expression Integer +--E 143 + +--S 144 of 477 +r0026:= -1/225*(120+9/(1+x^2)^2+20/(1+x^2)-15*x*(8+3/(1+x^2)^2+_ + 4/(1+x^2))*acot(x))/a^3/(a*(1+x^2))^(1/2) +--R +--R +--R 5 3 4 2 +--R (120x + 300x + 225x)acot(x) - 120x - 260x - 149 +--R (102) --------------------------------------------------- +--R +--------+ +--R 3 4 3 2 3 | 2 +--R (225a x + 450a x + 225a )\|a x + a +--R Type: Expression Integer +--E 144 + +--S 145 of 477 +a0026:= integrate(t0026,x) +--R +--R +--R (103) +--R 9 7 5 3 2x 8 +--R (- 120x - 1740x - 5745x - 7500x - 3600x)atan(------) - 1250x +--R 2 +--R x - 1 +--R + +--R 6 4 2 +--R - 5540x - 7800x - 3600x +--R * +--R +--------+ +--R | 2 +--R \|a x + a +--R + +--R 9 7 5 3 2x 10 +--R (600x + 3900x + 9045x + 9300x + 3600x)atan(------) + 298x +--R 2 +--R x - 1 +--R + +--R 8 6 4 2 +--R 3270x + 8990x + 9600x + 3600x +--R * +--R +-+ +--R \|a +--R / +--R +--------+ +--R 3 8 3 6 3 4 3 2 3 +-+ | 2 +--R (2250a x + 13500a x + 27450a x + 23400a x + 7200a )\|a \|a x + a +--R + +--R 4 10 4 8 4 6 4 4 4 2 4 +--R - 450a x - 6750a x - 24750a x - 38250a x - 27000a x - 7200a +--R Type: Union(Expression Integer,...) +--E 145 + +--S 146 of 477 +m0026:= a0026-r0026 +--R +--R +--R (104) +--R 9 7 5 3 2x +--R (- 600x - 3900x - 9045x - 9300x - 3600x)atan(------) +--R 2 +--R x - 1 +--R + +--R 9 7 5 3 10 +--R (1200x + 7800x + 18090x + 18600x + 7200x)acot(x) - 298x +--R + +--R 8 6 4 2 +--R - 4470x - 16390x - 25330x - 17880x - 4768 +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|a x + a +--R + +--R 11 9 7 5 3 +--R (120a x + 1860a x + 7485a x + 13245a x + 11100a x + 3600a x) +--R * +--R 2x +--R atan(------) +--R 2 +--R x - 1 +--R + +--R 11 9 7 5 3 +--R (- 240a x - 3720a x - 14970a x - 26490a x - 22200a x - 7200a x) +--R * +--R acot(x) +--R + +--R 10 8 6 4 2 +--R 1490a x + 10430a x + 27118a x + 33674a x + 20264a x + 4768a +--R / +--R 4 10 4 8 4 6 4 4 4 2 4 +--R (450a x + 6750a x + 24750a x + 38250a x + 27000a x + 7200a ) +--R * +--R +--------+ +--R | 2 +--R \|a x + a +--R + +--R 4 10 4 8 4 6 4 4 4 2 4 +-+ +--R (- 2250a x - 15750a x - 40950a x - 50850a x - 30600a x - 7200a )\|a +--R Type: Expression Integer +--E 146 + +--S 147 of 477 +d0026:= D(m0026,x) +--R +--R +--R 2x +--R atan(------) - 2acot(x) +--R 2 +--R x - 1 +--R (105) ---------------------------------------- +--R +--------+ +--R 3 6 3 4 3 2 3 | 2 +--R (2a x + 6a x + 6a x + 2a )\|a x + a +--R Type: Expression Integer +--E 147 + +--S 148 of 477 +t0027:= acot(x^(1/2))/x +--R +--R +--R +-+ +--R acot(\|x ) +--R (106) ---------- +--R x +--R Type: Expression Integer +--E 148 + +--S 149 of 477 +r0027:= -%i*polylog(2,-%i/x^(1/2))+%i*polylog(2,%i/x^(1/2)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Complex Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 149 + +--S 150 of 477 +a0027:= integrate(t0027,x) +--R +--R +--R x +--+ +--R ++ acot(\|%Q ) +--R (107) | ----------- d%Q +--R ++ %Q +--R Type: Union(Expression Integer,...) +--E 150 + +--S 151 of 477 +--m0027:= a0027-r0027 +--E 151 + +--S 152 of 477 +--d0027:= D(m0027,x) +--E 152 + +--S 153 of 477 +t0028:= x^2*asec(a*x) +--R +--R +--R 2 +--R (108) x asec(a x) +--R Type: Expression Integer +--E 153 + +--S 154 of 477 +r0028:= -1/6*(1-1/a^2/x^2)^(1/2)*x^2/a+1/3*x^3*asec(a*x)-_ + 1/6*atanh((1-1/a^2/x^2)^(1/2))/a^3 +--R +--R +--R +--------+ +--------+ +--R | 2 2 | 2 2 +--R |a x - 1 2 2 |a x - 1 3 3 +--R - atanh( |-------- ) - a x |-------- + 2a x asec(a x) +--R | 2 2 | 2 2 +--R \| a x \| a x +--R (109) ------------------------------------------------------- +--R 3 +--R 6a +--R Type: Expression Integer +--E 154 + +--S 155 of 477 +a0028:= integrate(t0028,x) +--R +--R +--R (110) +--R +----------+ +----------+ +--R +-+ | 2 2 | 2 2 +--R +-+ 2a x\|2 \|- a x + 1 3 3 2\|- a x + 1 +--R - 2\|2 atan(---------------------) + a x atan(--------------) +--R 2 2 2 2 +--R 3a x - 2 a x +--R + +--R +----------+ +--R a x | 2 2 +--R - 5atan(-------------) + a x\|- a x + 1 +--R +----------+ +--R | 2 2 +--R \|- a x + 1 +--R / +--R 3 +--R 6a +--R Type: Union(Expression Integer,...) +--E 155 + +--S 156 of 477 +m0028:= a0028-r0028 +--R +--R +--R (111) +--R +--------+ +----------+ +--R | 2 2 +-+ | 2 2 +--R |a x - 1 +-+ 2a x\|2 \|- a x + 1 +--R atanh( |-------- ) - 2\|2 atan(---------------------) +--R | 2 2 2 2 +--R \| a x 3a x - 2 +--R + +--R +----------+ +--------+ +--R | 2 2 | 2 2 +--R 3 3 2\|- a x + 1 a x 2 2 |a x - 1 +--R a x atan(--------------) - 5atan(-------------) + a x |-------- +--R 2 2 +----------+ | 2 2 +--R a x | 2 2 \| a x +--R \|- a x + 1 +--R + +--R +----------+ +--R | 2 2 3 3 +--R a x\|- a x + 1 - 2a x asec(a x) +--R / +--R 3 +--R 6a +--R Type: Expression Integer +--E 156 + +--S 157 of 477 +d0028:= D(m0028,x) +--R +--R +--R (112) +--R +--------+ +----------+ +--R | 2 2 +--------+ | 2 2 +--R 2 |a x - 1 | 2 2 2\|- a x + 1 +--R 3a x |-------- \|a x - 1 atan(--------------) +--R | 2 2 2 2 +--R \| a x a x +--R + +--R +--------+ +--------+ +--R | 2 2 +--------+ | 2 2 +--R 2 |a x - 1 | 2 2 2 |a x - 1 +--R (- 6a x asec(a x) |-------- + 2x)\|a x - 1 - 2a x |-------- +--R | 2 2 | 2 2 +--R \| a x \| a x +--R / +--R +--------+ +--R | 2 2 +--------+ +--R |a x - 1 | 2 2 +--R 6a |-------- \|a x - 1 +--R | 2 2 +--R \| a x +--R Type: Expression Integer +--E 157 + +--S 158 of 477 +t0029:= x^4*asec(a*x) +--R +--R +--R 4 +--R (113) x asec(a x) +--R Type: Expression Integer +--E 158 + +--S 159 of 477 +r0029:= -3/40*(1-1/a^2/x^2)^(1/2)*x^2/a^3-1/20*(1-1/a^2/x^2)^(1/2)*x^4/a+_ + 1/5*x^5*asec(a*x)-3/40*atanh((1-1/a^2/x^2)^(1/2))/a^5 +--R +--R +--R (114) +--R +--------+ +--------+ +--R | 2 2 | 2 2 +--R |a x - 1 4 4 2 2 |a x - 1 5 5 +--R - 3atanh( |-------- ) + (- 2a x - 3a x ) |-------- + 8a x asec(a x) +--R | 2 2 | 2 2 +--R \| a x \| a x +--R --------------------------------------------------------------------- +--R 5 +--R 40a +--R Type: Expression Integer +--E 159 + +--S 160 of 477 +a0029:= integrate(t0029,x) +--R +--R +--R (115) +--R +----------+ +----------+ +--R +-+ | 2 2 | 2 2 +--R +-+ 2a x\|2 \|- a x + 1 5 5 2\|- a x + 1 +--R - 16\|2 atan(---------------------) + 4a x atan(--------------) +--R 2 2 2 2 +--R 3a x - 2 a x +--R + +--R +----------+ +--R a x 3 3 | 2 2 +--R - 43atan(-------------) + (2a x + 11a x)\|- a x + 1 +--R +----------+ +--R | 2 2 +--R \|- a x + 1 +--R / +--R 5 +--R 40a +--R Type: Union(Expression Integer,...) +--E 160 + +--S 161 of 477 +m0029:= a0029-r0029 +--R +--R +--R (116) +--R +--------+ +----------+ +--R | 2 2 +-+ | 2 2 +--R |a x - 1 +-+ 2a x\|2 \|- a x + 1 +--R 3atanh( |-------- ) - 16\|2 atan(---------------------) +--R | 2 2 2 2 +--R \| a x 3a x - 2 +--R + +--R +----------+ +--R | 2 2 +--R 5 5 2\|- a x + 1 a x +--R 4a x atan(--------------) - 43atan(-------------) +--R 2 2 +----------+ +--R a x | 2 2 +--R \|- a x + 1 +--R + +--R +--------+ +--R | 2 2 +----------+ +--R 4 4 2 2 |a x - 1 3 3 | 2 2 5 5 +--R (2a x + 3a x ) |-------- + (2a x + 11a x)\|- a x + 1 - 8a x asec(a x) +--R | 2 2 +--R \| a x +--R / +--R 5 +--R 40a +--R Type: Expression Integer +--E 161 + +--S 162 of 477 +d0029:= D(m0029,x) +--R +--R +--R (117) +--R +--------+ +----------+ +--R | 2 2 +--------+ | 2 2 +--R 4 |a x - 1 | 2 2 2\|- a x + 1 +--R 5a x |-------- \|a x - 1 atan(--------------) +--R | 2 2 2 2 +--R \| a x a x +--R + +--R +--------+ +--------+ +--R | 2 2 +--------+ | 2 2 +--R 4 |a x - 1 3 | 2 2 4 |a x - 1 +--R (- 10a x asec(a x) |-------- + 2x )\|a x - 1 - 2a x |-------- +--R | 2 2 | 2 2 +--R \| a x \| a x +--R / +--R +--------+ +--R | 2 2 +--------+ +--R |a x - 1 | 2 2 +--R 10a |-------- \|a x - 1 +--R | 2 2 +--R \| a x +--R Type: Expression Integer +--E 162 + +--S 163 of 477 +t0030:= asec(a*x)/x^3 +--R +--R +--R asec(a x) +--R (118) --------- +--R 3 +--R x +--R Type: Expression Integer +--E 163 + +--S 164 of 477 +r0030:= 1/4*a*(1-1/a^2/x^2)^(1/2)/x-1/4*a^2*acsc(a*x)-1/2*asec(a*x)/x^2 +--R +--R +--R +--------+ +--R | 2 2 +--R |a x - 1 2 2 +--R a x |-------- - 2asec(a x) - a x acsc(a x) +--R | 2 2 +--R \| a x +--R (119) ------------------------------------------- +--R 2 +--R 4x +--R Type: Expression Integer +--E 164 + +--S 165 of 477 +a0030:= integrate(t0030,x) +--R +--R +--R (120) +--R +----------+ +----------+ +--R 2 2 | 2 2 2 2 | 2 2 +--R a x log(\|- a x + 1 + 1) - a x log(\|- a x + 1 - 1) +--R + +--R +----------+ +--R | 2 2 +--R 2 2 2\|- a x + 1 +--R (a x - 2)atan(--------------) +--R 2 2 +--R a x +--R / +--R 2 +--R 8x +--R Type: Union(Expression Integer,...) +--E 165 + +--S 166 of 477 +m0030:= a0030-r0030 +--R +--R +--R (121) +--R +----------+ +----------+ +--R 2 2 | 2 2 2 2 | 2 2 +--R a x log(\|- a x + 1 + 1) - a x log(\|- a x + 1 - 1) +--R + +--R +----------+ +--------+ +--R | 2 2 | 2 2 +--R 2 2 2\|- a x + 1 |a x - 1 +--R (a x - 2)atan(--------------) - 2a x |-------- + 4asec(a x) +--R 2 2 | 2 2 +--R a x \| a x +--R + +--R 2 2 +--R 2a x acsc(a x) +--R / +--R 2 +--R 8x +--R Type: Expression Integer +--E 166 + +--S 167 of 477 +d0030:= D(m0030,x) +--R +--R +--R (122) +--R +--------+ +----------+ +--R | 2 2 +--------+ | 2 2 +--R |a x - 1 | 2 2 2\|- a x + 1 +--R 2a x |-------- \|a x - 1 atan(--------------) +--R | 2 2 2 2 +--R \| a x a x +--R + +--R +--------+ +--R | 2 2 +--------+ +--R |a x - 1 2 2 | 2 2 +--R (- 4a x asec(a x) |-------- + a x - 2)\|a x - 1 +--R | 2 2 +--R \| a x +--R + +--R +--------+ +--R | 2 2 +--R 3 3 |a x - 1 +--R (- a x + 2a x) |-------- +--R | 2 2 +--R \| a x +--R / +--R +--------+ +--R | 2 2 +--------+ +--R 4 |a x - 1 | 2 2 +--R 4a x |-------- \|a x - 1 +--R | 2 2 +--R \| a x +--R Type: Expression Integer +--E 167 + +--S 168 of 477 +t0031:= x*asec(a+b*x) +--R +--R +--R (123) x asec(b x + a) +--R Type: Expression Integer +--E 168 + +--S 169 of 477 +r0031:= -1/2*(a+b*x)*(1-1/(a+b*x)^2)^(1/2)/b^2-a*(a+b*x)*asec(a+b*x)/b^2+_ + 1/2*(a+b*x)^2*asec(a+b*x)/b^2+a*atanh((1-1/(a+b*x)^2)^(1/2))/b^2 +--R +--R +--R (124) +--R +----------------------+ +--R | 2 2 2 +--R |b x + 2a b x + a - 1 +--R 2a atanh( |---------------------- ) +--R | 2 2 2 +--R \| b x + 2a b x + a +--R + +--R +----------------------+ +--R | 2 2 2 +--R |b x + 2a b x + a - 1 2 2 2 +--R (- b x - a) |---------------------- + (b x - a )asec(b x + a) +--R | 2 2 2 +--R \| b x + 2a b x + a +--R / +--R 2 +--R 2b +--R Type: Expression Integer +--E 169 + +--S 170 of 477 +a0031:= integrate(t0031,x) +--R +--R +--R (125) +--R - +--R +------------------------------------+ +--R | +--------------+ +--R | | 6 4 2 +--R | 4 |a + 4a + 4a 4 2 +--R |8b |-------------- - a - 12a - 4 +--R | | 8 +--R 2 | \| 2b +--R b |------------------------------------ +--R | 4 +--R \| 4b +--R * +--R log +--R +--------------+ +--R +------------------------+ | 6 4 2 +--R 6 | 2 2 2 |a + 4a + 4a +--R 8a b \|- b x - 2a b x - a + 1 |-------------- +--R | 8 +--R \| 2b +--R + +--R +------------------------+ +--R 5 3 2 | 2 2 2 +--R (2a + 8a + 8a)b \|- b x - 2a b x - a + 1 +--R * +--R +------------------------------------+ +--R | +--------------+ +--R | | 6 4 2 +--R | 4 |a + 4a + 4a 4 2 +--R |8b |-------------- - a - 12a - 4 +--R | | 8 +--R | \| 2b +--R |------------------------------------ +--R | 4 +--R \| 4b +--R + +--R +--------------+ +--R | 6 4 2 +--R 4 2 5 5 3 4 |a + 4a + 4a +--R ((- 2a + 8a - 8)b x + (- 2a + 8a - 8a)b ) |-------------- +--R | 8 +--R \| 2b +--R + +--R 7 5 3 +--R a - 2a - 4a + 8a +--R + +--R +--------------------------------------+ +--R | +--------------+ +--R | | 6 4 2 +--R | 4 |a + 4a + 4a 4 2 +--R |- 8b |-------------- - a - 12a - 4 +--R | | 8 +--R 2 | \| 2b +--R b |-------------------------------------- +--R | 4 +--R \| 4b +--R * +--R log +--R +--------------+ +--R +------------------------+ | 6 4 2 +--R 6 | 2 2 2 |a + 4a + 4a +--R 8a b \|- b x - 2a b x - a + 1 |-------------- +--R | 8 +--R \| 2b +--R + +--R +------------------------+ +--R 5 3 2 | 2 2 2 +--R (- 2a - 8a - 8a)b \|- b x - 2a b x - a + 1 +--R * +--R +--------------------------------------+ +--R | +--------------+ +--R | | 6 4 2 +--R | 4 |a + 4a + 4a 4 2 +--R |- 8b |-------------- - a - 12a - 4 +--R | | 8 +--R | \| 2b +--R |-------------------------------------- +--R | 4 +--R \| 4b +--R + +--R +--------------+ +--R | 6 4 2 +--R 4 2 5 5 3 4 |a + 4a + 4a 7 +--R ((2a - 8a + 8)b x + (2a - 8a + 8a)b ) |-------------- + a +--R | 8 +--R \| 2b +--R + +--R 5 3 +--R - 2a - 4a + 8a +--R + +--R - +--R +--------------------------------------+ +--R | +--------------+ +--R | | 6 4 2 +--R | 4 |a + 4a + 4a 4 2 +--R |- 8b |-------------- - a - 12a - 4 +--R | | 8 +--R 2 | \| 2b +--R b |-------------------------------------- +--R | 4 +--R \| 4b +--R * +--R log +--R +--------------+ +--R +------------------------+ | 6 4 2 +--R 6 | 2 2 2 |a + 4a + 4a +--R - 8a b \|- b x - 2a b x - a + 1 |-------------- +--R | 8 +--R \| 2b +--R + +--R +------------------------+ +--R 5 3 2 | 2 2 2 +--R (2a + 8a + 8a)b \|- b x - 2a b x - a + 1 +--R * +--R +--------------------------------------+ +--R | +--------------+ +--R | | 6 4 2 +--R | 4 |a + 4a + 4a 4 2 +--R |- 8b |-------------- - a - 12a - 4 +--R | | 8 +--R | \| 2b +--R |-------------------------------------- +--R | 4 +--R \| 4b +--R + +--R +--------------+ +--R | 6 4 2 +--R 4 2 5 5 3 4 |a + 4a + 4a 7 +--R ((2a - 8a + 8)b x + (2a - 8a + 8a)b ) |-------------- + a +--R | 8 +--R \| 2b +--R + +--R 5 3 +--R - 2a - 4a + 8a +--R + +--R +------------------------------------+ +--R | +--------------+ +--R | | 6 4 2 +--R | 4 |a + 4a + 4a 4 2 +--R |8b |-------------- - a - 12a - 4 +--R | | 8 +--R 2 | \| 2b +--R b |------------------------------------ +--R | 4 +--R \| 4b +--R * +--R log +--R +--------------+ +--R +------------------------+ | 6 4 2 +--R 6 | 2 2 2 |a + 4a + 4a +--R - 8a b \|- b x - 2a b x - a + 1 |-------------- +--R | 8 +--R \| 2b +--R + +--R +------------------------+ +--R 5 3 2 | 2 2 2 +--R (- 2a - 8a - 8a)b \|- b x - 2a b x - a + 1 +--R * +--R +------------------------------------+ +--R | +--------------+ +--R | | 6 4 2 +--R | 4 |a + 4a + 4a 4 2 +--R |8b |-------------- - a - 12a - 4 +--R | | 8 +--R | \| 2b +--R |------------------------------------ +--R | 4 +--R \| 4b +--R + +--R +--------------+ +--R | 6 4 2 +--R 4 2 5 5 3 4 |a + 4a + 4a +--R ((- 2a + 8a - 8)b x + (- 2a + 8a - 8a)b ) |-------------- +--R | 8 +--R \| 2b +--R + +--R 7 5 3 +--R a - 2a - 4a + 8a +--R + +--R +------------------------+ +--R | 2 2 2 +--R 2 2 2\|- b x - 2a b x - a + 1 +--R b x atan(----------------------------) +--R 2 2 2 +--R b x + 2a b x + a +--R + +--R +------------------------+ +--R b x + a | 2 2 2 +--R 4a atan(---------------------------) + 2\|- b x - 2a b x - a + 1 +--R +------------------------+ +--R | 2 2 2 +--R \|- b x - 2a b x - a + 1 +--R / +--R 2 +--R 4b +--R Type: Union(Expression Integer,...) +--E 170 + +--S 171 of 477 +m0031:= a0031-r0031 +--R +--R +--R (126) +--R - +--R +------------------------------------+ +--R | +--------------+ +--R | | 6 4 2 +--R | 4 |a + 4a + 4a 4 2 +--R |8b |-------------- - a - 12a - 4 +--R | | 8 +--R 2 | \| 2b +--R b |------------------------------------ +--R | 4 +--R \| 4b +--R * +--R log +--R +--------------+ +--R +------------------------+ | 6 4 2 +--R 6 | 2 2 2 |a + 4a + 4a +--R 8a b \|- b x - 2a b x - a + 1 |-------------- +--R | 8 +--R \| 2b +--R + +--R +------------------------+ +--R 5 3 2 | 2 2 2 +--R (2a + 8a + 8a)b \|- b x - 2a b x - a + 1 +--R * +--R +------------------------------------+ +--R | +--------------+ +--R | | 6 4 2 +--R | 4 |a + 4a + 4a 4 2 +--R |8b |-------------- - a - 12a - 4 +--R | | 8 +--R | \| 2b +--R |------------------------------------ +--R | 4 +--R \| 4b +--R + +--R +--------------+ +--R | 6 4 2 +--R 4 2 5 5 3 4 |a + 4a + 4a +--R ((- 2a + 8a - 8)b x + (- 2a + 8a - 8a)b ) |-------------- +--R | 8 +--R \| 2b +--R + +--R 7 5 3 +--R a - 2a - 4a + 8a +--R + +--R +--------------------------------------+ +--R | +--------------+ +--R | | 6 4 2 +--R | 4 |a + 4a + 4a 4 2 +--R |- 8b |-------------- - a - 12a - 4 +--R | | 8 +--R 2 | \| 2b +--R b |-------------------------------------- +--R | 4 +--R \| 4b +--R * +--R log +--R +--------------+ +--R +------------------------+ | 6 4 2 +--R 6 | 2 2 2 |a + 4a + 4a +--R 8a b \|- b x - 2a b x - a + 1 |-------------- +--R | 8 +--R \| 2b +--R + +--R +------------------------+ +--R 5 3 2 | 2 2 2 +--R (- 2a - 8a - 8a)b \|- b x - 2a b x - a + 1 +--R * +--R +--------------------------------------+ +--R | +--------------+ +--R | | 6 4 2 +--R | 4 |a + 4a + 4a 4 2 +--R |- 8b |-------------- - a - 12a - 4 +--R | | 8 +--R | \| 2b +--R |-------------------------------------- +--R | 4 +--R \| 4b +--R + +--R +--------------+ +--R | 6 4 2 +--R 4 2 5 5 3 4 |a + 4a + 4a 7 +--R ((2a - 8a + 8)b x + (2a - 8a + 8a)b ) |-------------- + a +--R | 8 +--R \| 2b +--R + +--R 5 3 +--R - 2a - 4a + 8a +--R + +--R - +--R +--------------------------------------+ +--R | +--------------+ +--R | | 6 4 2 +--R | 4 |a + 4a + 4a 4 2 +--R |- 8b |-------------- - a - 12a - 4 +--R | | 8 +--R 2 | \| 2b +--R b |-------------------------------------- +--R | 4 +--R \| 4b +--R * +--R log +--R +--------------+ +--R +------------------------+ | 6 4 2 +--R 6 | 2 2 2 |a + 4a + 4a +--R - 8a b \|- b x - 2a b x - a + 1 |-------------- +--R | 8 +--R \| 2b +--R + +--R +------------------------+ +--R 5 3 2 | 2 2 2 +--R (2a + 8a + 8a)b \|- b x - 2a b x - a + 1 +--R * +--R +--------------------------------------+ +--R | +--------------+ +--R | | 6 4 2 +--R | 4 |a + 4a + 4a 4 2 +--R |- 8b |-------------- - a - 12a - 4 +--R | | 8 +--R | \| 2b +--R |-------------------------------------- +--R | 4 +--R \| 4b +--R + +--R +--------------+ +--R | 6 4 2 +--R 4 2 5 5 3 4 |a + 4a + 4a 7 +--R ((2a - 8a + 8)b x + (2a - 8a + 8a)b ) |-------------- + a +--R | 8 +--R \| 2b +--R + +--R 5 3 +--R - 2a - 4a + 8a +--R + +--R +------------------------------------+ +--R | +--------------+ +--R | | 6 4 2 +--R | 4 |a + 4a + 4a 4 2 +--R |8b |-------------- - a - 12a - 4 +--R | | 8 +--R 2 | \| 2b +--R b |------------------------------------ +--R | 4 +--R \| 4b +--R * +--R log +--R +--------------+ +--R +------------------------+ | 6 4 2 +--R 6 | 2 2 2 |a + 4a + 4a +--R - 8a b \|- b x - 2a b x - a + 1 |-------------- +--R | 8 +--R \| 2b +--R + +--R +------------------------+ +--R 5 3 2 | 2 2 2 +--R (- 2a - 8a - 8a)b \|- b x - 2a b x - a + 1 +--R * +--R +------------------------------------+ +--R | +--------------+ +--R | | 6 4 2 +--R | 4 |a + 4a + 4a 4 2 +--R |8b |-------------- - a - 12a - 4 +--R | | 8 +--R | \| 2b +--R |------------------------------------ +--R | 4 +--R \| 4b +--R + +--R +--------------+ +--R | 6 4 2 +--R 4 2 5 5 3 4 |a + 4a + 4a +--R ((- 2a + 8a - 8)b x + (- 2a + 8a - 8a)b ) |-------------- +--R | 8 +--R \| 2b +--R + +--R 7 5 3 +--R a - 2a - 4a + 8a +--R + +--R +----------------------+ +--R | 2 2 2 +--R |b x + 2a b x + a - 1 +--R - 4a atanh( |---------------------- ) +--R | 2 2 2 +--R \| b x + 2a b x + a +--R + +--R +------------------------+ +--R | 2 2 2 +--R 2 2 2\|- b x - 2a b x - a + 1 +--R b x atan(----------------------------) +--R 2 2 2 +--R b x + 2a b x + a +--R + +--R b x + a +--R 4a atan(---------------------------) +--R +------------------------+ +--R | 2 2 2 +--R \|- b x - 2a b x - a + 1 +--R + +--R +----------------------+ +--R | 2 2 2 +------------------------+ +--R |b x + 2a b x + a - 1 | 2 2 2 +--R (2b x + 2a) |---------------------- + 2\|- b x - 2a b x - a + 1 +--R | 2 2 2 +--R \| b x + 2a b x + a +--R + +--R 2 2 2 +--R (- 2b x + 2a )asec(b x + a) +--R / +--R 2 +--R 4b +--R Type: Expression Integer +--E 171 + +--S 172 of 477 +d0031:= D(m0031,x) +--R +--R +--R (127) +--R +----------------------+ +--R | 2 2 2 +----------------------+ +--R 2 2 |b x + 2a b x + a - 1 | 2 2 2 +--R (b x + a b x) |---------------------- \|b x + 2a b x + a - 1 +--R | 2 2 2 +--R \| b x + 2a b x + a +--R * +--R +------------------------+ +--R | 2 2 2 +--R 2\|- b x - 2a b x - a + 1 +--R atan(----------------------------) +--R 2 2 2 +--R b x + 2a b x + a +--R + +--R +----------------------+ +--R | 2 2 2 +--R 2 2 |b x + 2a b x + a - 1 +--R ((- 2b x - 2a b x)asec(b x + a) |---------------------- + b x - a) +--R | 2 2 2 +--R \| b x + 2a b x + a +--R * +--R +----------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - 1 +--R + +--R +----------------------+ +--R | 2 2 2 +--R 2 2 2 |b x + 2a b x + a - 1 +--R (- b x + a ) |---------------------- +--R | 2 2 2 +--R \| b x + 2a b x + a +--R / +--R +----------------------+ +--R | 2 2 2 +----------------------+ +--R 2 |b x + 2a b x + a - 1 | 2 2 2 +--R (2b x + 2a b) |---------------------- \|b x + 2a b x + a - 1 +--R | 2 2 2 +--R \| b x + 2a b x + a +--R Type: Expression Integer +--E 172 + +--S 173 of 477 +t0032:= x^2*asec(a+b*x) +--R +--R +--R 2 +--R (128) x asec(b x + a) +--R Type: Expression Integer +--E 173 + +--S 174 of 477 +r0032:= a*(a+b*x)*(1-1/(a+b*x)^2)^(1/2)/b^3-1/6*(a+b*x)^2*_ + (1-1/(a+b*x)^2)^(1/2)/b^3+a^2*(a+b*x)*asec(a+b*x)/b^3-_ + a*(a+b*x)^2*asec(a+b*x)/b^3+1/3*(a+b*x)^3*asec(a+b*x)/b^3-_ + 1/6*atanh((1-1/(a+b*x)^2)^(1/2))/b^3-_ + a^2*atanh((1-1/(a+b*x)^2)^(1/2))/b^3 +--R +--R +--R (129) +--R +----------------------+ +--R | 2 2 2 +--R 2 |b x + 2a b x + a - 1 +--R (- 6a - 1)atanh( |---------------------- ) +--R | 2 2 2 +--R \| b x + 2a b x + a +--R + +--R +----------------------+ +--R | 2 2 2 +--R 2 2 2 |b x + 2a b x + a - 1 +--R (- b x + 4a b x + 5a ) |---------------------- +--R | 2 2 2 +--R \| b x + 2a b x + a +--R + +--R 3 3 3 +--R (2b x + 2a )asec(b x + a) +--R / +--R 3 +--R 6b +--R Type: Expression Integer +--E 174 + +--S 175 of 477 +a0032:= integrate(t0032,x) +--R +--R +--R (130) +--R 3 +--R 3b +--R * +--R +-------------------------------------------------------------------+ +--R | +-------------------------------------+ +--R | | 10 8 6 4 2 +--R | 6 |18a + 240a + 944a + 960a + 288a 6 4 2 +--R |18b |------------------------------------- - a - 30a - 60a - 8 +--R | | 12 +--R | \| 81b +--R |------------------------------------------------------------------- +--R | 6 +--R \| 9b +--R * +--R log +--R +------------------------+ +--R 2 9 | 2 2 2 +--R (81a + 54)b \|- b x - 2a b x - a + 1 +--R * +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R |18a + 240a + 944a + 960a + 288a +--R |------------------------------------- +--R | 12 +--R \| 81b +--R + +--R +------------------------+ +--R 8 6 4 2 3 | 2 2 2 +--R (9a + 114a + 396a + 216a )b \|- b x - 2a b x - a + 1 +--R * +--R ROOT +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R 6 |18a + 240a + 944a + 960a + 288a 6 4 +--R 18b |------------------------------------- - a - 30a +--R | 12 +--R \| 81b +--R + +--R 2 +--R - 60a - 8 +--R / +--R 6 +--R 9b +--R + +--R 6 4 2 7 +--R (- 9a + 54a - 108a + 72)b x +--R + +--R 7 5 3 6 +--R (- 9a + 54a - 108a + 72a)b +--R * +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R |18a + 240a + 944a + 960a + 288a +--R |------------------------------------- +--R | 12 +--R \| 81b +--R + +--R 11 9 7 5 3 +--R 3a + 2a - 72a + 144a - 16a - 96a +--R + +--R - +--R 3 +--R 3b +--R * +--R ROOT +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R 6 |18a + 240a + 944a + 960a + 288a 6 4 +--R - 18b |------------------------------------- - a - 30a +--R | 12 +--R \| 81b +--R + +--R 2 +--R - 60a - 8 +--R / +--R 6 +--R 9b +--R * +--R log +--R +------------------------+ +--R 2 9 | 2 2 2 +--R (81a + 54)b \|- b x - 2a b x - a + 1 +--R * +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R |18a + 240a + 944a + 960a + 288a +--R |------------------------------------- +--R | 12 +--R \| 81b +--R + +--R +------------------------+ +--R 8 6 4 2 3 | 2 2 2 +--R (- 9a - 114a - 396a - 216a )b \|- b x - 2a b x - a + 1 +--R * +--R ROOT +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R 6 |18a + 240a + 944a + 960a + 288a 6 +--R - 18b |------------------------------------- - a +--R | 12 +--R \| 81b +--R + +--R 4 2 +--R - 30a - 60a - 8 +--R / +--R 6 +--R 9b +--R + +--R 6 4 2 7 7 5 3 6 +--R ((9a - 54a + 108a - 72)b x + (9a - 54a + 108a - 72a)b ) +--R * +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R |18a + 240a + 944a + 960a + 288a +--R |------------------------------------- +--R | 12 +--R \| 81b +--R + +--R 11 9 7 5 3 +--R 3a + 2a - 72a + 144a - 16a - 96a +--R + +--R 3 +--R 3b +--R * +--R ROOT +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R 6 |18a + 240a + 944a + 960a + 288a 6 4 +--R - 18b |------------------------------------- - a - 30a +--R | 12 +--R \| 81b +--R + +--R 2 +--R - 60a - 8 +--R / +--R 6 +--R 9b +--R * +--R log +--R +------------------------+ +--R 2 9 | 2 2 2 +--R (- 81a - 54)b \|- b x - 2a b x - a + 1 +--R * +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R |18a + 240a + 944a + 960a + 288a +--R |------------------------------------- +--R | 12 +--R \| 81b +--R + +--R +------------------------+ +--R 8 6 4 2 3 | 2 2 2 +--R (9a + 114a + 396a + 216a )b \|- b x - 2a b x - a + 1 +--R * +--R ROOT +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R 6 |18a + 240a + 944a + 960a + 288a 6 +--R - 18b |------------------------------------- - a +--R | 12 +--R \| 81b +--R + +--R 4 2 +--R - 30a - 60a - 8 +--R / +--R 6 +--R 9b +--R + +--R 6 4 2 7 7 5 3 6 +--R ((9a - 54a + 108a - 72)b x + (9a - 54a + 108a - 72a)b ) +--R * +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R |18a + 240a + 944a + 960a + 288a +--R |------------------------------------- +--R | 12 +--R \| 81b +--R + +--R 11 9 7 5 3 +--R 3a + 2a - 72a + 144a - 16a - 96a +--R + +--R - +--R 3 +--R 3b +--R * +--R ROOT +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R 6 |18a + 240a + 944a + 960a + 288a 6 4 +--R 18b |------------------------------------- - a - 30a +--R | 12 +--R \| 81b +--R + +--R 2 +--R - 60a - 8 +--R / +--R 6 +--R 9b +--R * +--R log +--R +------------------------+ +--R 2 9 | 2 2 2 +--R (- 81a - 54)b \|- b x - 2a b x - a + 1 +--R * +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R |18a + 240a + 944a + 960a + 288a +--R |------------------------------------- +--R | 12 +--R \| 81b +--R + +--R +------------------------+ +--R 8 6 4 2 3 | 2 2 2 +--R (- 9a - 114a - 396a - 216a )b \|- b x - 2a b x - a + 1 +--R * +--R ROOT +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R 6 |18a + 240a + 944a + 960a + 288a 6 +--R 18b |------------------------------------- - a +--R | 12 +--R \| 81b +--R + +--R 4 2 +--R - 30a - 60a - 8 +--R / +--R 6 +--R 9b +--R + +--R 6 4 2 7 +--R (- 9a + 54a - 108a + 72)b x +--R + +--R 7 5 3 6 +--R (- 9a + 54a - 108a + 72a)b +--R * +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R |18a + 240a + 944a + 960a + 288a +--R |------------------------------------- +--R | 12 +--R \| 81b +--R + +--R 11 9 7 5 3 +--R 3a + 2a - 72a + 144a - 16a - 96a +--R + +--R +------------------------+ +--R | 2 2 2 +--R 3 3 2\|- b x - 2a b x - a + 1 +--R 2b x atan(----------------------------) +--R 2 2 2 +--R b x + 2a b x + a +--R + +--R 2 b x + a +--R (- 12a - 10)atan(---------------------------) +--R +------------------------+ +--R | 2 2 2 +--R \|- b x - 2a b x - a + 1 +--R + +--R +------------------------+ +--R | 2 2 2 +--R (2b x - 10a)\|- b x - 2a b x - a + 1 +--R / +--R 3 +--R 12b +--R Type: Union(Expression Integer,...) +--E 175 + +--S 176 of 477 +m0032:= a0032-r0032 +--R +--R +--R (131) +--R 3 +--R 3b +--R * +--R +-------------------------------------------------------------------+ +--R | +-------------------------------------+ +--R | | 10 8 6 4 2 +--R | 6 |18a + 240a + 944a + 960a + 288a 6 4 2 +--R |18b |------------------------------------- - a - 30a - 60a - 8 +--R | | 12 +--R | \| 81b +--R |------------------------------------------------------------------- +--R | 6 +--R \| 9b +--R * +--R log +--R +------------------------+ +--R 2 9 | 2 2 2 +--R (81a + 54)b \|- b x - 2a b x - a + 1 +--R * +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R |18a + 240a + 944a + 960a + 288a +--R |------------------------------------- +--R | 12 +--R \| 81b +--R + +--R +------------------------+ +--R 8 6 4 2 3 | 2 2 2 +--R (9a + 114a + 396a + 216a )b \|- b x - 2a b x - a + 1 +--R * +--R ROOT +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R 6 |18a + 240a + 944a + 960a + 288a 6 4 +--R 18b |------------------------------------- - a - 30a +--R | 12 +--R \| 81b +--R + +--R 2 +--R - 60a - 8 +--R / +--R 6 +--R 9b +--R + +--R 6 4 2 7 +--R (- 9a + 54a - 108a + 72)b x +--R + +--R 7 5 3 6 +--R (- 9a + 54a - 108a + 72a)b +--R * +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R |18a + 240a + 944a + 960a + 288a +--R |------------------------------------- +--R | 12 +--R \| 81b +--R + +--R 11 9 7 5 3 +--R 3a + 2a - 72a + 144a - 16a - 96a +--R + +--R - +--R 3 +--R 3b +--R * +--R ROOT +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R 6 |18a + 240a + 944a + 960a + 288a 6 4 +--R - 18b |------------------------------------- - a - 30a +--R | 12 +--R \| 81b +--R + +--R 2 +--R - 60a - 8 +--R / +--R 6 +--R 9b +--R * +--R log +--R +------------------------+ +--R 2 9 | 2 2 2 +--R (81a + 54)b \|- b x - 2a b x - a + 1 +--R * +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R |18a + 240a + 944a + 960a + 288a +--R |------------------------------------- +--R | 12 +--R \| 81b +--R + +--R +------------------------+ +--R 8 6 4 2 3 | 2 2 2 +--R (- 9a - 114a - 396a - 216a )b \|- b x - 2a b x - a + 1 +--R * +--R ROOT +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R 6 |18a + 240a + 944a + 960a + 288a 6 +--R - 18b |------------------------------------- - a +--R | 12 +--R \| 81b +--R + +--R 4 2 +--R - 30a - 60a - 8 +--R / +--R 6 +--R 9b +--R + +--R 6 4 2 7 7 5 3 6 +--R ((9a - 54a + 108a - 72)b x + (9a - 54a + 108a - 72a)b ) +--R * +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R |18a + 240a + 944a + 960a + 288a +--R |------------------------------------- +--R | 12 +--R \| 81b +--R + +--R 11 9 7 5 3 +--R 3a + 2a - 72a + 144a - 16a - 96a +--R + +--R 3 +--R 3b +--R * +--R ROOT +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R 6 |18a + 240a + 944a + 960a + 288a 6 4 +--R - 18b |------------------------------------- - a - 30a +--R | 12 +--R \| 81b +--R + +--R 2 +--R - 60a - 8 +--R / +--R 6 +--R 9b +--R * +--R log +--R +------------------------+ +--R 2 9 | 2 2 2 +--R (- 81a - 54)b \|- b x - 2a b x - a + 1 +--R * +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R |18a + 240a + 944a + 960a + 288a +--R |------------------------------------- +--R | 12 +--R \| 81b +--R + +--R +------------------------+ +--R 8 6 4 2 3 | 2 2 2 +--R (9a + 114a + 396a + 216a )b \|- b x - 2a b x - a + 1 +--R * +--R ROOT +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R 6 |18a + 240a + 944a + 960a + 288a 6 +--R - 18b |------------------------------------- - a +--R | 12 +--R \| 81b +--R + +--R 4 2 +--R - 30a - 60a - 8 +--R / +--R 6 +--R 9b +--R + +--R 6 4 2 7 7 5 3 6 +--R ((9a - 54a + 108a - 72)b x + (9a - 54a + 108a - 72a)b ) +--R * +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R |18a + 240a + 944a + 960a + 288a +--R |------------------------------------- +--R | 12 +--R \| 81b +--R + +--R 11 9 7 5 3 +--R 3a + 2a - 72a + 144a - 16a - 96a +--R + +--R - +--R 3 +--R 3b +--R * +--R ROOT +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R 6 |18a + 240a + 944a + 960a + 288a 6 4 +--R 18b |------------------------------------- - a - 30a +--R | 12 +--R \| 81b +--R + +--R 2 +--R - 60a - 8 +--R / +--R 6 +--R 9b +--R * +--R log +--R +------------------------+ +--R 2 9 | 2 2 2 +--R (- 81a - 54)b \|- b x - 2a b x - a + 1 +--R * +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R |18a + 240a + 944a + 960a + 288a +--R |------------------------------------- +--R | 12 +--R \| 81b +--R + +--R +------------------------+ +--R 8 6 4 2 3 | 2 2 2 +--R (- 9a - 114a - 396a - 216a )b \|- b x - 2a b x - a + 1 +--R * +--R ROOT +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R 6 |18a + 240a + 944a + 960a + 288a 6 +--R 18b |------------------------------------- - a +--R | 12 +--R \| 81b +--R + +--R 4 2 +--R - 30a - 60a - 8 +--R / +--R 6 +--R 9b +--R + +--R 6 4 2 7 +--R (- 9a + 54a - 108a + 72)b x +--R + +--R 7 5 3 6 +--R (- 9a + 54a - 108a + 72a)b +--R * +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R |18a + 240a + 944a + 960a + 288a +--R |------------------------------------- +--R | 12 +--R \| 81b +--R + +--R 11 9 7 5 3 +--R 3a + 2a - 72a + 144a - 16a - 96a +--R + +--R +----------------------+ +--R | 2 2 2 +--R 2 |b x + 2a b x + a - 1 +--R (12a + 2)atanh( |---------------------- ) +--R | 2 2 2 +--R \| b x + 2a b x + a +--R + +--R +------------------------+ +--R | 2 2 2 +--R 3 3 2\|- b x - 2a b x - a + 1 +--R 2b x atan(----------------------------) +--R 2 2 2 +--R b x + 2a b x + a +--R + +--R 2 b x + a +--R (- 12a - 10)atan(---------------------------) +--R +------------------------+ +--R | 2 2 2 +--R \|- b x - 2a b x - a + 1 +--R + +--R +----------------------+ +--R | 2 2 2 +--R 2 2 2 |b x + 2a b x + a - 1 +--R (2b x - 8a b x - 10a ) |---------------------- +--R | 2 2 2 +--R \| b x + 2a b x + a +--R + +--R +------------------------+ +--R | 2 2 2 3 3 3 +--R (2b x - 10a)\|- b x - 2a b x - a + 1 + (- 4b x - 4a )asec(b x + a) +--R / +--R 3 +--R 12b +--R Type: Expression Integer +--E 176 + +--S 177 of 477 +d0032:= D(m0032,x) +--R +--R +--R (132) +--R +----------------------+ +--R | 2 2 2 +----------------------+ +--R 3 3 2 2 |b x + 2a b x + a - 1 | 2 2 2 +--R (3b x + 3a b x ) |---------------------- \|b x + 2a b x + a - 1 +--R | 2 2 2 +--R \| b x + 2a b x + a +--R * +--R +------------------------+ +--R | 2 2 2 +--R 2\|- b x - 2a b x - a + 1 +--R atan(----------------------------) +--R 2 2 2 +--R b x + 2a b x + a +--R + +--R +----------------------+ +--R | 2 2 2 +--R 3 3 2 2 |b x + 2a b x + a - 1 2 2 +--R (- 6b x - 6a b x )asec(b x + a) |---------------------- + 2b x +--R | 2 2 2 +--R \| b x + 2a b x + a +--R + +--R 2 +--R - 2a b x + 2a +--R * +--R +----------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - 1 +--R + +--R +----------------------+ +--R | 2 2 2 +--R 3 3 3 |b x + 2a b x + a - 1 +--R (- 2b x - 2a ) |---------------------- +--R | 2 2 2 +--R \| b x + 2a b x + a +--R / +--R +----------------------+ +--R | 2 2 2 +----------------------+ +--R 3 2 |b x + 2a b x + a - 1 | 2 2 2 +--R (6b x + 6a b ) |---------------------- \|b x + 2a b x + a - 1 +--R | 2 2 2 +--R \| b x + 2a b x + a +--R Type: Expression Integer +--E 177 + +--S 178 of 477 +t0033:= asec(x^(1/2)) +--R +--R +--R +-+ +--R (133) asec(\|x ) +--R Type: Expression Integer +--E 178 + +--S 179 of 477 +r0033:= -(-1+x)^(1/2)+x*asec(x^(1/2)) +--R +--R +--R +-+ +-----+ +--R (134) x asec(\|x ) - \|x - 1 +--R Type: Expression Integer +--E 179 + +--S 180 of 477 +a0033:= integrate(t0033,x) +--R +--R +--R +-------+ +--R 2\|- x + 1 +-------+ +--R (x - 2)atan(-----------) + 2\|- x + 1 +--R x +--R (135) -------------------------------------- +--R 2 +--R Type: Union(Expression Integer,...) +--E 180 + +--S 181 of 477 +m0033:= a0033-r0033 +--R +--R +--R +-------+ +--R 2\|- x + 1 +-+ +-----+ +-------+ +--R (x - 2)atan(-----------) - 2x asec(\|x ) + 2\|x - 1 + 2\|- x + 1 +--R x +--R (136) ------------------------------------------------------------------ +--R 2 +--R Type: Expression Integer +--E 181 + +--S 182 of 477 +d0033:= D(m0033,x) +--R +--R +--R +-------+ +--R 2\|- x + 1 +-+ +--R atan(-----------) - 2asec(\|x ) +--R x +--R (137) ------------------------------- +--R 2 +--R Type: Expression Integer +--E 182 + +--S 183 of 477 +t0034:= asec(x^(1/2))/x^2 +--R +--R +--R +-+ +--R asec(\|x ) +--R (138) ---------- +--R 2 +--R x +--R Type: Expression Integer +--E 183 + +--S 184 of 477 +r0034:= -1/2*(-(-1+x)^(1/2)+x*acsc(x^(1/2))+2*asec(x^(1/2)))/x +--R +--R +--R +-+ +-+ +-----+ +--R - 2asec(\|x ) - x acsc(\|x ) + \|x - 1 +--R (139) --------------------------------------- +--R 2x +--R Type: Expression Integer +--E 184 + +--S 185 of 477 +a0034:= integrate(t0034,x) +--R +--R +--R (140) +--R +-------+ +--R +-------+ +-------+ 2\|- x + 1 +--R x log(\|- x + 1 + 1) - x log(\|- x + 1 - 1) + (x - 2)atan(-----------) +--R x +--R ------------------------------------------------------------------------ +--R 4x +--R Type: Union(Expression Integer,...) +--E 185 + +--S 186 of 477 +m0034:= a0034-r0034 +--R +--R +--R (141) +--R +-------+ +--R +-------+ +-------+ 2\|- x + 1 +--R x log(\|- x + 1 + 1) - x log(\|- x + 1 - 1) + (x - 2)atan(-----------) +--R x +--R + +--R +-+ +-+ +-----+ +--R 4asec(\|x ) + 2x acsc(\|x ) - 2\|x - 1 +--R / +--R 4x +--R Type: Expression Integer +--E 186 + +--S 187 of 477 +d0034:= D(m0034,x) +--R +--R +--R +-------+ +--R 2\|- x + 1 +-+ +--R atan(-----------) - 2asec(\|x ) +--R x +--R (142) ------------------------------- +--R 2 +--R 2x +--R Type: Expression Integer +--E 187 + +--S 188 of 477 +t0035:= asec(x^(1/2))/x^3 +--R +--R +--R +-+ +--R asec(\|x ) +--R (143) ---------- +--R 3 +--R x +--R Type: Expression Integer +--E 188 + +--S 189 of 477 +r0035:= -1/16*(-2*(-1+x)^(1/2)-3*(-1+x)^(1/2)*x+_ + 3*x^2*acsc(x^(1/2))+8*asec(x^(1/2)))/x^2 +--R +--R +--R +-+ 2 +-+ +-----+ +--R - 8asec(\|x ) - 3x acsc(\|x ) + (3x + 2)\|x - 1 +--R (144) ------------------------------------------------ +--R 2 +--R 16x +--R Type: Expression Integer +--E 189 + +--S 190 of 477 +a0035:= integrate(t0035,x) +--R +--R +--R (145) +--R 2 +-------+ 2 +-------+ +--R 2x log(\|- x + 1 + 1) - 2x log(\|- x + 1 - 1) +--R + +--R +-------+ +--R 2 2\|- x + 1 +-------+ +--R (x - 4)atan(-----------) + 2x\|- x + 1 +--R x +--R / +--R 2 +--R 16x +--R Type: Union(Expression Integer,...) +--E 190 + +--S 191 of 477 +m0035:= a0035-r0035 +--R +--R +--R (146) +--R 2 +-------+ 2 +-------+ +--R 2x log(\|- x + 1 + 1) - 2x log(\|- x + 1 - 1) +--R + +--R +-------+ +--R 2 2\|- x + 1 +-+ 2 +-+ +--R (x - 4)atan(-----------) + 8asec(\|x ) + 3x acsc(\|x ) +--R x +--R + +--R +-----+ +-------+ +--R (- 3x - 2)\|x - 1 + 2x\|- x + 1 +--R / +--R 2 +--R 16x +--R Type: Expression Integer +--E 191 + +--S 192 of 477 +d0035:= D(m0035,x) +--R +--R +--R +-------+ +--R 2\|- x + 1 +-+ +--R atan(-----------) - 2asec(\|x ) +--R x +--R (147) ------------------------------- +--R 3 +--R 2x +--R Type: Expression Integer +--E 192 + +--S 193 of 477 +t0036:= x^2*acsc(a*x) +--R +--R +--R 2 +--R (148) x acsc(a x) +--R Type: Expression Integer +--E 193 + +--S 194 of 477 +r0036:= 1/6*(1-1/a^2/x^2)^(1/2)*x^2/a+1/3*x^3*acsc(a*x)+_ + 1/6*atanh((1-1/a^2/x^2)^(1/2))/a^3 +--R +--R +--R +--------+ +--------+ +--R | 2 2 | 2 2 +--R |a x - 1 2 2 |a x - 1 3 3 +--R atanh( |-------- ) + a x |-------- + 2a x acsc(a x) +--R | 2 2 | 2 2 +--R \| a x \| a x +--R (149) ----------------------------------------------------- +--R 3 +--R 6a +--R Type: Expression Integer +--E 194 + +--S 195 of 477 +a0036:= integrate(t0036,x) +--R +--R +--R (150) +--R +----------+ +----------+ +--R +-+ | 2 2 | 2 2 +--R +-+ 2a x\|2 \|- a x + 1 3 3 2\|- a x + 1 +--R 2\|2 atan(---------------------) - a x atan(--------------) +--R 2 2 2 2 +--R 3a x - 2 a x +--R + +--R +----------+ +--R a x | 2 2 +--R 5atan(-------------) - a x\|- a x + 1 +--R +----------+ +--R | 2 2 +--R \|- a x + 1 +--R / +--R 3 +--R 6a +--R Type: Union(Expression Integer,...) +--E 195 + +--S 196 of 477 +m0036:= a0036-r0036 +--R +--R +--R (151) +--R +--------+ +----------+ +--R | 2 2 +-+ | 2 2 +--R |a x - 1 +-+ 2a x\|2 \|- a x + 1 +--R - atanh( |-------- ) + 2\|2 atan(---------------------) +--R | 2 2 2 2 +--R \| a x 3a x - 2 +--R + +--R +----------+ +--------+ +--R | 2 2 | 2 2 +--R 3 3 2\|- a x + 1 a x 2 2 |a x - 1 +--R - a x atan(--------------) + 5atan(-------------) - a x |-------- +--R 2 2 +----------+ | 2 2 +--R a x | 2 2 \| a x +--R \|- a x + 1 +--R + +--R +----------+ +--R | 2 2 3 3 +--R - a x\|- a x + 1 - 2a x acsc(a x) +--R / +--R 3 +--R 6a +--R Type: Expression Integer +--E 196 + +--S 197 of 477 +d0036:= D(m0036,x) +--R +--R +--R (152) +--R +--------+ +----------+ +--R | 2 2 +--------+ | 2 2 +--R 2 |a x - 1 | 2 2 2\|- a x + 1 +--R - 3a x |-------- \|a x - 1 atan(--------------) +--R | 2 2 2 2 +--R \| a x a x +--R + +--R +--------+ +--------+ +--R | 2 2 +--------+ | 2 2 +--R 2 |a x - 1 | 2 2 2 |a x - 1 +--R (- 6a x acsc(a x) |-------- - 2x)\|a x - 1 + 2a x |-------- +--R | 2 2 | 2 2 +--R \| a x \| a x +--R / +--R +--------+ +--R | 2 2 +--------+ +--R |a x - 1 | 2 2 +--R 6a |-------- \|a x - 1 +--R | 2 2 +--R \| a x +--R Type: Expression Integer +--E 197 + +--S 198 of 477 +t0037:= x^4*acsc(a*x) +--R +--R +--R 4 +--R (153) x acsc(a x) +--R Type: Expression Integer +--E 198 + +--S 199 of 477 +r0037:= 3/40*(1-1/a^2/x^2)^(1/2)*x^2/a^3+1/20*(1-1/a^2/x^2)^(1/2)*x^4/a+_ + 1/5*x^5*acsc(a*x)+3/40*atanh((1-1/a^2/x^2)^(1/2))/a^5 +--R +--R +--R +--------+ +--------+ +--R | 2 2 | 2 2 +--R |a x - 1 4 4 2 2 |a x - 1 5 5 +--R 3atanh( |-------- ) + (2a x + 3a x ) |-------- + 8a x acsc(a x) +--R | 2 2 | 2 2 +--R \| a x \| a x +--R (154) ----------------------------------------------------------------- +--R 5 +--R 40a +--R Type: Expression Integer +--E 199 + +--S 200 of 477 +a0037:= integrate(t0037,x) +--R +--R +--R (155) +--R +----------+ +----------+ +--R +-+ | 2 2 | 2 2 +--R +-+ 2a x\|2 \|- a x + 1 5 5 2\|- a x + 1 +--R 16\|2 atan(---------------------) - 4a x atan(--------------) +--R 2 2 2 2 +--R 3a x - 2 a x +--R + +--R +----------+ +--R a x 3 3 | 2 2 +--R 43atan(-------------) + (- 2a x - 11a x)\|- a x + 1 +--R +----------+ +--R | 2 2 +--R \|- a x + 1 +--R / +--R 5 +--R 40a +--R Type: Union(Expression Integer,...) +--E 200 + +--S 201 of 477 +m0037:= a0037-r0037 +--R +--R +--R (156) +--R +--------+ +----------+ +--R | 2 2 +-+ | 2 2 +--R |a x - 1 +-+ 2a x\|2 \|- a x + 1 +--R - 3atanh( |-------- ) + 16\|2 atan(---------------------) +--R | 2 2 2 2 +--R \| a x 3a x - 2 +--R + +--R +----------+ +--R | 2 2 +--R 5 5 2\|- a x + 1 a x +--R - 4a x atan(--------------) + 43atan(-------------) +--R 2 2 +----------+ +--R a x | 2 2 +--R \|- a x + 1 +--R + +--R +--------+ +--R | 2 2 +----------+ +--R 4 4 2 2 |a x - 1 3 3 | 2 2 +--R (- 2a x - 3a x ) |-------- + (- 2a x - 11a x)\|- a x + 1 +--R | 2 2 +--R \| a x +--R + +--R 5 5 +--R - 8a x acsc(a x) +--R / +--R 5 +--R 40a +--R Type: Expression Integer +--E 201 + +--S 202 of 477 +d0037:= D(m0037,x) +--R +--R +--R (157) +--R +--------+ +----------+ +--R | 2 2 +--------+ | 2 2 +--R 4 |a x - 1 | 2 2 2\|- a x + 1 +--R - 5a x |-------- \|a x - 1 atan(--------------) +--R | 2 2 2 2 +--R \| a x a x +--R + +--R +--------+ +--------+ +--R | 2 2 +--------+ | 2 2 +--R 4 |a x - 1 3 | 2 2 4 |a x - 1 +--R (- 10a x acsc(a x) |-------- - 2x )\|a x - 1 + 2a x |-------- +--R | 2 2 | 2 2 +--R \| a x \| a x +--R / +--R +--------+ +--R | 2 2 +--------+ +--R |a x - 1 | 2 2 +--R 10a |-------- \|a x - 1 +--R | 2 2 +--R \| a x +--R Type: Expression Integer +--E 202 + +--S 203 of 477 +t0038:= acsc(a*x)/x +--R +--R +--R acsc(a x) +--R (158) --------- +--R x +--R Type: Expression Integer +--E 203 + +--S 204 of 477 +r0038:= 1/2*%i*acsc(a*x)^2-acsc(a*x)*log(1-((1-1/a^2/x^2)^(1/2)+%i/a/x)^2)+_ + 1/2*%i*polylog(2,((1-1/a^2/x^2)^(1/2)+%i/a/x)^2) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Complex Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 204 + +--S 205 of 477 +a0038:= integrate(t0038,x) +--R +--R +--R x +--R ++ acsc(%Q a) +--R (159) | ---------- d%Q +--R ++ %Q +--R Type: Union(Expression Integer,...) +--E 205 + +--S 206 of 477 +--m0038:= a0038-r0038 +--E 206 + +--S 207 of 477 +--d0038:= D(m0038,x) +--E 207 + +--S 208 of 477 +t0039:= acsc(a*x)/x^3 +--R +--R +--R acsc(a x) +--R (160) --------- +--R 3 +--R x +--R Type: Expression Integer +--E 208 + +--S 209 of 477 +r0039:= -1/4*a*(1-1/a^2/x^2)^(1/2)/x+1/4*a^2*acsc(a*x)-1/2*acsc(a*x)/x^2 +--R +--R +--R +--------+ +--R | 2 2 +--R |a x - 1 2 2 +--R - a x |-------- + (a x - 2)acsc(a x) +--R | 2 2 +--R \| a x +--R (161) -------------------------------------- +--R 2 +--R 4x +--R Type: Expression Integer +--E 209 + +--S 210 of 477 +a0039:= integrate(t0039,x) +--R +--R +--R (162) +--R +----------+ +----------+ +--R 2 2 | 2 2 2 2 | 2 2 +--R - a x log(\|- a x + 1 + 1) + a x log(\|- a x + 1 - 1) +--R + +--R +----------+ +--R | 2 2 +--R 2 2 2\|- a x + 1 +--R (- a x + 2)atan(--------------) +--R 2 2 +--R a x +--R / +--R 2 +--R 8x +--R Type: Union(Expression Integer,...) +--E 210 + +--S 211 of 477 +m0039:= a0039-r0039 +--R +--R +--R (163) +--R +----------+ +----------+ +--R 2 2 | 2 2 2 2 | 2 2 +--R - a x log(\|- a x + 1 + 1) + a x log(\|- a x + 1 - 1) +--R + +--R +----------+ +--------+ +--R | 2 2 | 2 2 +--R 2 2 2\|- a x + 1 |a x - 1 2 2 +--R (- a x + 2)atan(--------------) + 2a x |-------- + (- 2a x + 4)acsc(a x) +--R 2 2 | 2 2 +--R a x \| a x +--R / +--R 2 +--R 8x +--R Type: Expression Integer +--E 211 + +--S 212 of 477 +d0039:= D(m0039,x) +--R +--R +--R (164) +--R +--------+ +----------+ +--R | 2 2 +--------+ | 2 2 +--R |a x - 1 | 2 2 2\|- a x + 1 +--R - 2a x |-------- \|a x - 1 atan(--------------) +--R | 2 2 2 2 +--R \| a x a x +--R + +--R +--------+ +--R | 2 2 +--------+ +--R |a x - 1 2 2 | 2 2 +--R (- 4a x acsc(a x) |-------- - a x + 2)\|a x - 1 +--R | 2 2 +--R \| a x +--R + +--R +--------+ +--R | 2 2 +--R 3 3 |a x - 1 +--R (a x - 2a x) |-------- +--R | 2 2 +--R \| a x +--R / +--R +--------+ +--R | 2 2 +--------+ +--R 4 |a x - 1 | 2 2 +--R 4a x |-------- \|a x - 1 +--R | 2 2 +--R \| a x +--R Type: Expression Integer +--E 212 + +--S 213 of 477 +t0040:= x*acsc(a+b*x) +--R +--R +--R (165) x acsc(b x + a) +--R Type: Expression Integer +--E 213 + +--S 214 of 477 +r0040:= 1/2*(a+b*x)*(1-1/(a+b*x)^2)^(1/2)/b^2-a*(a+b*x)*acsc(a+b*x)/b^2+_ + 1/2*(a+b*x)^2*acsc(a+b*x)/b^2-a*atanh((1-1/(a+b*x)^2)^(1/2))/b^2 +--R +--R +--R (166) +--R +----------------------+ +--R | 2 2 2 +--R |b x + 2a b x + a - 1 +--R - 2a atanh( |---------------------- ) +--R | 2 2 2 +--R \| b x + 2a b x + a +--R + +--R +----------------------+ +--R | 2 2 2 +--R |b x + 2a b x + a - 1 2 2 2 +--R (b x + a) |---------------------- + (b x - a )acsc(b x + a) +--R | 2 2 2 +--R \| b x + 2a b x + a +--R / +--R 2 +--R 2b +--R Type: Expression Integer +--E 214 + +--S 215 of 477 +a0040:= integrate(t0040,x) +--R +--R +--R (167) +--R +------------------------------------+ +--R | +--------------+ +--R | | 6 4 2 +--R | 4 |a + 4a + 4a 4 2 +--R |8b |-------------- - a - 12a - 4 +--R | | 8 +--R 2 | \| 2b +--R b |------------------------------------ +--R | 4 +--R \| 4b +--R * +--R log +--R +--------------+ +--R +------------------------+ | 6 4 2 +--R 6 | 2 2 2 |a + 4a + 4a +--R 8a b \|- b x - 2a b x - a + 1 |-------------- +--R | 8 +--R \| 2b +--R + +--R +------------------------+ +--R 5 3 2 | 2 2 2 +--R (2a + 8a + 8a)b \|- b x - 2a b x - a + 1 +--R * +--R +------------------------------------+ +--R | +--------------+ +--R | | 6 4 2 +--R | 4 |a + 4a + 4a 4 2 +--R |8b |-------------- - a - 12a - 4 +--R | | 8 +--R | \| 2b +--R |------------------------------------ +--R | 4 +--R \| 4b +--R + +--R +--------------+ +--R | 6 4 2 +--R 4 2 5 5 3 4 |a + 4a + 4a +--R ((- 2a + 8a - 8)b x + (- 2a + 8a - 8a)b ) |-------------- +--R | 8 +--R \| 2b +--R + +--R 7 5 3 +--R a - 2a - 4a + 8a +--R + +--R - +--R +--------------------------------------+ +--R | +--------------+ +--R | | 6 4 2 +--R | 4 |a + 4a + 4a 4 2 +--R |- 8b |-------------- - a - 12a - 4 +--R | | 8 +--R 2 | \| 2b +--R b |-------------------------------------- +--R | 4 +--R \| 4b +--R * +--R log +--R +--------------+ +--R +------------------------+ | 6 4 2 +--R 6 | 2 2 2 |a + 4a + 4a +--R 8a b \|- b x - 2a b x - a + 1 |-------------- +--R | 8 +--R \| 2b +--R + +--R +------------------------+ +--R 5 3 2 | 2 2 2 +--R (- 2a - 8a - 8a)b \|- b x - 2a b x - a + 1 +--R * +--R +--------------------------------------+ +--R | +--------------+ +--R | | 6 4 2 +--R | 4 |a + 4a + 4a 4 2 +--R |- 8b |-------------- - a - 12a - 4 +--R | | 8 +--R | \| 2b +--R |-------------------------------------- +--R | 4 +--R \| 4b +--R + +--R +--------------+ +--R | 6 4 2 +--R 4 2 5 5 3 4 |a + 4a + 4a 7 +--R ((2a - 8a + 8)b x + (2a - 8a + 8a)b ) |-------------- + a +--R | 8 +--R \| 2b +--R + +--R 5 3 +--R - 2a - 4a + 8a +--R + +--R +--------------------------------------+ +--R | +--------------+ +--R | | 6 4 2 +--R | 4 |a + 4a + 4a 4 2 +--R |- 8b |-------------- - a - 12a - 4 +--R | | 8 +--R 2 | \| 2b +--R b |-------------------------------------- +--R | 4 +--R \| 4b +--R * +--R log +--R +--------------+ +--R +------------------------+ | 6 4 2 +--R 6 | 2 2 2 |a + 4a + 4a +--R - 8a b \|- b x - 2a b x - a + 1 |-------------- +--R | 8 +--R \| 2b +--R + +--R +------------------------+ +--R 5 3 2 | 2 2 2 +--R (2a + 8a + 8a)b \|- b x - 2a b x - a + 1 +--R * +--R +--------------------------------------+ +--R | +--------------+ +--R | | 6 4 2 +--R | 4 |a + 4a + 4a 4 2 +--R |- 8b |-------------- - a - 12a - 4 +--R | | 8 +--R | \| 2b +--R |-------------------------------------- +--R | 4 +--R \| 4b +--R + +--R +--------------+ +--R | 6 4 2 +--R 4 2 5 5 3 4 |a + 4a + 4a 7 +--R ((2a - 8a + 8)b x + (2a - 8a + 8a)b ) |-------------- + a +--R | 8 +--R \| 2b +--R + +--R 5 3 +--R - 2a - 4a + 8a +--R + +--R - +--R +------------------------------------+ +--R | +--------------+ +--R | | 6 4 2 +--R | 4 |a + 4a + 4a 4 2 +--R |8b |-------------- - a - 12a - 4 +--R | | 8 +--R 2 | \| 2b +--R b |------------------------------------ +--R | 4 +--R \| 4b +--R * +--R log +--R +--------------+ +--R +------------------------+ | 6 4 2 +--R 6 | 2 2 2 |a + 4a + 4a +--R - 8a b \|- b x - 2a b x - a + 1 |-------------- +--R | 8 +--R \| 2b +--R + +--R +------------------------+ +--R 5 3 2 | 2 2 2 +--R (- 2a - 8a - 8a)b \|- b x - 2a b x - a + 1 +--R * +--R +------------------------------------+ +--R | +--------------+ +--R | | 6 4 2 +--R | 4 |a + 4a + 4a 4 2 +--R |8b |-------------- - a - 12a - 4 +--R | | 8 +--R | \| 2b +--R |------------------------------------ +--R | 4 +--R \| 4b +--R + +--R +--------------+ +--R | 6 4 2 +--R 4 2 5 5 3 4 |a + 4a + 4a +--R ((- 2a + 8a - 8)b x + (- 2a + 8a - 8a)b ) |-------------- +--R | 8 +--R \| 2b +--R + +--R 7 5 3 +--R a - 2a - 4a + 8a +--R + +--R +------------------------+ +--R | 2 2 2 +--R 2 2 2\|- b x - 2a b x - a + 1 +--R - b x atan(----------------------------) +--R 2 2 2 +--R b x + 2a b x + a +--R + +--R +------------------------+ +--R b x + a | 2 2 2 +--R - 4a atan(---------------------------) - 2\|- b x - 2a b x - a + 1 +--R +------------------------+ +--R | 2 2 2 +--R \|- b x - 2a b x - a + 1 +--R / +--R 2 +--R 4b +--R Type: Union(Expression Integer,...) +--E 215 + +--S 216 of 477 +m0040:= a0040-r0040 +--R +--R +--R (168) +--R +------------------------------------+ +--R | +--------------+ +--R | | 6 4 2 +--R | 4 |a + 4a + 4a 4 2 +--R |8b |-------------- - a - 12a - 4 +--R | | 8 +--R 2 | \| 2b +--R b |------------------------------------ +--R | 4 +--R \| 4b +--R * +--R log +--R +--------------+ +--R +------------------------+ | 6 4 2 +--R 6 | 2 2 2 |a + 4a + 4a +--R 8a b \|- b x - 2a b x - a + 1 |-------------- +--R | 8 +--R \| 2b +--R + +--R +------------------------+ +--R 5 3 2 | 2 2 2 +--R (2a + 8a + 8a)b \|- b x - 2a b x - a + 1 +--R * +--R +------------------------------------+ +--R | +--------------+ +--R | | 6 4 2 +--R | 4 |a + 4a + 4a 4 2 +--R |8b |-------------- - a - 12a - 4 +--R | | 8 +--R | \| 2b +--R |------------------------------------ +--R | 4 +--R \| 4b +--R + +--R +--------------+ +--R | 6 4 2 +--R 4 2 5 5 3 4 |a + 4a + 4a +--R ((- 2a + 8a - 8)b x + (- 2a + 8a - 8a)b ) |-------------- +--R | 8 +--R \| 2b +--R + +--R 7 5 3 +--R a - 2a - 4a + 8a +--R + +--R - +--R +--------------------------------------+ +--R | +--------------+ +--R | | 6 4 2 +--R | 4 |a + 4a + 4a 4 2 +--R |- 8b |-------------- - a - 12a - 4 +--R | | 8 +--R 2 | \| 2b +--R b |-------------------------------------- +--R | 4 +--R \| 4b +--R * +--R log +--R +--------------+ +--R +------------------------+ | 6 4 2 +--R 6 | 2 2 2 |a + 4a + 4a +--R 8a b \|- b x - 2a b x - a + 1 |-------------- +--R | 8 +--R \| 2b +--R + +--R +------------------------+ +--R 5 3 2 | 2 2 2 +--R (- 2a - 8a - 8a)b \|- b x - 2a b x - a + 1 +--R * +--R +--------------------------------------+ +--R | +--------------+ +--R | | 6 4 2 +--R | 4 |a + 4a + 4a 4 2 +--R |- 8b |-------------- - a - 12a - 4 +--R | | 8 +--R | \| 2b +--R |-------------------------------------- +--R | 4 +--R \| 4b +--R + +--R +--------------+ +--R | 6 4 2 +--R 4 2 5 5 3 4 |a + 4a + 4a 7 +--R ((2a - 8a + 8)b x + (2a - 8a + 8a)b ) |-------------- + a +--R | 8 +--R \| 2b +--R + +--R 5 3 +--R - 2a - 4a + 8a +--R + +--R +--------------------------------------+ +--R | +--------------+ +--R | | 6 4 2 +--R | 4 |a + 4a + 4a 4 2 +--R |- 8b |-------------- - a - 12a - 4 +--R | | 8 +--R 2 | \| 2b +--R b |-------------------------------------- +--R | 4 +--R \| 4b +--R * +--R log +--R +--------------+ +--R +------------------------+ | 6 4 2 +--R 6 | 2 2 2 |a + 4a + 4a +--R - 8a b \|- b x - 2a b x - a + 1 |-------------- +--R | 8 +--R \| 2b +--R + +--R +------------------------+ +--R 5 3 2 | 2 2 2 +--R (2a + 8a + 8a)b \|- b x - 2a b x - a + 1 +--R * +--R +--------------------------------------+ +--R | +--------------+ +--R | | 6 4 2 +--R | 4 |a + 4a + 4a 4 2 +--R |- 8b |-------------- - a - 12a - 4 +--R | | 8 +--R | \| 2b +--R |-------------------------------------- +--R | 4 +--R \| 4b +--R + +--R +--------------+ +--R | 6 4 2 +--R 4 2 5 5 3 4 |a + 4a + 4a 7 +--R ((2a - 8a + 8)b x + (2a - 8a + 8a)b ) |-------------- + a +--R | 8 +--R \| 2b +--R + +--R 5 3 +--R - 2a - 4a + 8a +--R + +--R - +--R +------------------------------------+ +--R | +--------------+ +--R | | 6 4 2 +--R | 4 |a + 4a + 4a 4 2 +--R |8b |-------------- - a - 12a - 4 +--R | | 8 +--R 2 | \| 2b +--R b |------------------------------------ +--R | 4 +--R \| 4b +--R * +--R log +--R +--------------+ +--R +------------------------+ | 6 4 2 +--R 6 | 2 2 2 |a + 4a + 4a +--R - 8a b \|- b x - 2a b x - a + 1 |-------------- +--R | 8 +--R \| 2b +--R + +--R +------------------------+ +--R 5 3 2 | 2 2 2 +--R (- 2a - 8a - 8a)b \|- b x - 2a b x - a + 1 +--R * +--R +------------------------------------+ +--R | +--------------+ +--R | | 6 4 2 +--R | 4 |a + 4a + 4a 4 2 +--R |8b |-------------- - a - 12a - 4 +--R | | 8 +--R | \| 2b +--R |------------------------------------ +--R | 4 +--R \| 4b +--R + +--R +--------------+ +--R | 6 4 2 +--R 4 2 5 5 3 4 |a + 4a + 4a +--R ((- 2a + 8a - 8)b x + (- 2a + 8a - 8a)b ) |-------------- +--R | 8 +--R \| 2b +--R + +--R 7 5 3 +--R a - 2a - 4a + 8a +--R + +--R +----------------------+ +--R | 2 2 2 +--R |b x + 2a b x + a - 1 +--R 4a atanh( |---------------------- ) +--R | 2 2 2 +--R \| b x + 2a b x + a +--R + +--R +------------------------+ +--R | 2 2 2 +--R 2 2 2\|- b x - 2a b x - a + 1 +--R - b x atan(----------------------------) +--R 2 2 2 +--R b x + 2a b x + a +--R + +--R b x + a +--R - 4a atan(---------------------------) +--R +------------------------+ +--R | 2 2 2 +--R \|- b x - 2a b x - a + 1 +--R + +--R +----------------------+ +--R | 2 2 2 +------------------------+ +--R |b x + 2a b x + a - 1 | 2 2 2 +--R (- 2b x - 2a) |---------------------- - 2\|- b x - 2a b x - a + 1 +--R | 2 2 2 +--R \| b x + 2a b x + a +--R + +--R 2 2 2 +--R (- 2b x + 2a )acsc(b x + a) +--R / +--R 2 +--R 4b +--R Type: Expression Integer +--E 216 + +--S 217 of 477 +d0040:= D(m0040,x) +--R +--R +--R (169) +--R +----------------------+ +--R | 2 2 2 +----------------------+ +--R 2 2 |b x + 2a b x + a - 1 | 2 2 2 +--R (- b x - a b x) |---------------------- \|b x + 2a b x + a - 1 +--R | 2 2 2 +--R \| b x + 2a b x + a +--R * +--R +------------------------+ +--R | 2 2 2 +--R 2\|- b x - 2a b x - a + 1 +--R atan(----------------------------) +--R 2 2 2 +--R b x + 2a b x + a +--R + +--R +----------------------+ +--R | 2 2 2 +--R 2 2 |b x + 2a b x + a - 1 +--R ((- 2b x - 2a b x)acsc(b x + a) |---------------------- - b x + a) +--R | 2 2 2 +--R \| b x + 2a b x + a +--R * +--R +----------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - 1 +--R + +--R +----------------------+ +--R | 2 2 2 +--R 2 2 2 |b x + 2a b x + a - 1 +--R (b x - a ) |---------------------- +--R | 2 2 2 +--R \| b x + 2a b x + a +--R / +--R +----------------------+ +--R | 2 2 2 +----------------------+ +--R 2 |b x + 2a b x + a - 1 | 2 2 2 +--R (2b x + 2a b) |---------------------- \|b x + 2a b x + a - 1 +--R | 2 2 2 +--R \| b x + 2a b x + a +--R Type: Expression Integer +--E 217 + +--S 218 of 477 +t0041:= x^2*acsc(a+b*x) +--R +--R +--R 2 +--R (170) x acsc(b x + a) +--R Type: Expression Integer +--E 218 + +--S 219 of 477 +r0041:= -a*(a+b*x)*(1-1/(a+b*x)^2)^(1/2)/b^3+1/6*(a+b*x)^2*_ + (1-1/(a+b*x)^2)^(1/2)/b^3+a^2*(a+b*x)*acsc(a+b*x)/b^3-_ + a*(a+b*x)^2*acsc(a+b*x)/b^3+1/3*(a+b*x)^3*acsc(a+b*x)/b^3+_ + 1/6*atanh((1-1/(a+b*x)^2)^(1/2))/b^3+_ + a^2*atanh((1-1/(a+b*x)^2)^(1/2))/b^3 +--R +--R +--R (171) +--R +----------------------+ +--R | 2 2 2 +--R 2 |b x + 2a b x + a - 1 +--R (6a + 1)atanh( |---------------------- ) +--R | 2 2 2 +--R \| b x + 2a b x + a +--R + +--R +----------------------+ +--R | 2 2 2 +--R 2 2 2 |b x + 2a b x + a - 1 3 3 3 +--R (b x - 4a b x - 5a ) |---------------------- + (2b x + 2a )acsc(b x + a) +--R | 2 2 2 +--R \| b x + 2a b x + a +--R / +--R 3 +--R 6b +--R Type: Expression Integer +--E 219 + +--S 220 of 477 +a0041:= integrate(t0041,x) +--R +--R +--R (172) +--R - +--R 3 +--R 3b +--R * +--R ROOT +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R 6 |18a + 240a + 944a + 960a + 288a 6 4 +--R 18b |------------------------------------- - a - 30a +--R | 12 +--R \| 81b +--R + +--R 2 +--R - 60a - 8 +--R / +--R 6 +--R 9b +--R * +--R log +--R +------------------------+ +--R 2 9 | 2 2 2 +--R (81a + 54)b \|- b x - 2a b x - a + 1 +--R * +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R |18a + 240a + 944a + 960a + 288a +--R |------------------------------------- +--R | 12 +--R \| 81b +--R + +--R +------------------------+ +--R 8 6 4 2 3 | 2 2 2 +--R (9a + 114a + 396a + 216a )b \|- b x - 2a b x - a + 1 +--R * +--R ROOT +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R 6 |18a + 240a + 944a + 960a + 288a 6 +--R 18b |------------------------------------- - a +--R | 12 +--R \| 81b +--R + +--R 4 2 +--R - 30a - 60a - 8 +--R / +--R 6 +--R 9b +--R + +--R 6 4 2 7 +--R (- 9a + 54a - 108a + 72)b x +--R + +--R 7 5 3 6 +--R (- 9a + 54a - 108a + 72a)b +--R * +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R |18a + 240a + 944a + 960a + 288a +--R |------------------------------------- +--R | 12 +--R \| 81b +--R + +--R 11 9 7 5 3 +--R 3a + 2a - 72a + 144a - 16a - 96a +--R + +--R 3 +--R 3b +--R * +--R ROOT +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R 6 |18a + 240a + 944a + 960a + 288a 6 4 +--R - 18b |------------------------------------- - a - 30a +--R | 12 +--R \| 81b +--R + +--R 2 +--R - 60a - 8 +--R / +--R 6 +--R 9b +--R * +--R log +--R +------------------------+ +--R 2 9 | 2 2 2 +--R (81a + 54)b \|- b x - 2a b x - a + 1 +--R * +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R |18a + 240a + 944a + 960a + 288a +--R |------------------------------------- +--R | 12 +--R \| 81b +--R + +--R +------------------------+ +--R 8 6 4 2 3 | 2 2 2 +--R (- 9a - 114a - 396a - 216a )b \|- b x - 2a b x - a + 1 +--R * +--R ROOT +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R 6 |18a + 240a + 944a + 960a + 288a 6 +--R - 18b |------------------------------------- - a +--R | 12 +--R \| 81b +--R + +--R 4 2 +--R - 30a - 60a - 8 +--R / +--R 6 +--R 9b +--R + +--R 6 4 2 7 7 5 3 6 +--R ((9a - 54a + 108a - 72)b x + (9a - 54a + 108a - 72a)b ) +--R * +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R |18a + 240a + 944a + 960a + 288a +--R |------------------------------------- +--R | 12 +--R \| 81b +--R + +--R 11 9 7 5 3 +--R 3a + 2a - 72a + 144a - 16a - 96a +--R + +--R - +--R 3 +--R 3b +--R * +--R ROOT +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R 6 |18a + 240a + 944a + 960a + 288a 6 4 +--R - 18b |------------------------------------- - a - 30a +--R | 12 +--R \| 81b +--R + +--R 2 +--R - 60a - 8 +--R / +--R 6 +--R 9b +--R * +--R log +--R +------------------------+ +--R 2 9 | 2 2 2 +--R (- 81a - 54)b \|- b x - 2a b x - a + 1 +--R * +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R |18a + 240a + 944a + 960a + 288a +--R |------------------------------------- +--R | 12 +--R \| 81b +--R + +--R +------------------------+ +--R 8 6 4 2 3 | 2 2 2 +--R (9a + 114a + 396a + 216a )b \|- b x - 2a b x - a + 1 +--R * +--R ROOT +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R 6 |18a + 240a + 944a + 960a + 288a 6 +--R - 18b |------------------------------------- - a +--R | 12 +--R \| 81b +--R + +--R 4 2 +--R - 30a - 60a - 8 +--R / +--R 6 +--R 9b +--R + +--R 6 4 2 7 7 5 3 6 +--R ((9a - 54a + 108a - 72)b x + (9a - 54a + 108a - 72a)b ) +--R * +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R |18a + 240a + 944a + 960a + 288a +--R |------------------------------------- +--R | 12 +--R \| 81b +--R + +--R 11 9 7 5 3 +--R 3a + 2a - 72a + 144a - 16a - 96a +--R + +--R 3 +--R 3b +--R * +--R +-------------------------------------------------------------------+ +--R | +-------------------------------------+ +--R | | 10 8 6 4 2 +--R | 6 |18a + 240a + 944a + 960a + 288a 6 4 2 +--R |18b |------------------------------------- - a - 30a - 60a - 8 +--R | | 12 +--R | \| 81b +--R |------------------------------------------------------------------- +--R | 6 +--R \| 9b +--R * +--R log +--R +------------------------+ +--R 2 9 | 2 2 2 +--R (- 81a - 54)b \|- b x - 2a b x - a + 1 +--R * +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R |18a + 240a + 944a + 960a + 288a +--R |------------------------------------- +--R | 12 +--R \| 81b +--R + +--R +------------------------+ +--R 8 6 4 2 3 | 2 2 2 +--R (- 9a - 114a - 396a - 216a )b \|- b x - 2a b x - a + 1 +--R * +--R ROOT +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R 6 |18a + 240a + 944a + 960a + 288a 6 4 +--R 18b |------------------------------------- - a - 30a +--R | 12 +--R \| 81b +--R + +--R 2 +--R - 60a - 8 +--R / +--R 6 +--R 9b +--R + +--R 6 4 2 7 +--R (- 9a + 54a - 108a + 72)b x +--R + +--R 7 5 3 6 +--R (- 9a + 54a - 108a + 72a)b +--R * +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R |18a + 240a + 944a + 960a + 288a +--R |------------------------------------- +--R | 12 +--R \| 81b +--R + +--R 11 9 7 5 3 +--R 3a + 2a - 72a + 144a - 16a - 96a +--R + +--R +------------------------+ +--R | 2 2 2 +--R 3 3 2\|- b x - 2a b x - a + 1 +--R - 2b x atan(----------------------------) +--R 2 2 2 +--R b x + 2a b x + a +--R + +--R 2 b x + a +--R (12a + 10)atan(---------------------------) +--R +------------------------+ +--R | 2 2 2 +--R \|- b x - 2a b x - a + 1 +--R + +--R +------------------------+ +--R | 2 2 2 +--R (- 2b x + 10a)\|- b x - 2a b x - a + 1 +--R / +--R 3 +--R 12b +--R Type: Union(Expression Integer,...) +--E 220 + +--S 221 of 477 +m0041:= a0041-r0041 +--R +--R +--R (173) +--R - +--R 3 +--R 3b +--R * +--R ROOT +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R 6 |18a + 240a + 944a + 960a + 288a 6 4 +--R 18b |------------------------------------- - a - 30a +--R | 12 +--R \| 81b +--R + +--R 2 +--R - 60a - 8 +--R / +--R 6 +--R 9b +--R * +--R log +--R +------------------------+ +--R 2 9 | 2 2 2 +--R (81a + 54)b \|- b x - 2a b x - a + 1 +--R * +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R |18a + 240a + 944a + 960a + 288a +--R |------------------------------------- +--R | 12 +--R \| 81b +--R + +--R +------------------------+ +--R 8 6 4 2 3 | 2 2 2 +--R (9a + 114a + 396a + 216a )b \|- b x - 2a b x - a + 1 +--R * +--R ROOT +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R 6 |18a + 240a + 944a + 960a + 288a 6 +--R 18b |------------------------------------- - a +--R | 12 +--R \| 81b +--R + +--R 4 2 +--R - 30a - 60a - 8 +--R / +--R 6 +--R 9b +--R + +--R 6 4 2 7 +--R (- 9a + 54a - 108a + 72)b x +--R + +--R 7 5 3 6 +--R (- 9a + 54a - 108a + 72a)b +--R * +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R |18a + 240a + 944a + 960a + 288a +--R |------------------------------------- +--R | 12 +--R \| 81b +--R + +--R 11 9 7 5 3 +--R 3a + 2a - 72a + 144a - 16a - 96a +--R + +--R 3 +--R 3b +--R * +--R ROOT +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R 6 |18a + 240a + 944a + 960a + 288a 6 4 +--R - 18b |------------------------------------- - a - 30a +--R | 12 +--R \| 81b +--R + +--R 2 +--R - 60a - 8 +--R / +--R 6 +--R 9b +--R * +--R log +--R +------------------------+ +--R 2 9 | 2 2 2 +--R (81a + 54)b \|- b x - 2a b x - a + 1 +--R * +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R |18a + 240a + 944a + 960a + 288a +--R |------------------------------------- +--R | 12 +--R \| 81b +--R + +--R +------------------------+ +--R 8 6 4 2 3 | 2 2 2 +--R (- 9a - 114a - 396a - 216a )b \|- b x - 2a b x - a + 1 +--R * +--R ROOT +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R 6 |18a + 240a + 944a + 960a + 288a 6 +--R - 18b |------------------------------------- - a +--R | 12 +--R \| 81b +--R + +--R 4 2 +--R - 30a - 60a - 8 +--R / +--R 6 +--R 9b +--R + +--R 6 4 2 7 7 5 3 6 +--R ((9a - 54a + 108a - 72)b x + (9a - 54a + 108a - 72a)b ) +--R * +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R |18a + 240a + 944a + 960a + 288a +--R |------------------------------------- +--R | 12 +--R \| 81b +--R + +--R 11 9 7 5 3 +--R 3a + 2a - 72a + 144a - 16a - 96a +--R + +--R - +--R 3 +--R 3b +--R * +--R ROOT +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R 6 |18a + 240a + 944a + 960a + 288a 6 4 +--R - 18b |------------------------------------- - a - 30a +--R | 12 +--R \| 81b +--R + +--R 2 +--R - 60a - 8 +--R / +--R 6 +--R 9b +--R * +--R log +--R +------------------------+ +--R 2 9 | 2 2 2 +--R (- 81a - 54)b \|- b x - 2a b x - a + 1 +--R * +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R |18a + 240a + 944a + 960a + 288a +--R |------------------------------------- +--R | 12 +--R \| 81b +--R + +--R +------------------------+ +--R 8 6 4 2 3 | 2 2 2 +--R (9a + 114a + 396a + 216a )b \|- b x - 2a b x - a + 1 +--R * +--R ROOT +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R 6 |18a + 240a + 944a + 960a + 288a 6 +--R - 18b |------------------------------------- - a +--R | 12 +--R \| 81b +--R + +--R 4 2 +--R - 30a - 60a - 8 +--R / +--R 6 +--R 9b +--R + +--R 6 4 2 7 7 5 3 6 +--R ((9a - 54a + 108a - 72)b x + (9a - 54a + 108a - 72a)b ) +--R * +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R |18a + 240a + 944a + 960a + 288a +--R |------------------------------------- +--R | 12 +--R \| 81b +--R + +--R 11 9 7 5 3 +--R 3a + 2a - 72a + 144a - 16a - 96a +--R + +--R 3 +--R 3b +--R * +--R +-------------------------------------------------------------------+ +--R | +-------------------------------------+ +--R | | 10 8 6 4 2 +--R | 6 |18a + 240a + 944a + 960a + 288a 6 4 2 +--R |18b |------------------------------------- - a - 30a - 60a - 8 +--R | | 12 +--R | \| 81b +--R |------------------------------------------------------------------- +--R | 6 +--R \| 9b +--R * +--R log +--R +------------------------+ +--R 2 9 | 2 2 2 +--R (- 81a - 54)b \|- b x - 2a b x - a + 1 +--R * +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R |18a + 240a + 944a + 960a + 288a +--R |------------------------------------- +--R | 12 +--R \| 81b +--R + +--R +------------------------+ +--R 8 6 4 2 3 | 2 2 2 +--R (- 9a - 114a - 396a - 216a )b \|- b x - 2a b x - a + 1 +--R * +--R ROOT +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R 6 |18a + 240a + 944a + 960a + 288a 6 4 +--R 18b |------------------------------------- - a - 30a +--R | 12 +--R \| 81b +--R + +--R 2 +--R - 60a - 8 +--R / +--R 6 +--R 9b +--R + +--R 6 4 2 7 +--R (- 9a + 54a - 108a + 72)b x +--R + +--R 7 5 3 6 +--R (- 9a + 54a - 108a + 72a)b +--R * +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R |18a + 240a + 944a + 960a + 288a +--R |------------------------------------- +--R | 12 +--R \| 81b +--R + +--R 11 9 7 5 3 +--R 3a + 2a - 72a + 144a - 16a - 96a +--R + +--R +----------------------+ +--R | 2 2 2 +--R 2 |b x + 2a b x + a - 1 +--R (- 12a - 2)atanh( |---------------------- ) +--R | 2 2 2 +--R \| b x + 2a b x + a +--R + +--R +------------------------+ +--R | 2 2 2 +--R 3 3 2\|- b x - 2a b x - a + 1 +--R - 2b x atan(----------------------------) +--R 2 2 2 +--R b x + 2a b x + a +--R + +--R 2 b x + a +--R (12a + 10)atan(---------------------------) +--R +------------------------+ +--R | 2 2 2 +--R \|- b x - 2a b x - a + 1 +--R + +--R +----------------------+ +--R | 2 2 2 +--R 2 2 2 |b x + 2a b x + a - 1 +--R (- 2b x + 8a b x + 10a ) |---------------------- +--R | 2 2 2 +--R \| b x + 2a b x + a +--R + +--R +------------------------+ +--R | 2 2 2 3 3 3 +--R (- 2b x + 10a)\|- b x - 2a b x - a + 1 + (- 4b x - 4a )acsc(b x + a) +--R / +--R 3 +--R 12b +--R Type: Expression Integer +--E 221 + +--S 222 of 477 +d0041:= D(m0041,x) +--R +--R +--R (174) +--R +----------------------+ +--R | 2 2 2 +----------------------+ +--R 3 3 2 2 |b x + 2a b x + a - 1 | 2 2 2 +--R (- 3b x - 3a b x ) |---------------------- \|b x + 2a b x + a - 1 +--R | 2 2 2 +--R \| b x + 2a b x + a +--R * +--R +------------------------+ +--R | 2 2 2 +--R 2\|- b x - 2a b x - a + 1 +--R atan(----------------------------) +--R 2 2 2 +--R b x + 2a b x + a +--R + +--R +----------------------+ +--R | 2 2 2 +--R 3 3 2 2 |b x + 2a b x + a - 1 2 2 +--R (- 6b x - 6a b x )acsc(b x + a) |---------------------- - 2b x +--R | 2 2 2 +--R \| b x + 2a b x + a +--R + +--R 2 +--R 2a b x - 2a +--R * +--R +----------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - 1 +--R + +--R +----------------------+ +--R | 2 2 2 +--R 3 3 3 |b x + 2a b x + a - 1 +--R (2b x + 2a ) |---------------------- +--R | 2 2 2 +--R \| b x + 2a b x + a +--R / +--R +----------------------+ +--R | 2 2 2 +----------------------+ +--R 3 2 |b x + 2a b x + a - 1 | 2 2 2 +--R (6b x + 6a b ) |---------------------- \|b x + 2a b x + a - 1 +--R | 2 2 2 +--R \| b x + 2a b x + a +--R Type: Expression Integer +--E 222 + +--S 223 of 477 +t0042:= acsc(x^(1/2)) +--R +--R +--R +-+ +--R (175) acsc(\|x ) +--R Type: Expression Integer +--E 223 + +--S 224 of 477 +r0042:= (-1+x)^(1/2)+x*acsc(x^(1/2)) +--R +--R +--R +-+ +-----+ +--R (176) x acsc(\|x ) + \|x - 1 +--R Type: Expression Integer +--E 224 + +--S 225 of 477 +a0042:= integrate(t0042,x) +--R +--R +--R +-------+ +--R 2\|- x + 1 +-------+ +--R (- x + 2)atan(-----------) - 2\|- x + 1 +--R x +--R (177) ---------------------------------------- +--R 2 +--R Type: Union(Expression Integer,...) +--E 225 + +--S 226 of 477 +m0042:= a0042-r0042 +--R +--R +--R +-------+ +--R 2\|- x + 1 +-+ +-----+ +-------+ +--R (- x + 2)atan(-----------) - 2x acsc(\|x ) - 2\|x - 1 - 2\|- x + 1 +--R x +--R (178) -------------------------------------------------------------------- +--R 2 +--R Type: Expression Integer +--E 226 + +--S 227 of 477 +d0042:= D(m0042,x) +--R +--R +--R +-------+ +--R 2\|- x + 1 +-+ +--R - atan(-----------) - 2acsc(\|x ) +--R x +--R (179) --------------------------------- +--R 2 +--R Type: Expression Integer +--E 227 + +--S 228 of 477 +t0043:= acsc(x^(1/2))/x +--R +--R +--R +-+ +--R acsc(\|x ) +--R (180) ---------- +--R x +--R Type: Expression Integer +--E 228 + +--S 229 of 477 +r0043:= %i*acsc(x^(1/2))^2-2*acsc(x^(1/2))*log(1-((1-1/x)^(1/2)+_ + %i/x^(1/2))^2)+%i*polylog(2,((1-1/x)^(1/2)+%i/x^(1/2))^2) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Complex Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 229 + +--S 230 of 477 +a0043:= integrate(t0043,x) +--R +--R +--R x +--+ +--R ++ acsc(\|%Q ) +--R (181) | ----------- d%Q +--R ++ %Q +--R Type: Union(Expression Integer,...) +--E 230 + +--S 231 of 477 +--m0043:= a0043-r0043 +--E 231 + +--S 232 of 477 +--d0043:= D(m0043,x) +--E 232 + +--S 233 of 477 +t0044:= acsc(x^(1/2))/x^2 +--R +--R +--R +-+ +--R acsc(\|x ) +--R (182) ---------- +--R 2 +--R x +--R Type: Expression Integer +--E 233 + +--S 234 of 477 +r0044:= -1/2*((-1+x)^(1/2)-x*acsc(x^(1/2))+2*acsc(x^(1/2)))/x +--R +--R +--R +-+ +-----+ +--R (x - 2)acsc(\|x ) - \|x - 1 +--R (183) ---------------------------- +--R 2x +--R Type: Expression Integer +--E 234 + +--S 235 of 477 +a0044:= integrate(t0044,x) +--R +--R +--R (184) +--R +-------+ +--R +-------+ +-------+ 2\|- x + 1 +--R - x log(\|- x + 1 + 1) + x log(\|- x + 1 - 1) + (- x + 2)atan(-----------) +--R x +--R ---------------------------------------------------------------------------- +--R 4x +--R Type: Union(Expression Integer,...) +--E 235 + +--S 236 of 477 +m0044:= a0044-r0044 +--R +--R +--R (185) +--R +-------+ +-------+ +--R - x log(\|- x + 1 + 1) + x log(\|- x + 1 - 1) +--R + +--R +-------+ +--R 2\|- x + 1 +-+ +-----+ +--R (- x + 2)atan(-----------) + (- 2x + 4)acsc(\|x ) + 2\|x - 1 +--R x +--R / +--R 4x +--R Type: Expression Integer +--E 236 + +--S 237 of 477 +d0044:= D(m0044,x) +--R +--R +--R +-------+ +--R 2\|- x + 1 +-+ +--R - atan(-----------) - 2acsc(\|x ) +--R x +--R (186) --------------------------------- +--R 2 +--R 2x +--R Type: Expression Integer +--E 237 + +--S 238 of 477 +t0045:= acsc(x^(1/2))/x^3 +--R +--R +--R +-+ +--R acsc(\|x ) +--R (187) ---------- +--R 3 +--R x +--R Type: Expression Integer +--E 238 + +--S 239 of 477 +r0045:= -1/16*(2*(-1+x)^(1/2)+3*(-1+x)^(1/2)*x-3*x^2*acsc(x^(1/2))+_ + 8*acsc(x^(1/2)))/x^2 +--R +--R +--R 2 +-+ +-----+ +--R (3x - 8)acsc(\|x ) + (- 3x - 2)\|x - 1 +--R (188) ---------------------------------------- +--R 2 +--R 16x +--R Type: Expression Integer +--E 239 + +--S 240 of 477 +a0045:= integrate(t0045,x) +--R +--R +--R (189) +--R 2 +-------+ 2 +-------+ +--R - 2x log(\|- x + 1 + 1) + 2x log(\|- x + 1 - 1) +--R + +--R +-------+ +--R 2 2\|- x + 1 +-------+ +--R (- x + 4)atan(-----------) - 2x\|- x + 1 +--R x +--R / +--R 2 +--R 16x +--R Type: Union(Expression Integer,...) +--E 240 + +--S 241 of 477 +m0045:= a0045-r0045 +--R +--R +--R (190) +--R 2 +-------+ 2 +-------+ +--R - 2x log(\|- x + 1 + 1) + 2x log(\|- x + 1 - 1) +--R + +--R +-------+ +--R 2 2\|- x + 1 2 +-+ +-----+ +--R (- x + 4)atan(-----------) + (- 3x + 8)acsc(\|x ) + (3x + 2)\|x - 1 +--R x +--R + +--R +-------+ +--R - 2x\|- x + 1 +--R / +--R 2 +--R 16x +--R Type: Expression Integer +--E 241 + +--S 242 of 477 +d0045:= D(m0045,x) +--R +--R +--R +-------+ +--R 2\|- x + 1 +-+ +--R - atan(-----------) - 2acsc(\|x ) +--R x +--R (191) --------------------------------- +--R 3 +--R 2x +--R Type: Expression Integer +--E 242 + +--S 243 of 477 +t0046:= asec(a+b*x) +--R +--R +--R (192) asec(b x + a) +--R Type: Expression Integer +--E 243 + +--S 244 of 477 +r0046:= (a+b*x)*asec(a+b*x)/b-atanh((1-1/(a+b*x)^2)^(1/2))/b +--R +--R +--R +----------------------+ +--R | 2 2 2 +--R |b x + 2a b x + a - 1 +--R - atanh( |---------------------- ) + (b x + a)asec(b x + a) +--R | 2 2 2 +--R \| b x + 2a b x + a +--R (193) ----------------------------------------------------------- +--R b +--R Type: Expression Integer +--E 244 + +--S 245 of 477 +a0046:= integrate(t0046,x) +--R +--R +--R (194) +--R +------------------+ +--R | +---+ +--R | | 2 +--R | 2 |2a 2 +--R |2b |--- - a - 2 +--R | | 4 +--R | \| b +--R b |------------------ +--R | 2 +--R \| b +--R * +--R log +--R +---+ +--R +------------------------+ | 2 +--R 3 | 2 2 2 |2a +--R b \|- b x - 2a b x - a + 1 |--- +--R | 4 +--R \| b +--R + +--R +------------------------+ +--R 2 | 2 2 2 +--R a b\|- b x - 2a b x - a + 1 +--R * +--R +------------------+ +--R | +---+ +--R | | 2 +--R | 2 |2a 2 +--R |2b |--- - a - 2 +--R | | 4 +--R | \| b +--R |------------------ +--R | 2 +--R \| b +--R + +--R +---+ +--R | 2 +--R 2 3 3 2 |2a 3 +--R ((- a + 2)b x + (- a + 2a)b ) |--- + a - 2a +--R | 4 +--R \| b +--R + +--R - +--R +--------------------+ +--R | +---+ +--R | | 2 +--R | 2 |2a 2 +--R |- 2b |--- - a - 2 +--R | | 4 +--R | \| b +--R b |-------------------- +--R | 2 +--R \| b +--R * +--R log +--R +---+ +--R +------------------------+ | 2 +--R 3 | 2 2 2 |2a +--R b \|- b x - 2a b x - a + 1 |--- +--R | 4 +--R \| b +--R + +--R +------------------------+ +--R 2 | 2 2 2 +--R - a b\|- b x - 2a b x - a + 1 +--R * +--R +--------------------+ +--R | +---+ +--R | | 2 +--R | 2 |2a 2 +--R |- 2b |--- - a - 2 +--R | | 4 +--R | \| b +--R |-------------------- +--R | 2 +--R \| b +--R + +--R +---+ +--R | 2 +--R 2 3 3 2 |2a 3 +--R ((a - 2)b x + (a - 2a)b ) |--- + a - 2a +--R | 4 +--R \| b +--R + +--R +--------------------+ +--R | +---+ +--R | | 2 +--R | 2 |2a 2 +--R |- 2b |--- - a - 2 +--R | | 4 +--R | \| b +--R b |-------------------- +--R | 2 +--R \| b +--R * +--R log +--R +---+ +--R +------------------------+ | 2 +--R 3 | 2 2 2 |2a +--R - b \|- b x - 2a b x - a + 1 |--- +--R | 4 +--R \| b +--R + +--R +------------------------+ +--R 2 | 2 2 2 +--R a b\|- b x - 2a b x - a + 1 +--R * +--R +--------------------+ +--R | +---+ +--R | | 2 +--R | 2 |2a 2 +--R |- 2b |--- - a - 2 +--R | | 4 +--R | \| b +--R |-------------------- +--R | 2 +--R \| b +--R + +--R +---+ +--R | 2 +--R 2 3 3 2 |2a 3 +--R ((a - 2)b x + (a - 2a)b ) |--- + a - 2a +--R | 4 +--R \| b +--R + +--R - +--R +------------------+ +--R | +---+ +--R | | 2 +--R | 2 |2a 2 +--R |2b |--- - a - 2 +--R | | 4 +--R | \| b +--R b |------------------ +--R | 2 +--R \| b +--R * +--R log +--R +---+ +--R +------------------------+ | 2 +--R 3 | 2 2 2 |2a +--R - b \|- b x - 2a b x - a + 1 |--- +--R | 4 +--R \| b +--R + +--R +------------------------+ +--R 2 | 2 2 2 +--R - a b\|- b x - 2a b x - a + 1 +--R * +--R +------------------+ +--R | +---+ +--R | | 2 +--R | 2 |2a 2 +--R |2b |--- - a - 2 +--R | | 4 +--R | \| b +--R |------------------ +--R | 2 +--R \| b +--R + +--R +---+ +--R | 2 +--R 2 3 3 2 |2a 3 +--R ((- a + 2)b x + (- a + 2a)b ) |--- + a - 2a +--R | 4 +--R \| b +--R + +--R +------------------------+ +--R | 2 2 2 +--R 2\|- b x - 2a b x - a + 1 +--R 2b x atan(----------------------------) +--R 2 2 2 +--R b x + 2a b x + a +--R + +--R b x + a +--R - 4atan(---------------------------) +--R +------------------------+ +--R | 2 2 2 +--R \|- b x - 2a b x - a + 1 +--R / +--R 4b +--R Type: Union(Expression Integer,...) +--E 245 + +--S 246 of 477 +m0046:= a0046-r0046 +--R +--R +--R (195) +--R +------------------+ +--R | +---+ +--R | | 2 +--R | 2 |2a 2 +--R |2b |--- - a - 2 +--R | | 4 +--R | \| b +--R b |------------------ +--R | 2 +--R \| b +--R * +--R log +--R +---+ +--R +------------------------+ | 2 +--R 3 | 2 2 2 |2a +--R b \|- b x - 2a b x - a + 1 |--- +--R | 4 +--R \| b +--R + +--R +------------------------+ +--R 2 | 2 2 2 +--R a b\|- b x - 2a b x - a + 1 +--R * +--R +------------------+ +--R | +---+ +--R | | 2 +--R | 2 |2a 2 +--R |2b |--- - a - 2 +--R | | 4 +--R | \| b +--R |------------------ +--R | 2 +--R \| b +--R + +--R +---+ +--R | 2 +--R 2 3 3 2 |2a 3 +--R ((- a + 2)b x + (- a + 2a)b ) |--- + a - 2a +--R | 4 +--R \| b +--R + +--R - +--R +--------------------+ +--R | +---+ +--R | | 2 +--R | 2 |2a 2 +--R |- 2b |--- - a - 2 +--R | | 4 +--R | \| b +--R b |-------------------- +--R | 2 +--R \| b +--R * +--R log +--R +---+ +--R +------------------------+ | 2 +--R 3 | 2 2 2 |2a +--R b \|- b x - 2a b x - a + 1 |--- +--R | 4 +--R \| b +--R + +--R +------------------------+ +--R 2 | 2 2 2 +--R - a b\|- b x - 2a b x - a + 1 +--R * +--R +--------------------+ +--R | +---+ +--R | | 2 +--R | 2 |2a 2 +--R |- 2b |--- - a - 2 +--R | | 4 +--R | \| b +--R |-------------------- +--R | 2 +--R \| b +--R + +--R +---+ +--R | 2 +--R 2 3 3 2 |2a 3 +--R ((a - 2)b x + (a - 2a)b ) |--- + a - 2a +--R | 4 +--R \| b +--R + +--R +--------------------+ +--R | +---+ +--R | | 2 +--R | 2 |2a 2 +--R |- 2b |--- - a - 2 +--R | | 4 +--R | \| b +--R b |-------------------- +--R | 2 +--R \| b +--R * +--R log +--R +---+ +--R +------------------------+ | 2 +--R 3 | 2 2 2 |2a +--R - b \|- b x - 2a b x - a + 1 |--- +--R | 4 +--R \| b +--R + +--R +------------------------+ +--R 2 | 2 2 2 +--R a b\|- b x - 2a b x - a + 1 +--R * +--R +--------------------+ +--R | +---+ +--R | | 2 +--R | 2 |2a 2 +--R |- 2b |--- - a - 2 +--R | | 4 +--R | \| b +--R |-------------------- +--R | 2 +--R \| b +--R + +--R +---+ +--R | 2 +--R 2 3 3 2 |2a 3 +--R ((a - 2)b x + (a - 2a)b ) |--- + a - 2a +--R | 4 +--R \| b +--R + +--R - +--R +------------------+ +--R | +---+ +--R | | 2 +--R | 2 |2a 2 +--R |2b |--- - a - 2 +--R | | 4 +--R | \| b +--R b |------------------ +--R | 2 +--R \| b +--R * +--R log +--R +---+ +--R +------------------------+ | 2 +--R 3 | 2 2 2 |2a +--R - b \|- b x - 2a b x - a + 1 |--- +--R | 4 +--R \| b +--R + +--R +------------------------+ +--R 2 | 2 2 2 +--R - a b\|- b x - 2a b x - a + 1 +--R * +--R +------------------+ +--R | +---+ +--R | | 2 +--R | 2 |2a 2 +--R |2b |--- - a - 2 +--R | | 4 +--R | \| b +--R |------------------ +--R | 2 +--R \| b +--R + +--R +---+ +--R | 2 +--R 2 3 3 2 |2a 3 +--R ((- a + 2)b x + (- a + 2a)b ) |--- + a - 2a +--R | 4 +--R \| b +--R + +--R +----------------------+ +--R | 2 2 2 +--R |b x + 2a b x + a - 1 +--R 4atanh( |---------------------- ) +--R | 2 2 2 +--R \| b x + 2a b x + a +--R + +--R +------------------------+ +--R | 2 2 2 +--R 2\|- b x - 2a b x - a + 1 +--R 2b x atan(----------------------------) +--R 2 2 2 +--R b x + 2a b x + a +--R + +--R b x + a +--R - 4atan(---------------------------) + (- 4b x - 4a)asec(b x + a) +--R +------------------------+ +--R | 2 2 2 +--R \|- b x - 2a b x - a + 1 +--R / +--R 4b +--R Type: Expression Integer +--E 246 + +--S 247 of 477 +d0046:= D(m0046,x) +--R +--R +--R (196) +--R +----------------------+ +--R | 2 2 2 +----------------------+ +--R |b x + 2a b x + a - 1 | 2 2 2 +--R (b x + a) |---------------------- \|b x + 2a b x + a - 1 +--R | 2 2 2 +--R \| b x + 2a b x + a +--R * +--R +------------------------+ +--R | 2 2 2 +--R 2\|- b x - 2a b x - a + 1 +--R atan(----------------------------) +--R 2 2 2 +--R b x + 2a b x + a +--R + +--R +----------------------+ +--R | 2 2 2 +--R |b x + 2a b x + a - 1 +--R ((- 2b x - 2a)asec(b x + a) |---------------------- + 2) +--R | 2 2 2 +--R \| b x + 2a b x + a +--R * +--R +----------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - 1 +--R + +--R +----------------------+ +--R | 2 2 2 +--R |b x + 2a b x + a - 1 +--R (- 2b x - 2a) |---------------------- +--R | 2 2 2 +--R \| b x + 2a b x + a +--R / +--R +----------------------+ +--R | 2 2 2 +----------------------+ +--R |b x + 2a b x + a - 1 | 2 2 2 +--R (2b x + 2a) |---------------------- \|b x + 2a b x + a - 1 +--R | 2 2 2 +--R \| b x + 2a b x + a +--R Type: Expression Integer +--E 247 + +--S 248 of 477 +t0047:= acsc(a+b*x) +--R +--R +--R (197) acsc(b x + a) +--R Type: Expression Integer +--E 248 + +--S 249 of 477 +r0047:= (a+b*x)*acsc(a+b*x)/b+atanh((1-1/(a+b*x)^2)^(1/2))/b +--R +--R +--R +----------------------+ +--R | 2 2 2 +--R |b x + 2a b x + a - 1 +--R atanh( |---------------------- ) + (b x + a)acsc(b x + a) +--R | 2 2 2 +--R \| b x + 2a b x + a +--R (198) --------------------------------------------------------- +--R b +--R Type: Expression Integer +--E 249 + +--S 250 of 477 +a0047:= integrate(t0047,x) +--R +--R +--R (199) +--R - +--R +------------------+ +--R | +---+ +--R | | 2 +--R | 2 |2a 2 +--R |2b |--- - a - 2 +--R | | 4 +--R | \| b +--R b |------------------ +--R | 2 +--R \| b +--R * +--R log +--R +---+ +--R +------------------------+ | 2 +--R 3 | 2 2 2 |2a +--R b \|- b x - 2a b x - a + 1 |--- +--R | 4 +--R \| b +--R + +--R +------------------------+ +--R 2 | 2 2 2 +--R a b\|- b x - 2a b x - a + 1 +--R * +--R +------------------+ +--R | +---+ +--R | | 2 +--R | 2 |2a 2 +--R |2b |--- - a - 2 +--R | | 4 +--R | \| b +--R |------------------ +--R | 2 +--R \| b +--R + +--R +---+ +--R | 2 +--R 2 3 3 2 |2a 3 +--R ((- a + 2)b x + (- a + 2a)b ) |--- + a - 2a +--R | 4 +--R \| b +--R + +--R +--------------------+ +--R | +---+ +--R | | 2 +--R | 2 |2a 2 +--R |- 2b |--- - a - 2 +--R | | 4 +--R | \| b +--R b |-------------------- +--R | 2 +--R \| b +--R * +--R log +--R +---+ +--R +------------------------+ | 2 +--R 3 | 2 2 2 |2a +--R b \|- b x - 2a b x - a + 1 |--- +--R | 4 +--R \| b +--R + +--R +------------------------+ +--R 2 | 2 2 2 +--R - a b\|- b x - 2a b x - a + 1 +--R * +--R +--------------------+ +--R | +---+ +--R | | 2 +--R | 2 |2a 2 +--R |- 2b |--- - a - 2 +--R | | 4 +--R | \| b +--R |-------------------- +--R | 2 +--R \| b +--R + +--R +---+ +--R | 2 +--R 2 3 3 2 |2a 3 +--R ((a - 2)b x + (a - 2a)b ) |--- + a - 2a +--R | 4 +--R \| b +--R + +--R - +--R +--------------------+ +--R | +---+ +--R | | 2 +--R | 2 |2a 2 +--R |- 2b |--- - a - 2 +--R | | 4 +--R | \| b +--R b |-------------------- +--R | 2 +--R \| b +--R * +--R log +--R +---+ +--R +------------------------+ | 2 +--R 3 | 2 2 2 |2a +--R - b \|- b x - 2a b x - a + 1 |--- +--R | 4 +--R \| b +--R + +--R +------------------------+ +--R 2 | 2 2 2 +--R a b\|- b x - 2a b x - a + 1 +--R * +--R +--------------------+ +--R | +---+ +--R | | 2 +--R | 2 |2a 2 +--R |- 2b |--- - a - 2 +--R | | 4 +--R | \| b +--R |-------------------- +--R | 2 +--R \| b +--R + +--R +---+ +--R | 2 +--R 2 3 3 2 |2a 3 +--R ((a - 2)b x + (a - 2a)b ) |--- + a - 2a +--R | 4 +--R \| b +--R + +--R +------------------+ +--R | +---+ +--R | | 2 +--R | 2 |2a 2 +--R |2b |--- - a - 2 +--R | | 4 +--R | \| b +--R b |------------------ +--R | 2 +--R \| b +--R * +--R log +--R +---+ +--R +------------------------+ | 2 +--R 3 | 2 2 2 |2a +--R - b \|- b x - 2a b x - a + 1 |--- +--R | 4 +--R \| b +--R + +--R +------------------------+ +--R 2 | 2 2 2 +--R - a b\|- b x - 2a b x - a + 1 +--R * +--R +------------------+ +--R | +---+ +--R | | 2 +--R | 2 |2a 2 +--R |2b |--- - a - 2 +--R | | 4 +--R | \| b +--R |------------------ +--R | 2 +--R \| b +--R + +--R +---+ +--R | 2 +--R 2 3 3 2 |2a 3 +--R ((- a + 2)b x + (- a + 2a)b ) |--- + a - 2a +--R | 4 +--R \| b +--R + +--R +------------------------+ +--R | 2 2 2 +--R 2\|- b x - 2a b x - a + 1 +--R - 2b x atan(----------------------------) +--R 2 2 2 +--R b x + 2a b x + a +--R + +--R b x + a +--R 4atan(---------------------------) +--R +------------------------+ +--R | 2 2 2 +--R \|- b x - 2a b x - a + 1 +--R / +--R 4b +--R Type: Union(Expression Integer,...) +--E 250 + +--S 251 of 477 +m0047:= a0047-r0047 +--R +--R +--R (200) +--R - +--R +------------------+ +--R | +---+ +--R | | 2 +--R | 2 |2a 2 +--R |2b |--- - a - 2 +--R | | 4 +--R | \| b +--R b |------------------ +--R | 2 +--R \| b +--R * +--R log +--R +---+ +--R +------------------------+ | 2 +--R 3 | 2 2 2 |2a +--R b \|- b x - 2a b x - a + 1 |--- +--R | 4 +--R \| b +--R + +--R +------------------------+ +--R 2 | 2 2 2 +--R a b\|- b x - 2a b x - a + 1 +--R * +--R +------------------+ +--R | +---+ +--R | | 2 +--R | 2 |2a 2 +--R |2b |--- - a - 2 +--R | | 4 +--R | \| b +--R |------------------ +--R | 2 +--R \| b +--R + +--R +---+ +--R | 2 +--R 2 3 3 2 |2a 3 +--R ((- a + 2)b x + (- a + 2a)b ) |--- + a - 2a +--R | 4 +--R \| b +--R + +--R +--------------------+ +--R | +---+ +--R | | 2 +--R | 2 |2a 2 +--R |- 2b |--- - a - 2 +--R | | 4 +--R | \| b +--R b |-------------------- +--R | 2 +--R \| b +--R * +--R log +--R +---+ +--R +------------------------+ | 2 +--R 3 | 2 2 2 |2a +--R b \|- b x - 2a b x - a + 1 |--- +--R | 4 +--R \| b +--R + +--R +------------------------+ +--R 2 | 2 2 2 +--R - a b\|- b x - 2a b x - a + 1 +--R * +--R +--------------------+ +--R | +---+ +--R | | 2 +--R | 2 |2a 2 +--R |- 2b |--- - a - 2 +--R | | 4 +--R | \| b +--R |-------------------- +--R | 2 +--R \| b +--R + +--R +---+ +--R | 2 +--R 2 3 3 2 |2a 3 +--R ((a - 2)b x + (a - 2a)b ) |--- + a - 2a +--R | 4 +--R \| b +--R + +--R - +--R +--------------------+ +--R | +---+ +--R | | 2 +--R | 2 |2a 2 +--R |- 2b |--- - a - 2 +--R | | 4 +--R | \| b +--R b |-------------------- +--R | 2 +--R \| b +--R * +--R log +--R +---+ +--R +------------------------+ | 2 +--R 3 | 2 2 2 |2a +--R - b \|- b x - 2a b x - a + 1 |--- +--R | 4 +--R \| b +--R + +--R +------------------------+ +--R 2 | 2 2 2 +--R a b\|- b x - 2a b x - a + 1 +--R * +--R +--------------------+ +--R | +---+ +--R | | 2 +--R | 2 |2a 2 +--R |- 2b |--- - a - 2 +--R | | 4 +--R | \| b +--R |-------------------- +--R | 2 +--R \| b +--R + +--R +---+ +--R | 2 +--R 2 3 3 2 |2a 3 +--R ((a - 2)b x + (a - 2a)b ) |--- + a - 2a +--R | 4 +--R \| b +--R + +--R +------------------+ +--R | +---+ +--R | | 2 +--R | 2 |2a 2 +--R |2b |--- - a - 2 +--R | | 4 +--R | \| b +--R b |------------------ +--R | 2 +--R \| b +--R * +--R log +--R +---+ +--R +------------------------+ | 2 +--R 3 | 2 2 2 |2a +--R - b \|- b x - 2a b x - a + 1 |--- +--R | 4 +--R \| b +--R + +--R +------------------------+ +--R 2 | 2 2 2 +--R - a b\|- b x - 2a b x - a + 1 +--R * +--R +------------------+ +--R | +---+ +--R | | 2 +--R | 2 |2a 2 +--R |2b |--- - a - 2 +--R | | 4 +--R | \| b +--R |------------------ +--R | 2 +--R \| b +--R + +--R +---+ +--R | 2 +--R 2 3 3 2 |2a 3 +--R ((- a + 2)b x + (- a + 2a)b ) |--- + a - 2a +--R | 4 +--R \| b +--R + +--R +----------------------+ +--R | 2 2 2 +--R |b x + 2a b x + a - 1 +--R - 4atanh( |---------------------- ) +--R | 2 2 2 +--R \| b x + 2a b x + a +--R + +--R +------------------------+ +--R | 2 2 2 +--R 2\|- b x - 2a b x - a + 1 +--R - 2b x atan(----------------------------) +--R 2 2 2 +--R b x + 2a b x + a +--R + +--R b x + a +--R 4atan(---------------------------) + (- 4b x - 4a)acsc(b x + a) +--R +------------------------+ +--R | 2 2 2 +--R \|- b x - 2a b x - a + 1 +--R / +--R 4b +--R Type: Expression Integer +--E 251 + +--S 252 of 477 +d0047:= D(m0047,x) +--R +--R +--R (201) +--R +----------------------+ +--R | 2 2 2 +----------------------+ +--R |b x + 2a b x + a - 1 | 2 2 2 +--R (- b x - a) |---------------------- \|b x + 2a b x + a - 1 +--R | 2 2 2 +--R \| b x + 2a b x + a +--R * +--R +------------------------+ +--R | 2 2 2 +--R 2\|- b x - 2a b x - a + 1 +--R atan(----------------------------) +--R 2 2 2 +--R b x + 2a b x + a +--R + +--R +----------------------+ +--R | 2 2 2 +--R |b x + 2a b x + a - 1 +--R ((- 2b x - 2a)acsc(b x + a) |---------------------- - 2) +--R | 2 2 2 +--R \| b x + 2a b x + a +--R * +--R +----------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - 1 +--R + +--R +----------------------+ +--R | 2 2 2 +--R |b x + 2a b x + a - 1 +--R (2b x + 2a) |---------------------- +--R | 2 2 2 +--R \| b x + 2a b x + a +--R / +--R +----------------------+ +--R | 2 2 2 +----------------------+ +--R |b x + 2a b x + a - 1 | 2 2 2 +--R (2b x + 2a) |---------------------- \|b x + 2a b x + a - 1 +--R | 2 2 2 +--R \| b x + 2a b x + a +--R Type: Expression Integer +--E 252 + +--S 253 of 477 +t0048:= atan(1/x) +--R +--R +--R 1 +--R (202) atan(-) +--R x +--R Type: Expression Integer +--E 253 + +--S 254 of 477 +r0048:= x*acot(x)+1/2*log(1+x^2) +--R +--R +--R 2 +--R log(x + 1) + 2x acot(x) +--R (203) ------------------------ +--R 2 +--R Type: Expression Integer +--E 254 + +--S 255 of 477 +a0048:= integrate(t0048,x) +--R +--R +--R 2 2x +--R log(x + 1) + x atan(------) +--R 2 +--R x - 1 +--R (204) ---------------------------- +--R 2 +--R Type: Union(Expression Integer,...) +--E 255 + +--S 256 of 477 +m0048:= a0048-r0048 +--R +--R +--R 2x +--R x atan(------) - 2x acot(x) +--R 2 +--R x - 1 +--R (205) --------------------------- +--R 2 +--R Type: Expression Integer +--E 256 + +--S 257 of 477 +d0048:= D(m0048,x) +--R +--R +--R 2x +--R atan(------) - 2acot(x) +--R 2 +--R x - 1 +--R (206) ----------------------- +--R 2 +--R Type: Expression Integer +--E 257 + +--S 258 of 477 +t0049:= acot(1/x) +--R +--R +--R 1 +--R (207) acot(-) +--R x +--R Type: Expression Integer +--E 258 + +--S 259 of 477 +r0049:= atan(x)*x-1/2*log(1+x^2) +--R +--R +--R 2 +--R - log(x + 1) + 2x atan(x) +--R (208) -------------------------- +--R 2 +--R Type: Expression Integer +--E 259 + +--S 260 of 477 +a0049:= integrate(t0049,x) +--R +--R +--R 2 2x +--R - log(x + 1) - x atan(------) +--R 2 +--R x - 1 +--R (209) ------------------------------ +--R 2 +--R Type: Union(Expression Integer,...) +--E 260 + +--S 261 of 477 +m0049:= a0049-r0049 +--R +--R +--R 2x +--R - 2x atan(x) - x atan(------) +--R 2 +--R x - 1 +--R (210) ----------------------------- +--R 2 +--R Type: Expression Integer +--E 261 + +--S 262 of 477 +d0049:= D(m0049,x) +--R +--R +--R 2x +--R - 2atan(x) - atan(------) +--R 2 +--R x - 1 +--R (211) ------------------------- +--R 2 +--R Type: Expression Integer +--E 262 + +--S 263 of 477 +t0050:= asec(1/x) +--R +--R +--R 1 +--R (212) asec(-) +--R x +--R Type: Expression Integer +--E 263 + +--S 264 of 477 +r0050:= -(1-x^2)^(1/2)+x*acos(x) +--R +--R +--R +--------+ +--R | 2 +--R (213) - \|- x + 1 + x acos(x) +--R Type: Expression Integer +--E 264 + +--S 265 of 477 +a0050:= integrate(t0050,x) +--R +--R +--R (214) +--R +------+ +--R +------+ 2 +-+ | 2 3 +-+ +--R +-+ | 2 (4x + 2)\|2 \|x - 1 + (- 4x + 2x)\|2 +--R x\|2 atan(2x\|x - 1 ) - atan(-----------------------------------------) +--R +------+ +--R 5 | 2 6 4 2 +--R (8x - 2x)\|x - 1 - 8x + 4x + 2x + 3 +--R + +--R +-+ +--R 2x\|2 +--R - atan(-------) +--R 2 +--R 2x - 1 +--R / +--R +-+ +--R 2\|2 +--R Type: Union(Expression Integer,...) +--E 265 + +--S 266 of 477 +m0050:= a0050-r0050 +--R +--R +--R (215) +--R +------+ +--R +------+ 2 +-+ | 2 3 +-+ +--R +-+ | 2 (4x + 2)\|2 \|x - 1 + (- 4x + 2x)\|2 +--R x\|2 atan(2x\|x - 1 ) - atan(-----------------------------------------) +--R +------+ +--R 5 | 2 6 4 2 +--R (8x - 2x)\|x - 1 - 8x + 4x + 2x + 3 +--R + +--R +--------+ +-+ +--R +-+ | 2 2x\|2 +-+ +--R 2\|2 \|- x + 1 - atan(-------) - 2x\|2 acos(x) +--R 2 +--R 2x - 1 +--R / +--R +-+ +--R 2\|2 +--R Type: Expression Integer +--E 266 + +--S 267 of 477 +d0050:= D(m0050,x) +--R +--R +--R +------+ +--R | 2 +--R atan(2x\|x - 1 ) - 2acos(x) +--R (216) ---------------------------- +--R 2 +--R Type: Expression Integer +--E 267 + +--S 268 of 477 +t0051:= acsc(1/x) +--R +--R +--R 1 +--R (217) acsc(-) +--R x +--R Type: Expression Integer +--E 268 + +--S 269 of 477 +r0051:= (1-x^2)^(1/2)+x*asin(x) +--R +--R +--R +--------+ +--R | 2 +--R (218) \|- x + 1 + x asin(x) +--R Type: Expression Integer +--E 269 + +--S 270 of 477 +a0051:= integrate(t0051,x) +--R +--R +--R (219) +--R +------+ +--R +-+ | 2 +--R - x\|2 atan(2x\|x - 1 ) +--R + +--R +------+ +--R 2 +-+ | 2 3 +-+ +-+ +--R (4x + 2)\|2 \|x - 1 + (- 4x + 2x)\|2 2x\|2 +--R atan(-----------------------------------------) + atan(-------) +--R +------+ 2 +--R 5 | 2 6 4 2 2x - 1 +--R (8x - 2x)\|x - 1 - 8x + 4x + 2x + 3 +--R / +--R +-+ +--R 2\|2 +--R Type: Union(Expression Integer,...) +--E 270 + +--S 271 of 477 +m0051:= a0051-r0051 +--R +--R +--R (220) +--R +------+ +--R +-+ | 2 +--R - x\|2 atan(2x\|x - 1 ) +--R + +--R +------+ +--R 2 +-+ | 2 3 +-+ +--------+ +--R (4x + 2)\|2 \|x - 1 + (- 4x + 2x)\|2 +-+ | 2 +--R atan(-----------------------------------------) - 2\|2 \|- x + 1 +--R +------+ +--R 5 | 2 6 4 2 +--R (8x - 2x)\|x - 1 - 8x + 4x + 2x + 3 +--R + +--R +-+ +--R 2x\|2 +-+ +--R atan(-------) - 2x\|2 asin(x) +--R 2 +--R 2x - 1 +--R / +--R +-+ +--R 2\|2 +--R Type: Expression Integer +--E 271 + +--S 272 of 477 +d0051:= D(m0051,x) +--R +--R +--R +------+ +--R | 2 +--R - atan(2x\|x - 1 ) - 2asin(x) +--R (221) ------------------------------ +--R 2 +--R Type: Expression Integer +--E 272 + +--S 273 of 477 +t0052:= atan(a+b*x)/x +--R +--R +--R atan(b x + a) +--R (222) ------------- +--R x +--R Type: Expression Integer +--E 273 + +--S 274 of 477 +r0052:= 1/2*%i*log(%i*b*x/(1-%i*a))*log(1-%i*a-%i*b*x)-_ + 1/2*%i*log(-%i*b*x/(1+%i*a))*log(1+%i*a+%i*b*x)+_ + 1/2*%i*polylog(2,1-%i*b*x/(1-%i*a))-_ + 1/2*%i*polylog(2,1+%i*b*x/(1+%i*a)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction Polynomial Complex Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 274 + +--S 275 of 477 +a0052:= integrate(t0052,x) +--R +--R +--R x +--R ++ atan(%Q b + a) +--R (223) | -------------- d%Q +--R ++ %Q +--R Type: Union(Expression Integer,...) +--E 275 + +--S 276 of 477 +--m0052:= a0052-r0052 +--E 276 + +--S 277 of 477 +--d0052:= D(m0052,x) +--E 277 + +--S 278 of 477 +t0053:= acot(a+b*x)/x +--R +--R +--R acot(b x + a) +--R (224) ------------- +--R x +--R Type: Expression Integer +--E 278 + +--S 279 of 477 +r0053:= 1/2*%i*(-log(x)*log((%i-a-b*x)/(%i-a))+_ + log(x)*log((%i+a+b*x)/(%i+a))+_ + log(x)*log(-(%i-a-b*x)/(a+b*x))-_ + log(x)*log((%i+a+b*x)/(a+b*x))-_ + polylog(2,b*x/(%i-a))+polylog(2,-b*x/(%i+a))) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction Polynomial Complex Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 279 + +--S 280 of 477 +a0053:= integrate(t0053,x) +--R +--R +--R x +--R ++ acot(%Q b + a) +--R (225) | -------------- d%Q +--R ++ %Q +--R Type: Union(Expression Integer,...) +--E 280 + +--S 281 of 477 +--m0053:= a0053-r0053 +--E 281 + +--S 282 of 477 +--d0053:= D(m0053,x) +--E 282 + +--S 283 of 477 +t0054:= asin(a+b*x)/(a*d/b+d*x) +--R +--R +--R b asin(b x + a) +--R (226) --------------- +--R b d x + a d +--R Type: Expression Integer +--E 283 + +--S 284 of 477 +r0054:= -1/2*%i*asin(a+b*x)^2/d+asin(a+b*x)*log(1-(%i*(a+b*x)+_ + (1-a^2-2*a*b*x-b^2*x^2)^(1/2))^2)/d-_ + 1/2*%i*polylog(2,(%i*(a+b*x)+(1-a^2-2*a*b*x-b^2*x^2)^(1/2))^2)/d +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Complex Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 284 + +--S 285 of 477 +a0054:= integrate(t0054,x) +--R +--R +--R x +--R ++ b asin(%Q b + a) +--R (227) | ---------------- d%Q +--R ++ (%Q b + a)d +--R Type: Union(Expression Integer,...) +--E 285 + +--S 286 of 477 +--m0054:= a0054-r0054 +--E 286 + +--S 287 of 477 +--d0054:= D(m0054,x) +--E 287 + +--S 288 of 477 +t0055:= atan(a+b*x)/(a*d/b+d*x) +--R +--R +--R b atan(b x + a) +--R (228) --------------- +--R b d x + a d +--R Type: Expression Integer +--E 288 + +--S 289 of 477 +r0055:= 1/2*%i*(polylog(2,-%i*(a+b*x))-polylog(2,%i*(a+b*x)))/d +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Polynomial Complex Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 289 + +--S 290 of 477 +a0055:= integrate(t0055,x) +--R +--R +--R x +--R ++ b atan(%Q b + a) +--R (229) | ---------------- d%Q +--R ++ (%Q b + a)d +--R Type: Union(Expression Integer,...) +--E 290 + +--S 291 of 477 +--m0055:= a0055-r0055 +--E 291 + +--S 292 of 477 +--d0055:= D(m0055,x) +--E 292 + +--S 293 of 477 +t0056:= acot(a+b*x)/(a*d/b+d*x) +--R +--R +--R b acot(b x + a) +--R (230) --------------- +--R b d x + a d +--R Type: Expression Integer +--E 293 + +--S 294 of 477 +r0056:= -1/2*%i*(polylog(2,-%i/(a+b*x))-polylog(2,%i/(a+b*x)))/d +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction Polynomial Complex Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 294 + +--S 295 of 477 +a0056:= integrate(t0056,x) +--R +--R +--R x +--R ++ b acot(%Q b + a) +--R (231) | ---------------- d%Q +--R ++ (%Q b + a)d +--R Type: Union(Expression Integer,...) +--E 295 + +--S 296 of 477 +--m0056:= a0056-r0056 +--E 296 + +--S 297 of 477 +--d0056:= D(m0056,x) +--E 297 + +--S 298 of 477 +t0057:= acsc(a+b*x)/(a*d/b+d*x) +--R +--R +--R b acsc(b x + a) +--R (232) --------------- +--R b d x + a d +--R Type: Expression Integer +--E 298 + +--S 299 of 477 +r0057:= 1/2*%i*acsc(a+b*x)^2/d-acsc(a+b*x)*log(1-(%i/(a+b*x)+_ + (1-1/(a+b*x)^2)^(1/2))^2)/d+1/2*%i*_ + polylog(2,(%i/(a+b*x)+(1-1/(a+b*x)^2)^(1/2))^2)/d +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Complex Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 299 + +--S 300 of 477 +a0057:= integrate(t0057,x) +--R +--R +--R x +--R ++ b acsc(%Q b + a) +--R (233) | ---------------- d%Q +--R ++ (%Q b + a)d +--R Type: Union(Expression Integer,...) +--E 300 + +--S 301 of 477 +--m0057:= a0057-r0057 +--E 301 + +--S 302 of 477 +--d0057:= D(m0057,x) +--E 302 + +--S 303 of 477 +t0058:= asin(a*x^n)/x +--R +--R +--R n +--R asin(a x ) +--R (234) ---------- +--R x +--R Type: Expression Integer +--E 303 + +--S 304 of 477 +r0058:= -1/2*%i*asin(a*x^n)^2/n+asin(a*x^n)*_ + log(1-(%i*a*x^n+(1-a^2*x^(2*n))^(1/2))^2)/n-_ + 1/2*%i*polylog(2,(%i*a*x^n+(1-a^2*x^(2*n))^(1/2))^2)/n +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Complex Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 304 + +--S 305 of 477 +a0058:= integrate(t0058,x) +--R +--R +--R >> Error detected within library code: +--R failed - cannot handle that integrand +--R +--R Continuing to read the file... +--R +--E 305 + +--S 306 of 477 +--m0058:= a0058-r0058 +--E 306 + +--S 307 of 477 +--d0058:= D(m0058,x) +--E 307 + +--S 308 of 477 +t0059:= atan(a*x^n)/x +--R +--R +--R n +--R atan(a x ) +--R (235) ---------- +--R x +--R Type: Expression Integer +--E 308 + +--S 309 of 477 +r0059:= 1/2*%i*(polylog(2,-%i*a*x^n)-polylog(2,%i*a*x^n))/n +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Complex Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 309 + +--S 310 of 477 +a0059:= integrate(t0059,x) +--R +--R +--R x n +--R ++ atan(a %Q ) +--R (236) | ----------- d%Q +--R ++ %Q +--R Type: Union(Expression Integer,...) +--E 310 + +--S 311 of 477 +--m0059:= a0059-r0059 +--E 311 + +--S 312 of 477 +--d0059:= D(m0059,x) +--E 312 + +--S 313 of 477 +t0060:= acot(a*x^n)/x +--R +--R +--R n +--R acot(a x ) +--R (237) ---------- +--R x +--R Type: Expression Integer +--E 313 + +--S 314 of 477 +r0060:= -1/2*%i*(polylog(2,-%i/a*x^(-n))-polylog(2,%i/a*x^(-n)))/n +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Complex Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 314 + +--S 315 of 477 +a0060:= integrate(t0060,x) +--R +--R +--R x n +--R ++ acot(a %Q ) +--R (238) | ----------- d%Q +--R ++ %Q +--R Type: Union(Expression Integer,...) +--E 315 + +--S 316 of 477 +--m0060:= a0060-r0060 +--E 316 + +--S 317 of 477 +--d0060:= D(m0060,x) +--E 317 + +--S 318 of 477 +t0061:= acsc(a*x^n)/x +--R +--R +--R n +--R acsc(a x ) +--R (239) ---------- +--R x +--R Type: Expression Integer +--E 318 + +--S 319 of 477 +r0061:= 1/2*%i*acsc(a*x^n)^2/n-acsc(a*x^n)*log(1-(%i/a/(x^n)+_ + (1-1/a^2/(x^(2*n)))^(1/2))^2)/n+1/2*%i*_ + polylog(2,(%i/a/(x^n)+(1-1/a^2/(x^(2*n)))^(1/2))^2)/n +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Complex Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 319 + +--S 320 of 477 +a0061:= integrate(t0061,x) +--R +--R +--R >> Error detected within library code: +--R failed - cannot handle that integrand +--R +--R Continuing to read the file... +--R +--E 320 + +--S 321 of 477 +--m0061:= a0061-r0061 +--E 321 + +--S 322 of 477 +--d0061:= D(m0061,x) +--E 322 + +--S 323 of 477 +t0062:= x^3*asec(a+b*x^4) +--R +--R +--R 3 4 +--R (240) x asec(b x + a) +--R Type: Expression Integer +--E 323 + +--S 324 of 477 +r0062:= 1/4*(a+b*x^4)*asec(a+b*x^4)/b-1/4*atanh((1-1/(a+b*x^4)^2)^(1/2))/b +--R +--R +--R +-----------------------+ +--R | 2 8 4 2 +--R |b x + 2a b x + a - 1 4 4 +--R - atanh( |----------------------- ) + (b x + a)asec(b x + a) +--R | 2 8 4 2 +--R \| b x + 2a b x + a +--R (241) -------------------------------------------------------------- +--R 4b +--R Type: Expression Integer +--E 324 + +--S 325 of 477 +a0062:= integrate(t0062,x) +--R +--R +--R >> Error detected within library code: +--R failed - cannot handle that integrand +--R +--R Continuing to read the file... +--R +--E 325 + +--S 326 of 477 +--m0062:= a0062-r0062 +--E 326 + +--S 327 of 477 +--d0062:= D(m0062,x) +--E 327 + +--S 328 of 477 +t0063:= x^3*acsc(a+b*x^4) +--R +--R +--R 3 4 +--R (242) x acsc(b x + a) +--R Type: Expression Integer +--E 328 + +--S 329 of 477 +r0063:= 1/4*(a+b*x^4)*acsc(a+b*x^4)/b+1/4*atanh((1-1/(a+b*x^4)^2)^(1/2))/b +--R +--R +--R +-----------------------+ +--R | 2 8 4 2 +--R |b x + 2a b x + a - 1 4 4 +--R atanh( |----------------------- ) + (b x + a)acsc(b x + a) +--R | 2 8 4 2 +--R \| b x + 2a b x + a +--R (243) ------------------------------------------------------------ +--R 4b +--R Type: Expression Integer +--E 329 + +--S 330 of 477 +a0063:= integrate(t0063,x) +--R +--R +--R >> Error detected within library code: +--R failed - cannot handle that integrand +--R +--R Continuing to read the file... +--R +--E 330 + +--S 331 of 477 +--m0063:= a0063-r0063 +--E 331 + +--S 332 of 477 +--d0063:= D(m0063,x) +--E 332 + +--S 333 of 477 +t0064:= x^(-1+n)*asin(a+b*x^n) +--R +--R +--R n - 1 n +--R (244) x asin(b x + a) +--R Type: Expression Integer +--E 333 + +--S 334 of 477 +r0064:= (1-(a+b*x^n)^2)^(1/2)/b/n+(a+b*x^n)*asin(a+b*x^n)/b/n +--R +--R +--R +----------------------------+ +--R | 2 n 2 n 2 n n +--R \|- b (x ) - 2a b x - a + 1 + (b x + a)asin(b x + a) +--R (245) ---------------------------------------------------------- +--R b n +--R Type: Expression Integer +--E 334 + +--S 335 of 477 +a0064:= integrate(t0064,x) +--R +--R +--R >> Error detected within library code: +--R failed - cannot handle that integrand +--R +--R Continuing to read the file... +--R +--E 335 + +--S 336 of 477 +--m0064:= a0064-r0064 +--E 336 + +--S 337 of 477 +--d0064:= D(m0064,x) +--E 337 + +--S 338 of 477 +t0065:= x^(-1+n)*acos(a+b*x^n) +--R +--R +--R n - 1 n +--R (246) x acos(b x + a) +--R Type: Expression Integer +--E 338 + +--S 339 of 477 +r0065:= -(1-(a+b*x^n)^2)^(1/2)/b/n+(a+b*x^n)*acos(a+b*x^n)/b/n +--R +--R +--R +----------------------------+ +--R | 2 n 2 n 2 n n +--R - \|- b (x ) - 2a b x - a + 1 + (b x + a)acos(b x + a) +--R (247) ------------------------------------------------------------ +--R b n +--R Type: Expression Integer +--E 339 + +--S 340 of 477 +a0065:= integrate(t0065,x) +--R +--R +--R >> Error detected within library code: +--R failed - cannot handle that integrand +--R +--R Continuing to read the file... +--R +--E 340 + +--S 341 of 477 +--m0065:= a0065-r0065 +--E 341 + +--S 342 of 477 +--d0065:= D(m0065,x) +--E 342 + +--S 343 of 477 +t0066:= x^(-1+n)*atan(a+b*x^n) +--R +--R +--R n - 1 n +--R (248) x atan(b x + a) +--R Type: Expression Integer +--E 343 + +--S 344 of 477 +r0066:= (a+b*x^n)*atan(a+b*x^n)/b/n-1/2*log(1+(a+b*x^n)^2)/b/n +--R +--R +--R 2 n 2 n 2 n n +--R - log(b (x ) + 2a b x + a + 1) + (2b x + 2a)atan(b x + a) +--R (249) -------------------------------------------------------------- +--R 2b n +--R Type: Expression Integer +--E 344 + +--S 345 of 477 +a0066:= integrate(t0066,x) +--R +--R +--R (250) +--R 2 n log(x) 2 n log(x) 2 +--R - log(b (%e ) + 2a b %e + a + 1) +--R + +--R n log(x) +--R n log(x) 2b %e + 2a +--R (- b %e - a)atan(------------------------------------------) +--R 2 n log(x) 2 n log(x) 2 +--R b (%e ) + 2a b %e + a - 1 +--R / +--R 2b n +--R Type: Union(Expression Integer,...) +--E 345 + +--S 346 of 477 +m0066:= a0066-r0066 +--R +--R +--R (251) +--R 2 n log(x) 2 n log(x) 2 +--R - log(b (%e ) + 2a b %e + a + 1) +--R + +--R n log(x) +--R n log(x) 2b %e + 2a +--R (- b %e - a)atan(------------------------------------------) +--R 2 n log(x) 2 n log(x) 2 +--R b (%e ) + 2a b %e + a - 1 +--R + +--R 2 n 2 n 2 n n +--R log(b (x ) + 2a b x + a + 1) + (- 2b x - 2a)atan(b x + a) +--R / +--R 2b n +--R Type: Expression Integer +--E 346 + +--S 347 of 477 +d0066:= D(m0066,x) +--R +--R +--R (252) +--R n log(x) +--R n log(x) 2b %e + 2a +--R - %e atan(------------------------------------------) +--R 2 n log(x) 2 n log(x) 2 +--R b (%e ) + 2a b %e + a - 1 +--R + +--R n - 1 n +--R - 2x x atan(b x + a) +--R / +--R 2x +--R Type: Expression Integer +--E 347 + +--S 348 of 477 +t0067:= x^(-1+n)*acot(a+b*x^n) +--R +--R +--R n - 1 n +--R (253) x acot(b x + a) +--R Type: Expression Integer +--E 348 + +--S 349 of 477 +r0067:= (a+b*x^n)*acot(a+b*x^n)/b/n+1/2*log(1+(a+b*x^n)^2)/b/n +--R +--R +--R 2 n 2 n 2 n n +--R log(b (x ) + 2a b x + a + 1) + (2b x + 2a)acot(b x + a) +--R (254) ------------------------------------------------------------ +--R 2b n +--R Type: Expression Integer +--E 349 + +--S 350 of 477 +a0067:= integrate(t0067,x) +--R +--R +--R (255) +--R 2 n log(x) 2 n log(x) 2 +--R log(b (%e ) + 2a b %e + a + 1) +--R + +--R n log(x) +--R n log(x) 2b %e + 2a +--R (b %e + a)atan(------------------------------------------) +--R 2 n log(x) 2 n log(x) 2 +--R b (%e ) + 2a b %e + a - 1 +--R / +--R 2b n +--R Type: Union(Expression Integer,...) +--E 350 + +--S 351 of 477 +m0067:= a0067-r0067 +--R +--R +--R (256) +--R 2 n log(x) 2 n log(x) 2 +--R log(b (%e ) + 2a b %e + a + 1) +--R + +--R n log(x) +--R n log(x) 2b %e + 2a +--R (b %e + a)atan(------------------------------------------) +--R 2 n log(x) 2 n log(x) 2 +--R b (%e ) + 2a b %e + a - 1 +--R + +--R 2 n 2 n 2 n n +--R - log(b (x ) + 2a b x + a + 1) + (- 2b x - 2a)acot(b x + a) +--R / +--R 2b n +--R Type: Expression Integer +--E 351 + +--S 352 of 477 +d0067:= D(m0067,x) +--R +--R +--R (257) +--R n log(x) +--R n log(x) 2b %e + 2a +--R %e atan(------------------------------------------) +--R 2 n log(x) 2 n log(x) 2 +--R b (%e ) + 2a b %e + a - 1 +--R + +--R n - 1 n +--R - 2x x acot(b x + a) +--R / +--R 2x +--R Type: Expression Integer +--E 352 + +--S 353 of 477 +t0068:= x^(-1+n)*asec(a+b*x^n) +--R +--R +--R n - 1 n +--R (258) x asec(b x + a) +--R Type: Expression Integer +--E 353 + +--S 354 of 477 +r0068:= (a+b*x^n)*asec(a+b*x^n)/b/n-atanh((1-1/(a+b*x^n)^2)^(1/2))/b/n +--R +--R +--R +--------------------------+ +--R | 2 n 2 n 2 +--R |b (x ) + 2a b x + a - 1 n n +--R - atanh( |-------------------------- ) + (b x + a)asec(b x + a) +--R | 2 n 2 n 2 +--R \| b (x ) + 2a b x + a +--R (259) ----------------------------------------------------------------- +--R b n +--R Type: Expression Integer +--E 354 + +--S 355 of 477 +a0068:= integrate(t0068,x) +--R +--R +--R >> Error detected within library code: +--R failed - cannot handle that integrand +--R +--R Continuing to read the file... +--R +--E 355 + +--S 356 of 477 +--m0068:= a0068-r0068 +--E 356 + +--S 357 of 477 +--d0068:= D(m0068,x) +--E 357 + +--S 358 of 477 +t0069:= x^(-1+n)*acsc(a+b*x^n) +--R +--R +--R n - 1 n +--R (260) x acsc(b x + a) +--R Type: Expression Integer +--E 358 + +--S 359 of 477 +r0069:= (a+b*x^n)*acsc(a+b*x^n)/b/n+atanh((1-1/(a+b*x^n)^2)^(1/2))/b/n +--R +--R +--R +--------------------------+ +--R | 2 n 2 n 2 +--R |b (x ) + 2a b x + a - 1 n n +--R atanh( |-------------------------- ) + (b x + a)acsc(b x + a) +--R | 2 n 2 n 2 +--R \| b (x ) + 2a b x + a +--R (261) --------------------------------------------------------------- +--R b n +--R Type: Expression Integer +--E 359 + +--S 360 of 477 +a0069:= integrate(t0069,x) +--R +--R +--R >> Error detected within library code: +--R failed - cannot handle that integrand +--R +--R Continuing to read the file... +--R +--E 360 + +--S 361 of 477 +--m0069:= a0069-r0069 +--E 361 + +--S 362 of 477 +--d0069:= D(m0069,x) +--E 362 + +--S 363 of 477 +t0070:= asin(exp(1)^(a+b*x)) +--R +--R +--R b x + a +--R (262) asin(%e ) +--R Type: Expression Integer +--E 363 + +--S 364 of 477 +r0070:= -1/2*(%i*asin(exp(a+b*x))^2-2*asin(exp(a+b*x))*_ + log(-2*%i*exp(a+b*x)*(%i*exp(a+b*x)+(1-exp(2*a+2*b*x))^(1/2)))+_ + %i*polylog(2,(%i*exp(a+b*x)+(1-exp(2*a+2*b*x))^(1/2))^2))/b +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Complex Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 364 + +--S 365 of 477 +a0070:= integrate(t0070,x) +--R +--R +--R >> Error detected within library code: +--R failed - cannot handle that integrand +--R +--R Continuing to read the file... +--R +--E 365 + +--S 366 of 477 +--m0070:= a0070-r0070 +--E 366 + +--S 367 of 477 +--d0070:= D(m0070,x) +--E 367 + +--S 368 of 477 +t0071:= acsc(exp(1)^(a+b*x)) +--R +--R +--R b x + a +--R (263) acsc(%e ) +--R Type: Expression Integer +--E 368 + +--S 369 of 477 +r0071:= 1/2*%i*acsc(exp(1)^(a+b*x))^2/b-acsc(exp(1)^(a+b*x))*_ + log(1-(%i*exp(1)^(-a-b*x)+(1-exp(1)^(-2*a-2*b*x))^(1/2))^2)/b+_ + 1/2*%i*polylog(2,(%i*exp(1)^(-a-b*x)+_ + (1-exp(1)^(-2*a-2*b*x))^(1/2))^2)/b +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Complex Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 369 + +--S 370 of 477 +a0071:= integrate(t0071,x) +--R +--R +--R >> Error detected within library code: +--R failed - cannot handle that integrand +--R +--R Continuing to read the file... +--R +--E 370 + +--S 371 of 477 +--m0071:= a0071-r0071 +--E 371 + +--S 372 of 477 +--d0071:= D(m0071,x) +--E 372 + +--S 373 of 477 +t0072:= acsc(c*exp(1)^(a+b*x)) +--R +--R +--R b x + a +--R (264) acsc(c %e ) +--R Type: Expression Integer +--E 373 + +--S 374 of 477 +r0072:= 1/2*%i*acsc(c*exp(1)^(a+b*x))^2/b-acsc(c*exp(1)^(a+b*x))*_ + log(1-(%i*exp(1)^(-a-b*x)/c+(1-exp(1)^(-2*a-2*b*x)/c^2)^(1/2))^2)/b+_ + 1/2*%i*polylog(2,(%i*exp(1)^(-a-b*x)/c+_ + (1-exp(1)^(-2*a-2*b*x)/c^2)^(1/2))^2)/b +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Complex Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 374 + +--S 375 of 477 +a0072:= integrate(t0072,x) +--R +--R +--R >> Error detected within library code: +--R failed - cannot handle that integrand +--R +--R Continuing to read the file... +--R +--E 375 + +--S 376 of 477 +--m0072:= a0072-r0072 +--E 376 + +--S 377 of 477 +--d0072:= D(m0072,x) +--E 377 + +--S 378 of 477 +t0073:= atan(exp(x)) +--R +--R +--R x +--R (265) atan(%e ) +--R Type: Expression Integer +--E 378 + +--S 379 of 477 +r0073:= 1/2*%i*polylog(2,-%i*exp(x))-_ + 1/2*%i*polylog(2,%i*exp(x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Complex Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 379 + +--S 380 of 477 +a0073:= integrate(t0073,x) +--R +--R +--R x +--R ++ %Q +--R (266) | atan(%e )d%Q +--R ++ +--R Type: Union(Expression Integer,...) +--E 380 + +--S 381 of 477 +--m0073:= a0073-r0073 +--E 381 + +--S 382 of 477 +--d0073:= D(m0073,x) +--E 382 + +--S 383 of 477 +t0074:= atan(exp(1)^(a+b*x)) +--R +--R +--R b x + a +--R (267) atan(%e ) +--R Type: Expression Integer +--E 383 + +--S 384 of 477 +r0074:= 1/2*%i*(polylog(2,-%i*exp(a+b*x))-polylog(2,%i*exp(a+b*x)))/b +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Complex Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 384 + +--S 385 of 477 +a0074:= integrate(t0074,x) +--R +--R +--R x +--R ++ %Q b + a +--R (268) | atan(%e )d%Q +--R ++ +--R Type: Union(Expression Integer,...) +--E 385 + +--S 386 of 477 +--m0074:= a0074-r0074 +--E 386 + +--S 387 of 477 +--d0074:= D(m0074,x) +--E 387 + +--S 388 of 477 +t0075:= x*atan(exp(1)^(a+b*x)) +--R +--R +--R b x + a +--R (269) x atan(%e ) +--R Type: Expression Integer +--E 388 + +--S 389 of 477 +r0075:= 1/2*%i*(x*polylog(2,-%i*exp(a+b*x))*b-_ + x*polylog(2,%i*exp(a+b*x))*b-_ + polylog(3,-%i*exp(a+b*x))+_ + polylog(3,%i*exp(a+b*x)))/b^2 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Complex Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 389 + +--S 390 of 477 +a0075:= integrate(t0075,x) +--R +--R +--R x +--R ++ %Q b + a +--R (270) | %Q atan(%e )d%Q +--R ++ +--R Type: Union(Expression Integer,...) +--E 390 + +--S 391 of 477 +--m0075:= a0075-r0075 +--E 391 + +--S 392 of 477 +--d0075:= D(m0075,x) +--E 392 + +--S 393 of 477 +t0076:= x^2*atan(exp(1)^(a+b*x)) +--R +--R +--R 2 b x + a +--R (271) x atan(%e ) +--R Type: Expression Integer +--E 393 + +--S 394 of 477 +r0076:= 1/2*%i*(x^2*polylog(2,-%i*exp(a+b*x))*b^2-_ + x^2*polylog(2,%i*exp(a+b*x))*b^2-_ + 2*x*polylog(3,-%i*exp(a+b*x))*b+_ + 2*x*polylog(3,%i*exp(a+b*x))*b+_ + 2*polylog(4,-%i*exp(a+b*x))-_ + 2*polylog(4,%i*exp(a+b*x)))/b^3 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Complex Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 394 + +--S 395 of 477 +a0076:= integrate(t0076,x) +--R +--R +--R x +--R ++ 2 %Q b + a +--R (272) | %Q atan(%e )d%Q +--R ++ +--R Type: Union(Expression Integer,...) +--E 395 + +--S 396 of 477 +--m0076:= a0076-r0076 +--E 396 + +--S 397 of 477 +--d0076:= D(m0076,x) +--E 397 + +--S 398 of 477 +t0077:= atan(a+b*f^(c+d*x)) +--R +--R +--R d x + c +--R (273) atan(b f + a) +--R Type: Expression Integer +--E 398 + +--S 399 of 477 +r0077:= 1/2*%i*(log(-b*f^(c+d*x)/(%i+a))*log(-%i*(%i+a+b*f^(c+d*x)))-_ + log(b*f^(c+d*x)/(%i-a))*log(%i*(-%i+a+b*f^(c+d*x)))+_ + polylog(2,(-1+%i*a+%i*b*f^(c+d*x))/(-1+%i*a))-_ + polylog(2,(1+%i*a+%i*b*f^(c+d*x))/(1+%i*a)))/d/log(f) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Complex Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 399 + +--S 400 of 477 +a0077:= integrate(t0077,x) +--R +--R +--R x +--R ++ %Q d + c +--R (274) | atan(b f + a)d%Q +--R ++ +--R Type: Union(Expression Integer,...) +--E 400 + +--S 401 of 477 +--m0077:= a0077-r0077 +--E 401 + +--S 402 of 477 +--d0077:= D(m0077,x) +--E 402 + +--S 403 of 477 +t0078:= x*atan(a+b*f^(c+d*x)) +--R +--R +--R d x + c +--R (275) x atan(b f + a) +--R Type: Expression Integer +--E 403 + +--S 404 of 477 +r0078:= 1/4*%i*x^2*log(1-%i*a-%i*b*f^(c+d*x))-_ + 1/4*%i*x^2*log(1+%i*a+%i*b*f^(c+d*x))-_ + 1/4*%i*x^2*log(1-%i*b*f^(c+d*x)/(1-%i*a))+_ + 1/4*%i*x^2*log(1+%i*b*f^(c+d*x)/(1+%i*a))-_ + 1/2*%i*x*polylog(2,%i*b*f^(c+d*x)/(1-%i*a))/d/log(f)+_ + 1/2*%i*x*polylog(2,-%i*b*f^(c+d*x)/(1+%i*a))/d/log(f)+_ + 1/2*%i*polylog(3,%i*b*f^(c+d*x)/(1-%i*a))/d^2/log(f)^2-_ + 1/2*%i*polylog(3,-%i*b*f^(c+d*x)/(1+%i*a))/d^2/log(f)^2 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Complex Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 404 + +--S 405 of 477 +a0078:= integrate(t0078,x) +--R +--R +--R x +--R ++ %Q d + c +--R (276) | %Q atan(b f + a)d%Q +--R ++ +--R Type: Union(Expression Integer,...) +--E 405 + +--S 406 of 477 +--m0078:= a0078-r0078 +--E 406 + +--S 407 of 477 +--d0078:= D(m0078,x) +--E 407 + +--S 408 of 477 +t0079:= x^2*atan(a+b*f^(c+d*x)) +--R +--R +--R 2 d x + c +--R (277) x atan(b f + a) +--R Type: Expression Integer +--E 408 + +--S 409 of 477 +r0079:= 1/6*%i*x^3*log(1-%i*a-%i*b*f^(c+d*x))-_ + 1/6*%i*x^3*log(1+%i*a+%i*b*f^(c+d*x))-_ + 1/6*%i*x^3*log(1-%i*b*f^(c+d*x)/(1-%i*a))+_ + 1/6*%i*x^3*log(1+%i*b*f^(c+d*x)/(1+%i*a))-_ + 1/2*%i*x^2*polylog(2,%i*b*f^(c+d*x)/(1-%i*a))/d/log(f)+_ + 1/2*%i*x^2*polylog(2,-%i*b*f^(c+d*x)/(1+%i*a))/d/log(f)+_ + %i*x*polylog(3,%i*b*f^(c+d*x)/(1-%i*a))/d^2/log(f)^2-_ + %i*x*polylog(3,-%i*b*f^(c+d*x)/(1+%i*a))/d^2/log(f)^2-_ + %i*polylog(4,%i*b*f^(c+d*x)/(1-%i*a))/d^3/log(f)^3+_ + %i*polylog(4,-%i*b*f^(c+d*x)/(1+%i*a))/d^3/log(f)^3 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Complex Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 409 + +--S 410 of 477 +a0079:= integrate(t0079,x) +--R +--R +--R x +--R ++ 2 %Q d + c +--R (278) | %Q atan(b f + a)d%Q +--R ++ +--R Type: Union(Expression Integer,...) +--E 410 + +--S 411 of 477 +--m0079:= a0079-r0079 +--E 411 + +--S 412 of 477 +--d0079:= D(m0079,x) +--E 412 + +--S 413 of 477 +t0080:= acot(exp(x)) +--R +--R +--R x +--R (279) acot(%e ) +--R Type: Expression Integer +--E 413 + +--S 414 of 477 +r0080:= -1/2*%i*polylog(2,-%i/exp(x))+1/2*%i*polylog(2,%i/exp(x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Complex Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 414 + +--S 415 of 477 +a0080:= integrate(t0080,x) +--R +--R +--R x +--R ++ %Q +--R (280) | acot(%e )d%Q +--R ++ +--R Type: Union(Expression Integer,...) +--E 415 + +--S 416 of 477 +--m0080:= a0080-r0080 +--E 416 + +--S 417 of 477 +--d0080:= D(m0080,x) +--E 417 + +--S 418 of 477 +t0081:= x*acot(exp(x)) +--R +--R +--R x +--R (281) x acot(%e ) +--R Type: Expression Integer +--E 418 + +--S 419 of 477 +r0081:= 1/2*%i*(-x*polylog(2,-%i*exp(-x))+x*_ + polylog(2,%i*exp(-x))-_ + polylog(3,-%i*exp(-x))+_ + polylog(3,%i*exp(-x))) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Complex Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 419 + +--S 420 of 477 +a0081:= integrate(t0081,x) +--R +--R +--R x +--R ++ %Q +--R (282) | %Q acot(%e )d%Q +--R ++ +--R Type: Union(Expression Integer,...) +--E 420 + +--S 421 of 477 +--m0081:= a0081-r0081 +--E 421 + +--S 422 of 477 +--d0081:= D(m0081,x) +--E 422 + +--S 423 of 477 +t0082:= x^2*acot(exp(x)) +--R +--R +--R 2 x +--R (283) x acot(%e ) +--R Type: Expression Integer +--E 423 + +--S 424 of 477 +r0082:= -1/2*%i*x^2*polylog(2,-%i/exp(x))+_ + 1/2*%i*x^2*polylog(2,%i/exp(x))-_ + %i*x*polylog(3,-%i/exp(x))+_ + %i*x*polylog(3,%i/exp(x))-_ + %i*polylog(4,-%i/exp(x))+_ + %i*polylog(4,%i/exp(x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Complex Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 424 + +--S 425 of 477 +a0082:= integrate(t0082,x) +--R +--R +--R x +--R ++ 2 %Q +--R (284) | %Q acot(%e )d%Q +--R ++ +--R Type: Union(Expression Integer,...) +--E 425 + +--S 426 of 477 +--m0082:= a0082-r0082 +--E 426 + +--S 427 of 477 +--d0082:= D(m0082,x) +--E 427 + +--S 428 of 477 +t0083:= acot(exp(1)^(a+b*x)) +--R +--R +--R b x + a +--R (285) acot(%e ) +--R Type: Expression Integer +--E 428 + +--S 429 of 477 +r0083:= -1/2*%i*(polylog(2,-%i*exp(-a-b*x))-polylog(2,%i*exp(-a-b*x)))/b +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Complex Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 429 + +--S 430 of 477 +a0083:= integrate(t0083,x) +--R +--R +--R x +--R ++ %Q b + a +--R (286) | acot(%e )d%Q +--R ++ +--R Type: Union(Expression Integer,...) +--E 430 + +--S 431 of 477 +--m0083:= a0083-r0083 +--E 431 + +--S 432 of 477 +--d0083:= D(m0083,x) +--E 432 + +--S 433 of 477 +t0084:= x*acot(exp(1)^(a+b*x)) +--R +--R +--R b x + a +--R (287) x acot(%e ) +--R Type: Expression Integer +--E 433 + +--S 434 of 477 +r0084:= -1/2*%i*(x*polylog(2,-%i*exp(-a-b*x))*b-_ + x*polylog(2,%i*exp(-a-b*x))*b+_ + polylog(3,-%i*exp(-a-b*x))-_ + polylog(3,%i*exp(-a-b*x)))/b^2 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Complex Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 434 + +--S 435 of 477 +a0084:= integrate(t0084,x) +--R +--R +--R x +--R ++ %Q b + a +--R (288) | %Q acot(%e )d%Q +--R ++ +--R Type: Union(Expression Integer,...) +--E 435 + +--S 436 of 477 +--m0084:= a0084-r0084 +--E 436 + +--S 437 of 477 +--d0084:= D(m0084,x) +--E 437 + +--S 438 of 477 +t0085:= x^2*acot(exp(1)^(a+b*x)) +--R +--R +--R 2 b x + a +--R (289) x acot(%e ) +--R Type: Expression Integer +--E 438 + +--S 439 of 477 +r0085:= -1/2*%i*(x^2*polylog(2,-%i*exp(-a-b*x))*b^2-_ + x^2*polylog(2,%i*exp(-a-b*x))*b^2+_ + 2*x*polylog(3,-%i*exp(-a-b*x))*b-_ + 2*x*polylog(3,%i*exp(-a-b*x))*b+_ + 2*polylog(4,-%i*exp(-a-b*x))-_ + 2*polylog(4,%i*exp(-a-b*x)))/b^3 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Complex Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 439 + +--S 440 of 477 +a0085:= integrate(t0085,x) +--R +--R +--R x +--R ++ 2 %Q b + a +--R (290) | %Q acot(%e )d%Q +--R ++ +--R Type: Union(Expression Integer,...) +--E 440 + +--S 441 of 477 +--m0085:= a0085-r0085 +--E 441 + +--S 442 of 477 +--d0085:= D(m0085,x) +--E 442 + +--S 443 of 477 +t0086:= acot(a+b*f^(c+d*x)) +--R +--R +--R d x + c +--R (291) acot(b f + a) +--R Type: Expression Integer +--E 443 + +--S 444 of 477 +r0086:= -1/2*%i*(log(f^(c+d*x))*_ + log(-(-%i+a+b*f^(c+d*x))/(%i-a))-_ + log(f^(c+d*x))*_ + log((%i+a+b*f^(c+d*x))/(%i+a))-_ + log(f^(c+d*x))*_ + log((-%i+a+b*f^(c+d*x))/(a+b*f^(c+d*x)))+_ + log(f^(c+d*x))*_ + log((%i+a+b*f^(c+d*x))/(a+b*f^(c+d*x)))+_ + polylog(2,b*f^(c+d*x)/(%i-a))-_ + polylog(2,-b*f^(c+d*x)/(%i+a)))/d/log(f) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Complex Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 444 + +--S 445 of 477 +a0086:= integrate(t0086,x) +--R +--R +--R x +--R ++ %Q d + c +--R (292) | acot(b f + a)d%Q +--R ++ +--R Type: Union(Expression Integer,...) +--E 445 + +--S 446 of 477 +--m0086:= a0086-r0086 +--E 446 + +--S 447 of 477 +--d0086:= D(m0086,x) +--E 447 + +--S 448 of 477 +t0087:= x*acot(a+b*f^(c+d*x)) +--R +--R +--R d x + c +--R (293) x acot(b f + a) +--R Type: Expression Integer +--E 448 + +--S 449 of 477 +r0087:= -1/4*%i*x^2*log(1-b*f^(c+d*x)/(%i-a))+_ + 1/4*%i*x^2*log(1+b*f^(c+d*x)/(%i+a))+_ + 1/4*%i*x^2*log(1-%i/(a+b*f^(c+d*x)))-_ + 1/4*%i*x^2*log(1+%i/(a+b*f^(c+d*x)))-_ + 1/2*%i*x*polylog(2,b*f^(c+d*x)/(%i-a))/d/log(f)+_ + 1/2*%i*x*polylog(2,-b*f^(c+d*x)/(%i+a))/d/log(f)+_ + 1/2*%i*polylog(3,b*f^(c+d*x)/(%i-a))/d^2/log(f)^2-_ + 1/2*%i*polylog(3,-b*f^(c+d*x)/(%i+a))/d^2/log(f)^2 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Complex Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 449 + +--S 450 of 477 +a0087:= integrate(t0087,x) +--R +--R +--R x +--R ++ %Q d + c +--R (294) | %Q acot(b f + a)d%Q +--R ++ +--R Type: Union(Expression Integer,...) +--E 450 + +--S 451 of 477 +--m0087:= a0087-r0087 +--E 451 + +--S 452 of 477 +--d0087:= D(m0087,x) +--E 452 + +--S 453 of 477 +t0088:= x^2*acot(a+b*f^(c+d*x)) +--R +--R +--R 2 d x + c +--R (295) x acot(b f + a) +--R Type: Expression Integer +--E 453 + +--S 454 of 477 +r0088:= -1/6*%i*x^3*log(1-b*f^(c+d*x)/(%i-a))+_ + 1/6*%i*x^3*log(1+b*f^(c+d*x)/(%i+a))+_ + 1/6*%i*x^3*log(1-%i/(a+b*f^(c+d*x)))-_ + 1/6*%i*x^3*log(1+%i/(a+b*f^(c+d*x)))-_ + 1/2*%i*x^2*polylog(2,b*f^(c+d*x)/(%i-a))/d/log(f)+_ + 1/2*%i*x^2*polylog(2,-b*f^(c+d*x)/(%i+a))/d/log(f)+_ + %i*x*polylog(3,b*f^(c+d*x)/(%i-a))/d^2/log(f)^2-_ + %i*x*polylog(3,-b*f^(c+d*x)/(%i+a))/d^2/log(f)^2-_ + %i*polylog(4,b*f^(c+d*x)/(%i-a))/d^3/log(f)^3+_ + %i*polylog(4,-b*f^(c+d*x)/(%i+a))/d^3/log(f)^3 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Complex Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 454 + +--S 455 of 477 +a0088:= integrate(t0088,x) +--R +--R +--R x +--R ++ 2 %Q d + c +--R (296) | %Q acot(b f + a)d%Q +--R ++ +--R Type: Union(Expression Integer,...) +--E 455 + +--S 456 of 477 +--m0088:= a0088-r0088 +--E 456 + +--S 457 of 477 +--d0088:= D(m0088,x) +--E 457 + +--S 458 of 477 +t0089:= atan(sinh(x)) +--R +--R +--R (297) atan(sinh(x)) +--R Type: Expression Integer +--E 458 + +--S 459 of 477 +r0089:= -2*x*atan(exp(x))+x*atan(sinh(x))+_ + %i*polylog(2,-%i*exp(x))-_ + %i*polylog(2,%i*exp(x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Complex Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 459 + +--S 460 of 477 +a0089:= integrate(t0089,x) +--R +--R +--R x +--R ++ +--R (298) | atan(sinh(%Q))d%Q +--R ++ +--R Type: Union(Expression Integer,...) +--E 460 + +--S 461 of 477 +--m0089:= a0089-r0089 +--E 461 + +--S 462 of 477 +--d0089:= D(m0089,x) +--E 462 + +--S 463 of 477 +t0090:= x*atan(sinh(x)) +--R +--R +--R (299) x atan(sinh(x)) +--R Type: Expression Integer +--E 463 + +--S 464 of 477 +r0090:= -x^2*atan(exp(x))+1/2*x^2*atan(sinh(x))+_ + %i*x*polylog(2,-%i*exp(x))-_ + %i*x*polylog(2,%i*exp(x))-_ + %i*polylog(3,-%i*exp(x))+_ + %i*polylog(3,%i*exp(x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Complex Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 464 + +--S 465 of 477 +a0090:= integrate(t0090,x) +--R +--R +--R x +--R ++ +--R (300) | %Q atan(sinh(%Q))d%Q +--R ++ +--R Type: Union(Expression Integer,...) +--E 465 + +--S 466 of 477 +--m0090:= a0090-r0090 +--E 466 + +--S 467 of 477 +--d0090:= D(m0090,x) +--E 467 + +--S 468 of 477 +t0091:= x^2*atan(sinh(x)) +--R +--R +--R 2 +--R (301) x atan(sinh(x)) +--R Type: Expression Integer +--E 468 + +--S 469 of 477 +r0091:= -2/3*x^3*atan(exp(x))+1/3*x^3*atan(sinh(x))+_ + %i*x^2*polylog(2,-%i*exp(x))-_ + %i*x^2*polylog(2,%i*exp(x))-_ + 2*%i*x*polylog(3,-%i*exp(x))+_ + 2*%i*x*polylog(3,%i*exp(x))+_ + 2*%i*polylog(4,-%i*exp(x))-_ + 2*%i*polylog(4,%i*exp(x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Complex Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 469 + +--S 470 of 477 +a0091:= integrate(t0091,x) +--R +--R +--R x +--R ++ 2 +--R (302) | %Q atan(sinh(%Q))d%Q +--R ++ +--R Type: Union(Expression Integer,...) +--E 470 + +--S 471 of 477 +--m0091:= a0091-r0091 +--E 471 + +--S 472 of 477 +--d0091:= D(m0091,x) +--E 472 + +--S 473 of 477 +t0092:= (1-x^2)^(1/2)*acos(x) +--R +--R +--R +--------+ +--R | 2 +--R (303) acos(x)\|- x + 1 +--R Type: Expression Integer +--E 473 + +--S 474 of 477 +r0092:= 1/4*x^2+1/2*x*(1-x^2)^(1/2)*acos(x)-1/4*acos(x)^2 +--R +--R +--R +--------+ +--R | 2 2 2 +--R 2x acos(x)\|- x + 1 - acos(x) + x +--R (304) ------------------------------------- +--R 4 +--R Type: Expression Integer +--E 474 + +--S 475 of 477 +a0092:= integrate(t0092,x) +--R +--R +--R +--------+ 2 +--------+ +--R | 2 +--------+ | 2 +--R 2x\|- x + 1 | 2 2x\|- x + 1 2 +--R - atan(-------------) + 4x\|- x + 1 atan(-------------) + 4x +--R 2 2 +--R 2x - 1 2x - 1 +--R (305) --------------------------------------------------------------- +--R 16 +--R Type: Union(Expression Integer,...) +--E 475 + +--S 476 of 477 +m0092:= a0092-r0092 +--R +--R +--R (306) +--R +--------+ 2 +--------+ +--R | 2 +--------+ | 2 +--R 2x\|- x + 1 | 2 2x\|- x + 1 +--R - atan(-------------) + 4x\|- x + 1 atan(-------------) +--R 2 2 +--R 2x - 1 2x - 1 +--R + +--R +--------+ +--R | 2 2 +--R - 8x acos(x)\|- x + 1 + 4acos(x) +--R / +--R 16 +--R Type: Expression Integer +--E 476 + +--S 477 of 477 +d0092:= D(m0092,x) +--R +--R +--R +--------+ +--R | 2 +--R 2 2x\|- x + 1 2 +--R (- x + 1)atan(-------------) + (2x - 2)acos(x) +--R 2 +--R 2x - 1 +--R (307) ------------------------------------------------ +--R +--------+ +--R | 2 +--R 2\|- x + 1 +--R Type: Expression Integer +--E 477 + +)spool +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} Albert D. Rich ``Rule-based Mathematics'' +\verb|www.apmaths.uwo.ca/~arich| +\end{thebibliography} +\end{document}