diff --git a/changelog b/changelog index 78d6279..857fe9b 100644 --- a/changelog +++ b/changelog @@ -1,3 +1,6 @@ +20100620 tpd src/axiom-website/patches.html 20100620.01.tpd.patch +20100620 tpd src/input/Makefile rule-based inverse hyperbolic integration +20100620 tpd src/input/richinvhyper200-296.input inverse hyperbolic int. 20100619 tpd src/axiom-website/patches.html 20100619.04.tpd.patch 20100619 tpd src/input/Makefile rule-based inverse hyperbolic integration 20100619 tpd src/input/richinvhyper100-199.input inverse hyperbolic int. diff --git a/src/axiom-website/patches.html b/src/axiom-website/patches.html index 5cfa6bb..031e771 100644 --- a/src/axiom-website/patches.html +++ b/src/axiom-website/patches.html @@ -2926,6 +2926,8 @@ src/input/richhyper1000-1098.input rule-based hyper integration
src/input/richinvhyper000-099.input inverse hyperbolic integration
20100619.04.tpd.patch src/input/richinvhyper100-199.input inverse hyperbolic int.
+20100620.01.tpd.patch +src/input/richinvhyper200-296.input inverse hyperbolic int.
diff --git a/src/input/Makefile.pamphlet b/src/input/Makefile.pamphlet index 964d52e..a2974d2 100644 --- a/src/input/Makefile.pamphlet +++ b/src/input/Makefile.pamphlet @@ -388,6 +388,7 @@ REGRES= ackermann.regress \ richhyper1000-1098.regress \ richinvhyper000-099.regress \ richinvhyper100-199.regress \ + richinvhyper200-296.regress \ richinvtrig000-092.regress \ richlog000-099.regress \ richlog100-199.regress \ @@ -735,6 +736,7 @@ FILES= ${OUT}/ackermann.input \ ${OUT}/richhyper1000-1098.input \ ${OUT}/richinvhyper000-099.input \ ${OUT}/richinvhyper100-199.input \ + ${OUT}/richinvhyper200-296.input \ ${OUT}/richinvtrig000-092.input \ ${OUT}/richlog000-099.input \ ${OUT}/richlog100-199.input \ @@ -1111,6 +1113,7 @@ DOCFILES= \ ${DOC}/richhyper1000-1098.input.dvi \ ${DOC}/richinvhyper000-099.input.dvi \ ${DOC}/richinvhyper100-199.input.dvi \ + ${DOC}/richinvhyper200-296.input.dvi \ ${DOC}/richinvtrig000-092.input.dvi \ ${DOC}/richlog000-099.input.dvi \ ${DOC}/richlog100-199.input.dvi \ diff --git a/src/input/richinvhyper200-296.input.pamphlet b/src/input/richinvhyper200-296.input.pamphlet new file mode 100644 index 0000000..e8458d4 --- /dev/null +++ b/src/input/richinvhyper200-296.input.pamphlet @@ -0,0 +1,13572 @@ +\documentclass{article} +\usepackage{axiom} +\begin{document} +\title{\$SPAD/src/input richinvhyper200-296.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f richinvhyper200-296.output +)spool richinvhyper200-296.output +)set message auto off +)clear all + +--S 1 of 489 +t0200:= x*atanh(cosh(x)) +--R +--R +--R (1) x atanh(cosh(x)) +--R Type: Expression Integer +--E 1 + +--S 2 of 489 +r0200:= -x^2*atanh(exp(x))+1/2*x^2*atanh(cosh(x))-x*polylog(2,-exp(x))+_ + x*polylog(2,exp(x))+polylog(3,-exp(x))-polylog(3,exp(x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 2 + +--S 3 of 489 +a0200:= integrate(t0200,x) +--R +--R +--R x +--R ++ +--R (2) | %I atanh(cosh(%I))d%I +--R ++ +--R Type: Union(Expression Integer,...) +--E 3 + +--S 4 of 489 +--m0200:= a0200-r0200 +--E 4 + +--S 5 of 489 +--d0200:= D(m0200,x) +--E 5 + +--S 6 of 489 +t0201:= x^2*atanh(cosh(x)) +--R +--R +--R 2 +--R (3) x atanh(cosh(x)) +--R Type: Expression Integer +--E 6 + +--S 7 of 489 +r0201:= -2/3*x^3*atanh(exp(x))+1/3*x^3*atanh(cosh(x))-_ + x^2*polylog(2,-exp(x))+x^2*polylog(2,exp(x))+_ + 2*x*polylog(3,-exp(x))-2*x*polylog(3,exp(x))-_ + 2*polylog(4,-exp(x))+2*polylog(4,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 Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 7 + +--S 8 of 489 +a0201:= integrate(t0201,x) +--R +--R +--R x +--R ++ 2 +--R (4) | %I atanh(cosh(%I))d%I +--R ++ +--R Type: Union(Expression Integer,...) +--E 8 + +--S 9 of 489 +--m0201:= a0201-r0201 +--E 9 + +--S 10 of 489 +--d0201:= D(m0201,x) +--E 10 + +--S 11 of 489 +t0202:= acoth(cosh(x)) +--R +--R +--R (5) acoth(cosh(x)) +--R Type: Expression Integer +--E 11 + +--S 12 of 489 +r0202:= x*acoth(cosh(x))-2*x*atanh(exp(x))-polylog(2,-exp(x))+polylog(2,exp(x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 12 + +--S 13 of 489 +a0202:= integrate(t0202,x) +--R +--R +--R x +--R ++ +--R (6) | acoth(cosh(%I))d%I +--R ++ +--R Type: Union(Expression Integer,...) +--E 13 + +--S 14 of 489 +--m0202:= a0202-r0202 +--E 14 + +--S 15 of 489 +--d0202:= D(m0202,x) +--E 15 + +--S 16 of 489 +t0203:= x*acoth(cosh(x)) +--R +--R +--R (7) x acoth(cosh(x)) +--R Type: Expression Integer +--E 16 + +--S 17 of 489 +r0203:= 1/2*x^2*acoth(cosh(x))-x^2*atanh(exp(x))-x*polylog(2,-exp(x))+_ + x*polylog(2,exp(x))+polylog(3,-exp(x))-polylog(3,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 Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 17 + +--S 18 of 489 +a0203:= integrate(t0203,x) +--R +--R +--R x +--R ++ +--R (8) | %I acoth(cosh(%I))d%I +--R ++ +--R Type: Union(Expression Integer,...) +--E 18 + +--S 19 of 489 +--m0203:= a0203-r0203 +--E 19 + +--S 20 of 489 +--d0203:= D(m0203,x) +--E 20 + +--S 21 of 489 +t0204:= x^2*acoth(cosh(x)) +--R +--R +--R 2 +--R (9) x acoth(cosh(x)) +--R Type: Expression Integer +--E 21 + +--S 22 of 489 +r0204:= 1/3*x^3*acoth(cosh(x))-2/3*x^3*atanh(exp(x))-x^2*polylog(2,-exp(x))+_ + x^2*polylog(2,exp(x))+2*x*polylog(3,-exp(x))-_ + 2*x*polylog(3,exp(x))-2*polylog(4,-exp(x))+2*polylog(4,exp(x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 22 + +--S 23 of 489 +a0204:= integrate(t0204,x) +--R +--R +--R x +--R ++ 2 +--R (10) | %I acoth(cosh(%I))d%I +--R ++ +--R Type: Union(Expression Integer,...) +--E 23 + +--S 24 of 489 +--m0204:= a0204-r0204 +--E 24 + +--S 25 of 489 +--d0204:= D(m0204,x) +--E 25 + +--S 26 of 489 +t0205:= x^2*exp(1)^acosh(x) +--R +--R +--R 2 acosh(x) +--R (11) x %e +--R Type: Expression Integer +--E 26 + +--S 27 of 489 +r0205:= 1/4*x^4-1/8*(-1+x)^(1/2)*x*(1+x)^(1/2)+1/4*(-1+x)^(1/2)*_ + (1+x)^(1/2)*x^3-1/8*acosh(x) +--R +--R +--R 3 +-----+ +-----+ 4 +--R (2x - x)\|x - 1 \|x + 1 - acosh(x) + 2x +--R (12) ------------------------------------------ +--R 8 +--R Type: Expression Integer +--E 27 + +--S 28 of 489 +a0205:= integrate(t0205,x) +--R +--R +--R (13) +--R +------+ +------+ +--R 3 | 2 4 2 | 2 +--R ((8x - 4x)\|x - 1 - 8x + 8x - 1)log(\|x - 1 - x) +--R + +--R +------+ +--R 5 3 | 2 6 4 2 +--R (16x - 10x + x)\|x - 1 - 16x + 18x - 4x +--R / +--R +------+ +--R 3 | 2 4 2 +--R (64x - 32x)\|x - 1 - 64x + 64x - 8 +--R Type: Union(Expression Integer,...) +--E 28 + +--S 29 of 489 +m0205:= a0205-r0205 +--R +--R +--R (14) +--R +------+ +------+ +--R 3 | 2 4 2 | 2 +--R ((8x - 4x)\|x - 1 - 8x + 8x - 1)log(\|x - 1 - x) +--R + +--R 6 4 2 +-----+ +-----+ 3 7 +--R (- 16x + 16x - 4x )\|x - 1 \|x + 1 + (8x - 4x)acosh(x) - 16x +--R + +--R 5 3 +--R 24x - 10x + x +--R * +--R +------+ +--R | 2 +--R \|x - 1 +--R + +--R 7 5 3 +-----+ +-----+ 4 2 +--R (16x - 24x + 10x - x)\|x - 1 \|x + 1 + (- 8x + 8x - 1)acosh(x) +--R + +--R 8 6 4 2 +--R 16x - 32x + 20x - 4x +--R / +--R +------+ +--R 3 | 2 4 2 +--R (64x - 32x)\|x - 1 - 64x + 64x - 8 +--R Type: Expression Integer +--E 29 + +--S 30 of 489 +d0205:= D(m0205,x) +--R +--R +--R (15) +--R 11 9 7 5 3 +-----+ +-----+ +--R (- 1024x + 2560x - 2304x + 896x - 144x + 8x)\|x - 1 \|x + 1 +--R + +--R 12 10 8 6 4 2 +--R - 1024x + 3072x - 3456x + 1792x - 424x + 40x - 1 +--R * +--R +------+ +--R | 2 +--R \|x - 1 +--R + +--R 12 10 8 6 4 2 +-----+ +-----+ +--R (1024x - 3072x + 3456x - 1792x + 424x - 40x + 1)\|x - 1 \|x + 1 +--R + +--R 13 11 9 7 5 3 +--R 1024x - 3584x + 4864x - 3200x + 1040x - 152x + 8x +--R / +--R +------+ +--R 8 6 4 2 +-----+ +-----+ | 2 +--R (1024x - 2048x + 1280x - 256x + 8)\|x - 1 \|x + 1 \|x - 1 +--R + +--R 9 7 5 3 +-----+ +-----+ +--R (- 1024x + 2560x - 2176x + 704x - 64x)\|x - 1 \|x + 1 +--R Type: Expression Integer +--E 30 + +--S 31 of 489 +t0206:= exp(1)^acosh(x) +--R +--R +--R acosh(x) +--R (16) %e +--R Type: Expression Integer +--E 31 + +--S 32 of 489 +r0206:= 1/2*x^2+1/2*(-1+x)^(1/2)*x*(1+x)^(1/2)-1/2*acosh(x) +--R +--R +--R +-----+ +-----+ 2 +--R x\|x - 1 \|x + 1 - acosh(x) + x +--R (17) --------------------------------- +--R 2 +--R Type: Expression Integer +--E 32 + +--S 33 of 489 +a0206:= integrate(t0206,x) +--R +--R +--R +------+ +------+ +------+ +--R | 2 2 | 2 | 2 2 +--R (2x\|x - 1 - 2x + 1)log(\|x - 1 - x) + x\|x - 1 - x +--R (18) ----------------------------------------------------------- +--R +------+ +--R | 2 2 +--R 4x\|x - 1 - 4x + 2 +--R Type: Union(Expression Integer,...) +--E 33 + +--S 34 of 489 +m0206:= a0206-r0206 +--R +--R +--R (19) +--R +------+ +------+ +--R | 2 2 | 2 +--R (2x\|x - 1 - 2x + 1)log(\|x - 1 - x) +--R + +--R +------+ +--R 2 +-----+ +-----+ 3 | 2 +--R (- 2x \|x - 1 \|x + 1 + 2x acosh(x) - 2x + x)\|x - 1 +--R + +--R 3 +-----+ +-----+ 2 4 2 +--R (2x - x)\|x - 1 \|x + 1 + (- 2x + 1)acosh(x) + 2x - 2x +--R / +--R +------+ +--R | 2 2 +--R 4x\|x - 1 - 4x + 2 +--R Type: Expression Integer +--E 34 + +--S 35 of 489 +d0206:= D(m0206,x) +--R +--R +--R (20) +--R +------+ +--R 5 3 +-----+ +-----+ 6 4 2 | 2 +--R ((- 16x + 16x - 4x)\|x - 1 \|x + 1 - 16x + 24x - 10x + 1)\|x - 1 +--R + +--R 6 4 2 +-----+ +-----+ 7 5 3 +--R (16x - 24x + 10x - 1)\|x - 1 \|x + 1 + 16x - 32x + 20x - 4x +--R / +--R +------+ +--R 4 2 +-----+ +-----+ | 2 +--R (16x - 16x + 2)\|x - 1 \|x + 1 \|x - 1 +--R + +--R 5 3 +-----+ +-----+ +--R (- 16x + 24x - 8x)\|x - 1 \|x + 1 +--R Type: Expression Integer +--E 35 + +--S 36 of 489 +t0207:= exp(1)^acosh(x)/x +--R +--R +--R acosh(x) +--R %e +--R (21) ---------- +--R x +--R Type: Expression Integer +--E 36 + +--S 37 of 489 +r0207:= x+(-1+x)^(1/2)*(1+x)^(1/2)-2*atan((-1+x)^(1/2)/(1+x)^(1/2)) +--R +--R +--R +-----+ +--R \|x - 1 +-----+ +-----+ +--R (22) - 2atan(--------) + \|x - 1 \|x + 1 + x +--R +-----+ +--R \|x + 1 +--R Type: Expression Integer +--E 37 + +--S 38 of 489 +a0207:= integrate(t0207,x) +--R +--R +--R +------+ +------+ +--R | 2 | 2 +--R (- 2\|x - 1 + 2x)atan(\|x - 1 - x) - 1 +--R (23) ------------------------------------------ +--R +------+ +--R | 2 +--R \|x - 1 - x +--R Type: Union(Expression Integer,...) +--E 38 + +--S 39 of 489 +m0207:= a0207-r0207 +--R +--R +--R (24) +--R +------+ +------+ +------+ +-----+ +--R | 2 | 2 | 2 \|x - 1 +--R (- 2\|x - 1 + 2x)atan(\|x - 1 - x) + (2\|x - 1 - 2x)atan(--------) +--R +-----+ +--R \|x + 1 +--R + +--R +------+ +--R +-----+ +-----+ | 2 +-----+ +-----+ 2 +--R (- \|x - 1 \|x + 1 - x)\|x - 1 + x\|x - 1 \|x + 1 + x - 1 +--R / +--R +------+ +--R | 2 +--R \|x - 1 - x +--R Type: Expression Integer +--E 39 + +--S 40 of 489 +d0207:= D(m0207,x) +--R +--R +--R (25) +--R +------+ +--R 3 +-----+ +-----+ 4 2 | 2 +--R ((- 2x + 2x)\|x - 1 \|x + 1 - 2x + 3x - 1)\|x - 1 +--R + +--R 4 2 +-----+ +-----+ 5 3 +--R (2x - 3x + 1)\|x - 1 \|x + 1 + 2x - 4x + 2x +--R / +--R +------+ +--R 3 +-----+ +-----+ | 2 4 2 +-----+ +-----+ +--R (2x - x)\|x - 1 \|x + 1 \|x - 1 + (- 2x + 2x )\|x - 1 \|x + 1 +--R Type: Expression Integer +--E 40 + +--S 41 of 489 +t0208:= exp(1)^acosh(x)/x^2 +--R +--R +--R acosh(x) +--R %e +--R (26) ---------- +--R 2 +--R x +--R Type: Expression Integer +--E 41 + +--S 42 of 489 +r0208:= -(-1+x)^(1/2)*(1+x)^(1/2)/x+acosh(x)+log(x) +--R +--R +--R +-----+ +-----+ +--R - \|x - 1 \|x + 1 + x log(x) + x acosh(x) +--R (27) ------------------------------------------ +--R x +--R Type: Expression Integer +--E 42 + +--S 43 of 489 +a0208:= integrate(t0208,x) +--R +--R +--R (28) +--R +------+ +------+ +------+ +--R | 2 2 | 2 | 2 2 +--R (- x\|x - 1 + x )log(\|x - 1 - x) + x log(x)\|x - 1 - x log(x) + 1 +--R ------------------------------------------------------------------------ +--R +------+ +--R | 2 2 +--R x\|x - 1 - x +--R Type: Union(Expression Integer,...) +--E 43 + +--S 44 of 489 +m0208:= a0208-r0208 +--R +--R +--R (29) +--R +------+ +------+ +--R | 2 2 | 2 +--R (- x\|x - 1 + x )log(\|x - 1 - x) +--R + +--R +------+ +--R +-----+ +-----+ | 2 +-----+ +-----+ 2 +--R (\|x - 1 \|x + 1 - x acosh(x))\|x - 1 - x\|x - 1 \|x + 1 + x acosh(x) +--R + +--R 1 +--R / +--R +------+ +--R | 2 2 +--R x\|x - 1 - x +--R Type: Expression Integer +--E 44 + +--S 45 of 489 +d0208:= D(m0208,x) +--R +--R +--R (30) +--R +------+ +--R +-----+ +-----+ 2 | 2 2 +-----+ +-----+ +--R (2x\|x - 1 \|x + 1 + 2x - 1)\|x - 1 + (- 2x + 1)\|x - 1 \|x + 1 +--R + +--R 3 +--R - 2x + 2x +--R / +--R +------+ +--R 4 2 +-----+ +-----+ | 2 5 3 +-----+ +-----+ +--R (2x - x )\|x - 1 \|x + 1 \|x - 1 + (- 2x + 2x )\|x - 1 \|x + 1 +--R Type: Expression Integer +--E 45 + +--S 46 of 489 +t0209:= exp(1)^(3*atanh(x)) +--R +--R +--R 3atanh(x) +--R (31) %e +--R Type: Expression Integer +--E 46 + +--S 47 of 489 +r0209:= -(-5+x)*(1+x)^(1/2)/(1-x)^(1/2)-3*asin(x) +--R +--R +--R +-----+ +-------+ +--R (- x + 5)\|x + 1 - 3asin(x)\|- x + 1 +--R (32) -------------------------------------- +--R +-------+ +--R \|- x + 1 +--R Type: Expression Integer +--E 47 + +--S 48 of 489 +a0209:= integrate(t0209,x) +--R +--R +--R +-------+ +-------+ +--R |- x - 1 |- x - 1 +--R (33) - 6atan( |------- ) + (- x + 5) |------- +--R \| x - 1 \| x - 1 +--R Type: Union(Expression Integer,...) +--E 48 + +--S 49 of 489 +m0209:= a0209-r0209 +--R +--R +--R (34) +--R +-------+ +--R +-------+ |- x - 1 +-----+ +--R - 6\|- x + 1 atan( |------- ) + (x - 5)\|x + 1 +--R \| x - 1 +--R + +--R +-------+ +--R +-------+ |- x - 1 +-------+ +--R (- x + 5)\|- x + 1 |------- + 3asin(x)\|- x + 1 +--R \| x - 1 +--R / +--R +-------+ +--R \|- x + 1 +--R Type: Expression Integer +--E 49 + +--S 50 of 489 +d0209:= D(m0209,x) +--R +--R +--R (35) +--R +-------+ +--R 2 +-------+ |- x - 1 +--R (3x - 6x + 3)\|- x + 1 |------- +--R \| x - 1 +--R + +--R +--------+ +--R 2 | 2 +-------+ +--R (x + 2x + 1)\|- x + 1 \|- x + 1 +--R * +--R +-----+ +--R \|x + 1 +--R + +--R +--------+ +-------+ +--R 3 2 | 2 |- x - 1 +--R (x - 2x + 5x - 4)\|- x + 1 |------- +--R \| x - 1 +--R / +--R +--------+ +-------+ +--R 2 | 2 +-------+ |- x - 1 +-----+ +--R (x - 2x + 1)\|- x + 1 \|- x + 1 |------- \|x + 1 +--R \| x - 1 +--R Type: Expression Integer +--E 50 + +--S 51 of 489 +t0210:= x^2*exp(1)^(1/2*atanh(x)) +--R +--R +--R atanh(x) +--R -------- +--R 2 2 +--R (36) x %e +--R Type: Expression Integer +--E 51 + +--S 52 of 489 +r0210:= -29/24*exp(1)^(1/2*atanh(x))*(1-x)+13/12*exp(1)^(1/2*atanh(x))*_ + (1-x)^2-1/3*exp(1)^(1/2*atanh(x))*(1-x)^3+3/16*atan(-1+2^(1/2)*_ + exp(1)^(1/2*atanh(x)))*2^(1/2)+3/16*atan(1+2^(1/2)*exp(1)^(1/2*_ + atanh(x)))*2^(1/2)-3/32*log(1-2^(1/2)*exp(1)^(1/2*atanh(x))+_ + exp(1)^atanh(x))*2^(1/2)+3/32*log(1+2^(1/2)*exp(1)^(1/2*atanh(x))+_ + exp(1)^atanh(x))*2^(1/2) +--R +--R +--R (37) +--R atanh(x) +--R -------- +--R +-+ atanh(x) +-+ 2 +--R 9\|2 log(%e + \|2 %e + 1) +--R + +--R atanh(x) +--R -------- +--R +-+ atanh(x) +-+ 2 +--R - 9\|2 log(%e - \|2 %e + 1) +--R + +--R atanh(x) atanh(x) +--R -------- -------- +--R +-+ +-+ 2 +-+ +-+ 2 +--R 18\|2 atan(\|2 %e + 1) + 18\|2 atan(\|2 %e - 1) +--R + +--R atanh(x) +--R -------- +--R 3 2 2 +--R (32x + 8x + 4x - 44)%e +--R / +--R 96 +--R Type: Expression Integer +--E 52 + +--S 53 of 489 +a0210:= integrate(t0210,x) +--R +--R +--R (38) +--R - x - 1 2 - x - 1 +--R log(-------) log(-------) +--R x - 1 x - 1 +--R ------------ ------------ +--R +-+ 4 +-+ 4 +--R 9\|2 log((%e ) + \|2 %e + 1) +--R + +--R - x - 1 2 - x - 1 +--R log(-------) log(-------) +--R x - 1 x - 1 +--R ------------ ------------ +--R +-+ 4 +-+ 4 +--R - 9\|2 log((%e ) - \|2 %e + 1) +--R + +--R +-+ 1 +-+ 1 +--R - 18\|2 atan(----------------------) - 18\|2 atan(----------------------) +--R - x - 1 - x - 1 +--R log(-------) log(-------) +--R x - 1 x - 1 +--R ------------ ------------ +--R +-+ 4 +-+ 4 +--R \|2 %e - 1 \|2 %e + 1 +--R + +--R - x - 1 +--R log(-------) +--R x - 1 +--R ------------ +--R 3 2 4 +--R (32x + 8x + 4x - 44)%e +--R / +--R 96 +--R Type: Union(Expression Integer,...) +--E 53 + +--S 54 of 489 +m0210:= a0210-r0210 +--R +--R +--R (39) +--R - x - 1 2 - x - 1 +--R log(-------) log(-------) +--R x - 1 x - 1 +--R ------------ ------------ +--R +-+ 4 +-+ 4 +--R 9\|2 log((%e ) + \|2 %e + 1) +--R + +--R - x - 1 2 - x - 1 +--R log(-------) log(-------) +--R x - 1 x - 1 +--R ------------ ------------ +--R +-+ 4 +-+ 4 +--R - 9\|2 log((%e ) - \|2 %e + 1) +--R + +--R atanh(x) +--R -------- +--R +-+ atanh(x) +-+ 2 +--R - 9\|2 log(%e + \|2 %e + 1) +--R + +--R atanh(x) +--R -------- +--R +-+ atanh(x) +-+ 2 +--R 9\|2 log(%e - \|2 %e + 1) +--R + +--R atanh(x) atanh(x) +--R -------- -------- +--R +-+ +-+ 2 +-+ +-+ 2 +--R - 18\|2 atan(\|2 %e + 1) - 18\|2 atan(\|2 %e - 1) +--R + +--R +-+ 1 +-+ 1 +--R - 18\|2 atan(----------------------) - 18\|2 atan(----------------------) +--R - x - 1 - x - 1 +--R log(-------) log(-------) +--R x - 1 x - 1 +--R ------------ ------------ +--R +-+ 4 +-+ 4 +--R \|2 %e - 1 \|2 %e + 1 +--R + +--R - x - 1 +--R log(-------) +--R x - 1 atanh(x) +--R ------------ -------- +--R 3 2 4 3 2 2 +--R (32x + 8x + 4x - 44)%e + (- 32x - 8x - 4x + 44)%e +--R / +--R 96 +--R Type: Expression Integer +--E 54 + +--S 55 of 489 +d0210:= D(m0210,x) +--R +--R +--R (40) +--R atanh(x) 4 +--R -------- +--R 4 2 2 4 2 +--R ((16x - 16x - 3x + 3)(%e ) + 16x - 16x - 3x + 3) +--R * +--R atanh(x) 2 +--R (%e ) +--R + +--R atanh(x) 4 +--R -------- +--R 4 2 2 4 2 +--R ((32x - 32x - 6x + 6)(%e ) + 32x - 32x - 6x + 6) +--R * +--R atanh(x) +--R %e +--R + +--R atanh(x) 6 +--R -------- +--R 4 2 2 +--R (- 32x + 32x + 6x - 6)(%e ) +--R + +--R atanh(x) 4 +--R -------- +--R 4 2 2 +--R (16x - 16x - 3x + 3)(%e ) +--R + +--R atanh(x) 2 +--R -------- +--R 4 2 2 4 2 +--R (- 32x + 32x + 6x - 6)(%e ) + 16x - 16x - 3x + 3 +--R * +--R - x - 1 5 +--R log(-------) +--R x - 1 +--R ------------ +--R 4 +--R (%e ) +--R + +--R atanh(x) 5 atanh(x) 3 +--R -------- -------- +--R 4 2 2 2 +--R (- 16x + 16x + 3x - 3)(%e ) + 3(%e ) +--R + +--R atanh(x) +--R -------- +--R 4 2 2 +--R (- 16x + 16x + 3x)%e +--R * +--R atanh(x) 2 +--R (%e ) +--R + +--R atanh(x) 5 atanh(x) 3 +--R -------- -------- +--R 4 2 2 2 +--R (- 32x + 32x + 6x - 9)(%e ) + 6(%e ) +--R + +--R atanh(x) +--R -------- +--R 4 2 2 +--R (- 32x + 32x + 6x - 3)%e +--R * +--R atanh(x) +--R %e +--R + +--R atanh(x) 7 +--R -------- +--R 4 2 2 +--R (32x - 32x - 6x + 6)(%e ) +--R + +--R atanh(x) 5 +--R -------- +--R 4 2 2 +--R (- 16x + 16x + 3x - 6)(%e ) +--R + +--R atanh(x) 3 +--R -------- +--R 4 2 2 +--R (32x - 32x - 6x + 3)(%e ) +--R + +--R atanh(x) +--R -------- +--R 4 2 2 +--R (- 16x + 16x + 3x + 3)%e +--R * +--R - x - 1 4 +--R log(-------) +--R x - 1 +--R ------------ +--R 4 +--R (%e ) +--R + +--R atanh(x) 4 +--R -------- +--R 4 2 2 4 2 +--R ((16x - 16x - 3x - 3)(%e ) + 16x - 16x - 3x - 3) +--R * +--R atanh(x) 2 +--R (%e ) +--R + +--R atanh(x) 4 +--R -------- +--R 4 2 2 4 2 +--R ((32x - 32x - 6x - 6)(%e ) + 32x - 32x - 6x - 6) +--R * +--R atanh(x) +--R %e +--R + +--R atanh(x) 6 +--R -------- +--R 4 2 2 +--R (- 32x + 32x + 6x + 6)(%e ) +--R + +--R atanh(x) 4 +--R -------- +--R 4 2 2 +--R (16x - 16x - 3x - 3)(%e ) +--R + +--R atanh(x) 2 +--R -------- +--R 4 2 2 4 2 +--R (- 32x + 32x + 6x + 6)(%e ) + 16x - 16x - 3x - 3 +--R * +--R - x - 1 +--R log(-------) +--R x - 1 +--R ------------ +--R 4 +--R %e +--R + +--R atanh(x) 5 atanh(x) 3 +--R -------- -------- +--R 4 2 2 2 +--R (- 16x + 16x + 3x - 3)(%e ) + 3(%e ) +--R + +--R atanh(x) +--R -------- +--R 4 2 2 +--R (- 16x + 16x + 3x)%e +--R * +--R atanh(x) 2 +--R (%e ) +--R + +--R atanh(x) 5 atanh(x) 3 +--R -------- -------- +--R 4 2 2 2 +--R (- 32x + 32x + 6x - 9)(%e ) + 6(%e ) +--R + +--R atanh(x) +--R -------- +--R 4 2 2 +--R (- 32x + 32x + 6x - 3)%e +--R * +--R atanh(x) +--R %e +--R + +--R atanh(x) 7 +--R -------- +--R 4 2 2 +--R (32x - 32x - 6x + 6)(%e ) +--R + +--R atanh(x) 5 +--R -------- +--R 4 2 2 +--R (- 16x + 16x + 3x - 6)(%e ) +--R + +--R atanh(x) 3 atanh(x) +--R -------- -------- +--R 4 2 2 4 2 2 +--R (32x - 32x - 6x + 3)(%e ) + (- 16x + 16x + 3x + 3)%e +--R / +--R atanh(x) 4 +--R -------- +--R 2 2 2 atanh(x) 2 +--R ((16x - 16)(%e ) + 16x - 16)(%e ) +--R + +--R atanh(x) 4 +--R -------- +--R 2 2 2 atanh(x) +--R ((32x - 32)(%e ) + 32x - 32)%e +--R + +--R atanh(x) 6 atanh(x) 4 +--R -------- -------- +--R 2 2 2 2 +--R (- 32x + 32)(%e ) + (16x - 16)(%e ) +--R + +--R atanh(x) 2 +--R -------- +--R 2 2 2 +--R (- 32x + 32)(%e ) + 16x - 16 +--R * +--R - x - 1 4 +--R log(-------) +--R x - 1 +--R ------------ +--R 4 +--R (%e ) +--R + +--R atanh(x) 4 +--R -------- +--R 2 2 2 atanh(x) 2 +--R ((16x - 16)(%e ) + 16x - 16)(%e ) +--R + +--R atanh(x) 4 +--R -------- +--R 2 2 2 atanh(x) +--R ((32x - 32)(%e ) + 32x - 32)%e +--R + +--R atanh(x) 6 atanh(x) 4 +--R -------- -------- +--R 2 2 2 2 +--R (- 32x + 32)(%e ) + (16x - 16)(%e ) +--R + +--R atanh(x) 2 +--R -------- +--R 2 2 2 +--R (- 32x + 32)(%e ) + 16x - 16 +--R Type: Expression Integer +--E 55 + +--S 56 of 489 +t0211:= x*exp(1)^(1/2*atanh(x)) +--R +--R +--R atanh(x) +--R -------- +--R 2 +--R (41) x %e +--R Type: Expression Integer +--E 56 + +--S 57 of 489 +r0211:= -5/4*exp(1)^(1/2*atanh(x))*(1-x)+1/2*exp(1)^(1/2*atanh(x))*(1-x)^2+_ + 1/8*atan(-1+2^(1/2)*exp(1)^(1/2*atanh(x)))*2^(1/2)+_ + 1/8*atan(1+2^(1/2)*exp(1)^(1/2*atanh(x)))*2^(1/2)-_ + 1/16*log(1-2^(1/2)*exp(1)^(1/2*atanh(x))+exp(1)^atanh(x))*2^(1/2)+_ + 1/16*log(1+2^(1/2)*exp(1)^(1/2*atanh(x))+exp(1)^atanh(x))*2^(1/2) +--R +--R +--R (42) +--R atanh(x) +--R -------- +--R +-+ atanh(x) +-+ 2 +--R \|2 log(%e + \|2 %e + 1) +--R + +--R atanh(x) +--R -------- +--R +-+ atanh(x) +-+ 2 +--R - \|2 log(%e - \|2 %e + 1) +--R + +--R atanh(x) atanh(x) +--R -------- -------- +--R +-+ +-+ 2 +-+ +-+ 2 +--R 2\|2 atan(\|2 %e + 1) + 2\|2 atan(\|2 %e - 1) +--R + +--R atanh(x) +--R -------- +--R 2 2 +--R (8x + 4x - 12)%e +--R / +--R 16 +--R Type: Expression Integer +--E 57 + +--S 58 of 489 +a0211:= integrate(t0211,x) +--R +--R +--R (43) +--R - x - 1 2 - x - 1 +--R log(-------) log(-------) +--R x - 1 x - 1 +--R ------------ ------------ +--R +-+ 4 +-+ 4 +--R \|2 log((%e ) + \|2 %e + 1) +--R + +--R - x - 1 2 - x - 1 +--R log(-------) log(-------) +--R x - 1 x - 1 +--R ------------ ------------ +--R +-+ 4 +-+ 4 +--R - \|2 log((%e ) - \|2 %e + 1) +--R + +--R +-+ 1 +-+ 1 +--R - 2\|2 atan(----------------------) - 2\|2 atan(----------------------) +--R - x - 1 - x - 1 +--R log(-------) log(-------) +--R x - 1 x - 1 +--R ------------ ------------ +--R +-+ 4 +-+ 4 +--R \|2 %e - 1 \|2 %e + 1 +--R + +--R - x - 1 +--R log(-------) +--R x - 1 +--R ------------ +--R 2 4 +--R (8x + 4x - 12)%e +--R / +--R 16 +--R Type: Union(Expression Integer,...) +--E 58 + +--S 59 of 489 +m0211:= a0211-r0211 +--R +--R +--R (44) +--R - x - 1 2 - x - 1 +--R log(-------) log(-------) +--R x - 1 x - 1 +--R ------------ ------------ +--R +-+ 4 +-+ 4 +--R \|2 log((%e ) + \|2 %e + 1) +--R + +--R - x - 1 2 - x - 1 +--R log(-------) log(-------) +--R x - 1 x - 1 +--R ------------ ------------ +--R +-+ 4 +-+ 4 +--R - \|2 log((%e ) - \|2 %e + 1) +--R + +--R atanh(x) +--R -------- +--R +-+ atanh(x) +-+ 2 +--R - \|2 log(%e + \|2 %e + 1) +--R + +--R atanh(x) atanh(x) +--R -------- -------- +--R +-+ atanh(x) +-+ 2 +-+ +-+ 2 +--R \|2 log(%e - \|2 %e + 1) - 2\|2 atan(\|2 %e + 1) +--R + +--R atanh(x) +--R -------- +--R +-+ +-+ 2 +-+ 1 +--R - 2\|2 atan(\|2 %e - 1) - 2\|2 atan(----------------------) +--R - x - 1 +--R log(-------) +--R x - 1 +--R ------------ +--R +-+ 4 +--R \|2 %e - 1 +--R + +--R - x - 1 +--R log(-------) +--R x - 1 +--R ------------ +--R +-+ 1 2 4 +--R - 2\|2 atan(----------------------) + (8x + 4x - 12)%e +--R - x - 1 +--R log(-------) +--R x - 1 +--R ------------ +--R +-+ 4 +--R \|2 %e + 1 +--R + +--R atanh(x) +--R -------- +--R 2 2 +--R (- 8x - 4x + 12)%e +--R / +--R 16 +--R Type: Expression Integer +--E 59 + +--S 60 of 489 +d0211:= D(m0211,x) +--R +--R +--R (45) +--R atanh(x) 4 +--R -------- +--R 3 2 3 atanh(x) 2 +--R ((8x - 9x + 1)(%e ) + 8x - 9x + 1)(%e ) +--R + +--R atanh(x) 4 +--R -------- +--R 3 2 3 atanh(x) +--R ((16x - 18x + 2)(%e ) + 16x - 18x + 2)%e +--R + +--R atanh(x) 6 atanh(x) 4 +--R -------- -------- +--R 3 2 3 2 +--R (- 16x + 18x - 2)(%e ) + (8x - 9x + 1)(%e ) +--R + +--R atanh(x) 2 +--R -------- +--R 3 2 3 +--R (- 16x + 18x - 2)(%e ) + 8x - 9x + 1 +--R * +--R - x - 1 5 +--R log(-------) +--R x - 1 +--R ------------ +--R 4 +--R (%e ) +--R + +--R atanh(x) 5 atanh(x) 3 +--R -------- -------- +--R 3 2 2 +--R (- 8x + 9x - 1)(%e ) + (%e ) +--R + +--R atanh(x) +--R -------- +--R 3 2 +--R (- 8x + 9x)%e +--R * +--R atanh(x) 2 +--R (%e ) +--R + +--R atanh(x) 5 atanh(x) 3 +--R -------- -------- +--R 3 2 2 +--R (- 16x + 18x - 3)(%e ) + 2(%e ) +--R + +--R atanh(x) +--R -------- +--R 3 2 +--R (- 16x + 18x - 1)%e +--R * +--R atanh(x) +--R %e +--R + +--R atanh(x) 7 atanh(x) 5 +--R -------- -------- +--R 3 2 3 2 +--R (16x - 18x + 2)(%e ) + (- 8x + 9x - 2)(%e ) +--R + +--R atanh(x) 3 atanh(x) +--R -------- -------- +--R 3 2 3 2 +--R (16x - 18x + 1)(%e ) + (- 8x + 9x + 1)%e +--R * +--R - x - 1 4 +--R log(-------) +--R x - 1 +--R ------------ +--R 4 +--R (%e ) +--R + +--R atanh(x) 4 +--R -------- +--R 3 2 3 atanh(x) 2 +--R ((8x - 9x - 1)(%e ) + 8x - 9x - 1)(%e ) +--R + +--R atanh(x) 4 +--R -------- +--R 3 2 3 atanh(x) +--R ((16x - 18x - 2)(%e ) + 16x - 18x - 2)%e +--R + +--R atanh(x) 6 atanh(x) 4 +--R -------- -------- +--R 3 2 3 2 +--R (- 16x + 18x + 2)(%e ) + (8x - 9x - 1)(%e ) +--R + +--R atanh(x) 2 +--R -------- +--R 3 2 3 +--R (- 16x + 18x + 2)(%e ) + 8x - 9x - 1 +--R * +--R - x - 1 +--R log(-------) +--R x - 1 +--R ------------ +--R 4 +--R %e +--R + +--R atanh(x) 5 atanh(x) 3 +--R -------- -------- +--R 3 2 2 +--R (- 8x + 9x - 1)(%e ) + (%e ) +--R + +--R atanh(x) +--R -------- +--R 3 2 +--R (- 8x + 9x)%e +--R * +--R atanh(x) 2 +--R (%e ) +--R + +--R atanh(x) 5 atanh(x) 3 +--R -------- -------- +--R 3 2 2 +--R (- 16x + 18x - 3)(%e ) + 2(%e ) +--R + +--R atanh(x) +--R -------- +--R 3 2 +--R (- 16x + 18x - 1)%e +--R * +--R atanh(x) +--R %e +--R + +--R atanh(x) 7 atanh(x) 5 +--R -------- -------- +--R 3 2 3 2 +--R (16x - 18x + 2)(%e ) + (- 8x + 9x - 2)(%e ) +--R + +--R atanh(x) 3 atanh(x) +--R -------- -------- +--R 3 2 3 2 +--R (16x - 18x + 1)(%e ) + (- 8x + 9x + 1)%e +--R / +--R atanh(x) 4 +--R -------- +--R 2 2 2 atanh(x) 2 +--R ((8x - 8)(%e ) + 8x - 8)(%e ) +--R + +--R atanh(x) 4 +--R -------- +--R 2 2 2 atanh(x) +--R ((16x - 16)(%e ) + 16x - 16)%e +--R + +--R atanh(x) 6 atanh(x) 4 +--R -------- -------- +--R 2 2 2 2 +--R (- 16x + 16)(%e ) + (8x - 8)(%e ) +--R + +--R atanh(x) 2 +--R -------- +--R 2 2 2 +--R (- 16x + 16)(%e ) + 8x - 8 +--R * +--R - x - 1 4 +--R log(-------) +--R x - 1 +--R ------------ +--R 4 +--R (%e ) +--R + +--R atanh(x) 4 +--R -------- +--R 2 2 2 atanh(x) 2 +--R ((8x - 8)(%e ) + 8x - 8)(%e ) +--R + +--R atanh(x) 4 +--R -------- +--R 2 2 2 atanh(x) +--R ((16x - 16)(%e ) + 16x - 16)%e +--R + +--R atanh(x) 6 atanh(x) 4 +--R -------- -------- +--R 2 2 2 2 +--R (- 16x + 16)(%e ) + (8x - 8)(%e ) +--R + +--R atanh(x) 2 +--R -------- +--R 2 2 2 +--R (- 16x + 16)(%e ) + 8x - 8 +--R Type: Expression Integer +--E 60 + +--S 61 of 489 +t0212:= exp(1)^(1/2*atanh(x)) +--R +--R +--R atanh(x) +--R -------- +--R 2 +--R (46) %e +--R Type: Expression Integer +--E 61 + +--S 62 of 489 +r0212:= -(1-x)^(3/4)*(1+x)^(1/4)-1/2*atan(-1+2^(1/2)*(1-x)^(1/4)/_ + (1+x)^(1/4))*2^(1/2)-1/2*atan(1+2^(1/2)*(1-x)^(1/4)/(1+x)^(1/4))*_ + 2^(1/2)-1/4*log(1+(1-x)^(1/2)/(1+x)^(1/2)-2^(1/2)*(1-x)^(1/4)/_ + (1+x)^(1/4))*2^(1/2)+1/4*log(1+(1-x)^(1/2)/(1+x)^(1/2)+2^(1/2)*_ + (1-x)^(1/4)/(1+x)^(1/4))*2^(1/2) +--R +--R +--R (47) +--R +-----+ +-------+ 4+-----+ +-+4+-------+ +-----+ +--R +-+ (\|x + 1 + \|- x + 1 )\|x + 1 + \|2 \|- x + 1 \|x + 1 +--R \|2 log(--------------------------------------------------------) +--R +-----+4+-----+ +--R \|x + 1 \|x + 1 +--R + +--R +-----+ +-------+ 4+-----+ +-+4+-------+ +-----+ +--R +-+ (\|x + 1 + \|- x + 1 )\|x + 1 - \|2 \|- x + 1 \|x + 1 +--R - \|2 log(--------------------------------------------------------) +--R +-----+4+-----+ +--R \|x + 1 \|x + 1 +--R + +--R 4+-----+ +-+4+-------+ +--R +-+ \|x + 1 + \|2 \|- x + 1 +--R - 2\|2 atan(-------------------------) +--R 4+-----+ +--R \|x + 1 +--R + +--R 4+-----+ +-+4+-------+ +--R +-+ \|x + 1 - \|2 \|- x + 1 4+-------+3 4+-----+ +--R 2\|2 atan(-------------------------) - 4\|- x + 1 \|x + 1 +--R 4+-----+ +--R \|x + 1 +--R / +--R 4 +--R Type: Expression Integer +--E 62 + +--S 63 of 489 +a0212:= integrate(t0212,x) +--R +--R +--R (48) +--R - x - 1 2 - x - 1 +--R log(-------) log(-------) +--R x - 1 x - 1 +--R ------------ ------------ +--R +-+ 4 +-+ 4 +--R \|2 log((%e ) + \|2 %e + 1) +--R + +--R - x - 1 2 - x - 1 +--R log(-------) log(-------) +--R x - 1 x - 1 +--R ------------ ------------ +--R +-+ 4 +-+ 4 +--R - \|2 log((%e ) - \|2 %e + 1) +--R + +--R +-+ 1 +-+ 1 +--R - 2\|2 atan(----------------------) - 2\|2 atan(----------------------) +--R - x - 1 - x - 1 +--R log(-------) log(-------) +--R x - 1 x - 1 +--R ------------ ------------ +--R +-+ 4 +-+ 4 +--R \|2 %e - 1 \|2 %e + 1 +--R + +--R - x - 1 +--R log(-------) +--R x - 1 +--R ------------ +--R 4 +--R (4x - 4)%e +--R / +--R 4 +--R Type: Union(Expression Integer,...) +--E 63 + +--S 64 of 489 +m0212:= a0212-r0212 +--R +--R +--R (49) +--R - x - 1 2 - x - 1 +--R log(-------) log(-------) +--R x - 1 x - 1 +--R ------------ ------------ +--R +-+ 4 +-+ 4 +--R \|2 log((%e ) + \|2 %e + 1) +--R + +--R - x - 1 2 - x - 1 +--R log(-------) log(-------) +--R x - 1 x - 1 +--R ------------ ------------ +--R +-+ 4 +-+ 4 +--R - \|2 log((%e ) - \|2 %e + 1) +--R + +--R +-+ 1 +-+ 1 +--R - 2\|2 atan(----------------------) - 2\|2 atan(----------------------) +--R - x - 1 - x - 1 +--R log(-------) log(-------) +--R x - 1 x - 1 +--R ------------ ------------ +--R +-+ 4 +-+ 4 +--R \|2 %e - 1 \|2 %e + 1 +--R + +--R +-----+ +-------+ 4+-----+ +-+4+-------+ +-----+ +--R +-+ (\|x + 1 + \|- x + 1 )\|x + 1 + \|2 \|- x + 1 \|x + 1 +--R - \|2 log(--------------------------------------------------------) +--R +-----+4+-----+ +--R \|x + 1 \|x + 1 +--R + +--R +-----+ +-------+ 4+-----+ +-+4+-------+ +-----+ +--R +-+ (\|x + 1 + \|- x + 1 )\|x + 1 - \|2 \|- x + 1 \|x + 1 +--R \|2 log(--------------------------------------------------------) +--R +-----+4+-----+ +--R \|x + 1 \|x + 1 +--R + +--R - x - 1 +--R log(-------) +--R x - 1 +--R ------------ 4+-----+ +-+4+-------+ +--R 4 +-+ \|x + 1 + \|2 \|- x + 1 +--R (4x - 4)%e + 2\|2 atan(-------------------------) +--R 4+-----+ +--R \|x + 1 +--R + +--R 4+-----+ +-+4+-------+ +--R +-+ \|x + 1 - \|2 \|- x + 1 4+-------+3 4+-----+ +--R - 2\|2 atan(-------------------------) + 4\|- x + 1 \|x + 1 +--R 4+-----+ +--R \|x + 1 +--R / +--R 4 +--R Type: Expression Integer +--E 64 + +--S 65 of 489 +d0212:= D(m0212,x) +--R +--R +--R (50) +--R 2 4+-------+3 4+-----+3 +--R (4x - 2x - 2)\|- x + 1 \|x + 1 +--R + +--R 2 +-------+4+-------+ +-----+ +--R (- 4x + 2x + 2)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 2 4+-------+ +--R (- 4x + 2x + 2)\|- x + 1 +--R * +--R 4+-----+ +--R \|x + 1 +--R * +--R - x - 1 5 +--R log(-------) +--R x - 1 +--R ------------ +--R 4 +--R (%e ) +--R + +--R 2 +-------+ +-----+ 2 4+-----+2 +--R ((4x - x - 3)\|- x + 1 \|x + 1 + 3x - x - 2)\|x + 1 +--R + +--R +-------+4+-------+2 +-----+ +--R (- x - 2)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 3 2 4+-------+2 +--R (- 4x - 3x + 4x + 3)\|- x + 1 +--R * +--R - x - 1 4 +--R log(-------) +--R x - 1 +--R ------------ +--R 4 +--R (%e ) +--R + +--R 2 4+-------+3 4+-----+3 +--R (4x - 2x - 6)\|- x + 1 \|x + 1 +--R + +--R 2 +-------+4+-------+ +-----+ +--R (- 4x + 2x + 6)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 2 4+-------+ +--R (- 4x + 2x + 6)\|- x + 1 +--R * +--R 4+-----+ +--R \|x + 1 +--R * +--R - x - 1 +--R log(-------) +--R x - 1 +--R ------------ +--R 4 +--R %e +--R + +--R 2 +-------+ +-----+ 2 4+-----+2 +--R ((4x - x - 3)\|- x + 1 \|x + 1 + 3x - x - 2)\|x + 1 +--R + +--R +-------+4+-------+2 +-----+ 3 2 4+-------+2 +--R (- x - 2)\|- x + 1 \|- x + 1 \|x + 1 + (- 4x - 3x + 4x + 3)\|- x + 1 +--R / +--R 2 4+-------+3 4+-----+3 +--R (4x - 4)\|- x + 1 \|x + 1 +--R + +--R 2 +-------+4+-------+ +-----+ 2 4+-------+ +--R ((- 4x + 4)\|- x + 1 \|- x + 1 \|x + 1 + (- 4x + 4)\|- x + 1 ) +--R * +--R 4+-----+ +--R \|x + 1 +--R * +--R - x - 1 4 +--R log(-------) +--R x - 1 +--R ------------ +--R 4 +--R (%e ) +--R + +--R 2 4+-------+3 4+-----+3 +--R (4x - 4)\|- x + 1 \|x + 1 +--R + +--R 2 +-------+4+-------+ +-----+ 2 4+-------+ 4+-----+ +--R ((- 4x + 4)\|- x + 1 \|- x + 1 \|x + 1 + (- 4x + 4)\|- x + 1 )\|x + 1 +--R Type: Expression Integer +--E 65 + +--S 66 of 489 +t0213:= exp(1)^(1/2*atanh(x))/x +--R +--R +--R atanh(x) +--R -------- +--R 2 +--R %e +--R (51) ---------- +--R x +--R Type: Expression Integer +--E 66 + +--S 67 of 489 +r0213:= -2*atan(exp(1)^(1/2*atanh(x)))+atan(-1+2^(1/2)*_ + exp(1)^(1/2*atanh(x)))*2^(1/2)+atan(1+2^(1/2)*_ + exp(1)^(1/2*atanh(x)))*2^(1/2)+log(-1+exp(1)^(1/2*atanh(x)))-_ + log(1+exp(1)^(1/2*atanh(x)))-1/2*log(1-2^(1/2)*_ + exp(1)^(1/2*atanh(x))+exp(1)^atanh(x))*2^(1/2)+_ + 1/2*log(1+2^(1/2)*exp(1)^(1/2*atanh(x))+exp(1)^atanh(x))*2^(1/2) +--R +--R +--R (52) +--R atanh(x) +--R -------- +--R +-+ atanh(x) +-+ 2 +--R \|2 log(%e + \|2 %e + 1) +--R + +--R atanh(x) atanh(x) +--R -------- -------- +--R +-+ atanh(x) +-+ 2 2 +--R - \|2 log(%e - \|2 %e + 1) - 2log(%e + 1) +--R + +--R atanh(x) atanh(x) +--R -------- -------- +--R 2 +-+ +-+ 2 +--R 2log(%e - 1) + 2\|2 atan(\|2 %e + 1) +--R + +--R atanh(x) atanh(x) +--R -------- -------- +--R +-+ +-+ 2 2 +--R 2\|2 atan(\|2 %e - 1) - 4atan(%e ) +--R / +--R 2 +--R Type: Expression Integer +--E 67 + +--S 68 of 489 +a0213:= integrate(t0213,x) +--R +--R +--R (53) +--R - x - 1 2 - x - 1 +--R log(-------) log(-------) +--R x - 1 x - 1 +--R ------------ ------------ +--R 4 +-+ 4 +--R log((%e ) + \|2 %e + 1) +--R + +--R - x - 1 2 - x - 1 +--R log(-------) log(-------) +--R x - 1 x - 1 +--R ------------ ------------ +--R 4 +-+ 4 +--R - log((%e ) - \|2 %e + 1) +--R + +--R - x - 1 - x - 1 +--R log(-------) log(-------) +--R x - 1 x - 1 +--R ------------ ------------ +--R +-+ 4 +-+ 4 +--R - \|2 log(%e + 1) + \|2 log(%e - 1) +--R + +--R - x - 1 +--R log(-------) +--R x - 1 +--R ------------ +--R 4 +--R +-+ 2%e 1 +--R \|2 atan(---------------------) - 2atan(----------------------) +--R - x - 1 2 - x - 1 +--R log(-------) log(-------) +--R x - 1 x - 1 +--R ------------ ------------ +--R 4 +-+ 4 +--R (%e ) - 1 \|2 %e - 1 +--R + +--R 1 +--R - 2atan(----------------------) +--R - x - 1 +--R log(-------) +--R x - 1 +--R ------------ +--R +-+ 4 +--R \|2 %e + 1 +--R / +--R +-+ +--R \|2 +--R Type: Union(Expression Integer,...) +--E 68 + +--S 69 of 489 +m0213:= a0213-r0213 +--R +--R +--R (54) +--R - x - 1 2 - x - 1 +--R log(-------) log(-------) +--R x - 1 x - 1 +--R ------------ ------------ +--R 4 +-+ 4 +--R log((%e ) + \|2 %e + 1) +--R + +--R - x - 1 2 - x - 1 +--R log(-------) log(-------) +--R x - 1 x - 1 +--R ------------ ------------ +--R 4 +-+ 4 +--R - log((%e ) - \|2 %e + 1) +--R + +--R - x - 1 - x - 1 +--R log(-------) log(-------) +--R x - 1 x - 1 +--R ------------ ------------ +--R +-+ 4 +-+ 4 +--R - \|2 log(%e + 1) + \|2 log(%e - 1) +--R + +--R atanh(x) +--R -------- +--R atanh(x) +-+ 2 +--R - log(%e + \|2 %e + 1) +--R + +--R atanh(x) atanh(x) +--R -------- -------- +--R atanh(x) +-+ 2 +-+ 2 +--R log(%e - \|2 %e + 1) + \|2 log(%e + 1) +--R + +--R atanh(x) atanh(x) +--R -------- -------- +--R +-+ 2 +-+ 2 +--R - \|2 log(%e - 1) - 2atan(\|2 %e + 1) +--R + +--R atanh(x) atanh(x) +--R -------- -------- +--R +-+ 2 +-+ 2 +--R - 2atan(\|2 %e - 1) + 2\|2 atan(%e ) +--R + +--R - x - 1 +--R log(-------) +--R x - 1 +--R ------------ +--R 4 +--R +-+ 2%e 1 +--R \|2 atan(---------------------) - 2atan(----------------------) +--R - x - 1 2 - x - 1 +--R log(-------) log(-------) +--R x - 1 x - 1 +--R ------------ ------------ +--R 4 +-+ 4 +--R (%e ) - 1 \|2 %e - 1 +--R + +--R 1 +--R - 2atan(----------------------) +--R - x - 1 +--R log(-------) +--R x - 1 +--R ------------ +--R +-+ 4 +--R \|2 %e + 1 +--R / +--R +-+ +--R \|2 +--R Type: Expression Integer +--E 69 + +--S 70 of 489 +d0213:= D(m0213,x) +--R +--R +--R (55) +--R atanh(x) 7 atanh(x) 5 atanh(x) 3 atanh(x) +--R -------- -------- -------- -------- +--R 2 2 2 2 +--R ((%e ) + 3(%e ) - (%e ) + %e ) +--R * +--R atanh(x) 2 +--R (%e ) +--R + +--R atanh(x) 9 atanh(x) 7 atanh(x) 5 +--R -------- -------- -------- +--R 2 2 2 +--R - (%e ) + 2(%e ) + 6(%e ) +--R + +--R atanh(x) 3 atanh(x) +--R -------- -------- +--R 2 2 +--R - 2(%e ) + 3%e +--R * +--R atanh(x) +--R %e +--R + +--R atanh(x) 9 atanh(x) 7 atanh(x) 5 atanh(x) 3 +--R -------- -------- -------- -------- +--R 2 2 2 2 +--R - (%e ) - 5(%e ) + 5(%e ) - 3(%e ) +--R * +--R - x - 1 8 +--R log(-------) +--R x - 1 +--R ------------ +--R 4 +--R (%e ) +--R + +--R atanh(x) 8 +--R -------- +--R 2 atanh(x) 2 +--R (- 4(%e ) + 4)(%e ) +--R + +--R atanh(x) 8 atanh(x) 10 atanh(x) 8 +--R -------- -------- -------- +--R 2 atanh(x) 2 2 +--R (- 8(%e ) + 8)%e + 8(%e ) - 4(%e ) +--R + +--R atanh(x) 2 +--R -------- +--R 2 +--R - 8(%e ) + 4 +--R * +--R - x - 1 5 +--R log(-------) +--R x - 1 +--R ------------ +--R 4 +--R (%e ) +--R + +--R atanh(x) 7 atanh(x) 5 atanh(x) 3 atanh(x) +--R -------- -------- -------- -------- +--R 2 2 2 2 +--R (- (%e ) - 3(%e ) + (%e ) - %e ) +--R * +--R atanh(x) 2 +--R (%e ) +--R + +--R atanh(x) 9 atanh(x) 7 atanh(x) 5 atanh(x) 3 +--R -------- -------- -------- -------- +--R 2 2 2 2 +--R (%e ) - 2(%e ) - 6(%e ) + 2(%e ) +--R + +--R atanh(x) +--R -------- +--R 2 +--R - 3%e +--R * +--R atanh(x) +--R %e +--R + +--R atanh(x) 9 atanh(x) 7 atanh(x) 5 atanh(x) 3 +--R -------- -------- -------- -------- +--R 2 2 2 2 +--R (%e ) + 5(%e ) - 5(%e ) + 3(%e ) +--R / +--R atanh(x) 8 +--R -------- +--R 2 2 2 atanh(x) 2 +--R ((x - 1)(%e ) - x + 1)(%e ) +--R + +--R atanh(x) 8 +--R -------- +--R 2 2 2 atanh(x) +--R ((2x - 2)(%e ) - 2x + 2)%e +--R + +--R atanh(x) 10 atanh(x) 8 +--R -------- -------- +--R 2 2 2 2 +--R (- 2x + 2)(%e ) + (x - 1)(%e ) +--R + +--R atanh(x) 2 +--R -------- +--R 2 2 2 +--R (2x - 2)(%e ) - x + 1 +--R * +--R - x - 1 8 +--R log(-------) +--R x - 1 +--R ------------ +--R 4 +--R (%e ) +--R + +--R atanh(x) 8 +--R -------- +--R 2 2 2 atanh(x) 2 +--R ((- x + 1)(%e ) + x - 1)(%e ) +--R + +--R atanh(x) 8 atanh(x) 10 +--R -------- -------- +--R 2 2 2 atanh(x) 2 2 +--R ((- 2x + 2)(%e ) + 2x - 2)%e + (2x - 2)(%e ) +--R + +--R atanh(x) 8 atanh(x) 2 +--R -------- -------- +--R 2 2 2 2 2 +--R (- x + 1)(%e ) + (- 2x + 2)(%e ) + x - 1 +--R Type: Expression Integer +--E 70 + +--S 71 of 489 +t0214:= exp(1)^(1/2*atanh(x))/x^2 +--R +--R +--R atanh(x) +--R -------- +--R 2 +--R %e +--R (56) ---------- +--R 2 +--R x +--R Type: Expression Integer +--E 71 + +--S 72 of 489 +r0214:= 1/(2-2*exp(1)^(1/2*atanh(x)))-1/(2+2*exp(1)^(1/2*atanh(x)))+_ + exp(1)^(1/2*atanh(x))/(1+exp(1)^atanh(x))-_ + atan(exp(1)^(1/2*atanh(x)))+1/2*log(-1+exp(1)^(1/2*atanh(x)))-_ + 1/2*log(1+exp(1)^(1/2*atanh(x))) +--R +--R +--R (57) +--R atanh(x) 2 atanh(x) 2 atanh(x) +--R -------- -------- -------- +--R 2 atanh(x) 2 2 +--R ((- (%e ) + 1)%e - (%e ) + 1)log(%e + 1) +--R + +--R atanh(x) 2 atanh(x) 2 atanh(x) +--R -------- -------- -------- +--R 2 atanh(x) 2 2 +--R (((%e ) - 1)%e + (%e ) - 1)log(%e - 1) +--R + +--R atanh(x) 2 atanh(x) 2 atanh(x) +--R -------- -------- -------- +--R 2 atanh(x) 2 2 +--R ((- 2(%e ) + 2)%e - 2(%e ) + 2)atan(%e ) +--R + +--R atanh(x) atanh(x) 3 atanh(x) +--R -------- -------- -------- +--R 2 atanh(x) 2 2 +--R - 2%e %e + 2(%e ) - 4%e +--R / +--R atanh(x) 2 atanh(x) 2 +--R -------- -------- +--R 2 atanh(x) 2 +--R (2(%e ) - 2)%e + 2(%e ) - 2 +--R Type: Expression Integer +--E 72 + +--S 73 of 489 +a0214:= integrate(t0214,x) +--R +--R +--R (58) +--R - x - 1 - x - 1 +--R log(-------) log(-------) +--R x - 1 x - 1 +--R ------------ ------------ +--R 4 4 +--R - x log(%e + 1) + x log(%e - 1) +--R + +--R - x - 1 - x - 1 +--R log(-------) log(-------) +--R x - 1 x - 1 +--R ------------ ------------ +--R 4 4 +--R - 2x atan(%e ) + (2x - 2)%e +--R / +--R 2x +--R Type: Union(Expression Integer,...) +--E 73 + +--S 74 of 489 +m0214:= a0214-r0214 +--R +--R +--R (59) +--R atanh(x) 2 atanh(x) 2 +--R -------- -------- +--R 2 atanh(x) 2 +--R ((- x (%e ) + x)%e - x (%e ) + x) +--R * +--R - x - 1 +--R log(-------) +--R x - 1 +--R ------------ +--R 4 +--R log(%e + 1) +--R + +--R atanh(x) 2 atanh(x) 2 +--R -------- -------- +--R 2 atanh(x) 2 +--R ((x (%e ) - x)%e + x (%e ) - x) +--R * +--R - x - 1 +--R log(-------) +--R x - 1 +--R ------------ +--R 4 +--R log(%e - 1) +--R + +--R atanh(x) 2 atanh(x) 2 +--R -------- -------- +--R 2 atanh(x) 2 +--R ((x (%e ) - x)%e + x (%e ) - x) +--R * +--R atanh(x) +--R -------- +--R 2 +--R log(%e + 1) +--R + +--R atanh(x) 2 atanh(x) 2 +--R -------- -------- +--R 2 atanh(x) 2 +--R ((- x (%e ) + x)%e - x (%e ) + x) +--R * +--R atanh(x) +--R -------- +--R 2 +--R log(%e - 1) +--R + +--R atanh(x) 2 atanh(x) 2 +--R -------- -------- +--R 2 atanh(x) 2 +--R ((- 2x (%e ) + 2x)%e - 2x (%e ) + 2x) +--R * +--R - x - 1 +--R log(-------) +--R x - 1 +--R ------------ +--R 4 +--R atan(%e ) +--R + +--R atanh(x) 2 atanh(x) 2 +--R -------- -------- +--R 2 atanh(x) 2 +--R ((2x (%e ) - 2x)%e + 2x (%e ) - 2x) +--R * +--R atanh(x) +--R -------- +--R 2 +--R atan(%e ) +--R + +--R atanh(x) 2 atanh(x) 2 +--R -------- -------- +--R 2 atanh(x) 2 +--R ((2x - 2)(%e ) - 2x + 2)%e + (2x - 2)(%e ) +--R + +--R - 2x + 2 +--R * +--R - x - 1 +--R log(-------) +--R x - 1 +--R ------------ +--R 4 +--R %e +--R + +--R atanh(x) atanh(x) 3 atanh(x) +--R -------- -------- -------- +--R 2 atanh(x) 2 2 +--R 2x %e %e - 2x (%e ) + 4x %e +--R / +--R atanh(x) 2 atanh(x) 2 +--R -------- -------- +--R 2 atanh(x) 2 +--R (2x (%e ) - 2x)%e + 2x (%e ) - 2x +--R Type: Expression Integer +--E 74 + +--S 75 of 489 +d0214:= D(m0214,x) +--R +--R +--R (60) +--R atanh(x) 6 atanh(x) 4 +--R -------- -------- +--R 2 2 2 2 +--R (x + x - 2)(%e ) + (- x - x + 2)(%e ) +--R + +--R atanh(x) 2 +--R -------- +--R 2 2 2 +--R (- x - x + 2)(%e ) + x + x - 2 +--R * +--R atanh(x) 2 +--R (%e ) +--R + +--R atanh(x) 6 atanh(x) 4 +--R -------- -------- +--R 2 2 2 2 +--R (2x + 2x - 4)(%e ) + (- 2x - 2x + 4)(%e ) +--R + +--R atanh(x) 2 +--R -------- +--R 2 2 2 +--R (- 2x - 2x + 4)(%e ) + 2x + 2x - 4 +--R * +--R atanh(x) +--R %e +--R + +--R atanh(x) 6 atanh(x) 4 +--R -------- -------- +--R 2 2 2 2 +--R (x + x - 2)(%e ) + (- x - x + 2)(%e ) +--R + +--R atanh(x) 2 +--R -------- +--R 2 2 2 +--R (- x - x + 2)(%e ) + x + x - 2 +--R * +--R - x - 1 5 +--R log(-------) +--R x - 1 +--R ------------ +--R 4 +--R (%e ) +--R + +--R atanh(x) 5 atanh(x) 3 atanh(x) +--R -------- -------- -------- +--R 2 2 2 2 2 2 atanh(x) 2 +--R (x (%e ) + 4x (%e ) - x %e )(%e ) +--R + +--R atanh(x) 7 atanh(x) 5 atanh(x) 3 +--R -------- -------- -------- +--R 2 2 2 2 2 2 +--R - x (%e ) + 3x (%e ) + 9x (%e ) +--R + +--R atanh(x) +--R -------- +--R 2 2 +--R - 3x %e +--R * +--R atanh(x) +--R %e +--R + +--R atanh(x) 7 atanh(x) 3 +--R -------- -------- +--R 2 2 2 2 +--R x (%e ) + 3x (%e ) +--R * +--R - x - 1 4 +--R log(-------) +--R x - 1 +--R ------------ +--R 4 +--R (%e ) +--R + +--R atanh(x) 6 atanh(x) 4 +--R -------- -------- +--R 2 2 2 2 +--R (- 3x - x + 2)(%e ) + (3x + x - 2)(%e ) +--R + +--R atanh(x) 2 +--R -------- +--R 2 2 2 +--R (3x + x - 2)(%e ) - 3x - x + 2 +--R * +--R atanh(x) 2 +--R (%e ) +--R + +--R atanh(x) 6 atanh(x) 4 +--R -------- -------- +--R 2 2 2 2 +--R (- 6x - 2x + 4)(%e ) + (6x + 2x - 4)(%e ) +--R + +--R atanh(x) 2 +--R -------- +--R 2 2 2 +--R (6x + 2x - 4)(%e ) - 6x - 2x + 4 +--R * +--R atanh(x) +--R %e +--R + +--R atanh(x) 6 atanh(x) 4 +--R -------- -------- +--R 2 2 2 2 +--R (- 3x - x + 2)(%e ) + (3x + x - 2)(%e ) +--R + +--R atanh(x) 2 +--R -------- +--R 2 2 2 +--R (3x + x - 2)(%e ) - 3x - x + 2 +--R * +--R - x - 1 +--R log(-------) +--R x - 1 +--R ------------ +--R 4 +--R %e +--R + +--R atanh(x) 5 atanh(x) 3 atanh(x) +--R -------- -------- -------- +--R 2 2 2 2 2 2 atanh(x) 2 +--R (- x (%e ) - 4x (%e ) + x %e )(%e ) +--R + +--R atanh(x) 7 atanh(x) 5 atanh(x) 3 atanh(x) +--R -------- -------- -------- -------- +--R 2 2 2 2 2 2 2 2 +--R (x (%e ) - 3x (%e ) - 9x (%e ) + 3x %e ) +--R * +--R atanh(x) +--R %e +--R + +--R atanh(x) 7 atanh(x) 3 +--R -------- -------- +--R 2 2 2 2 +--R - x (%e ) - 3x (%e ) +--R / +--R atanh(x) 6 atanh(x) 4 +--R -------- -------- +--R 4 2 2 4 2 2 +--R (2x - 2x )(%e ) + (- 2x + 2x )(%e ) +--R + +--R atanh(x) 2 +--R -------- +--R 4 2 2 4 2 +--R (- 2x + 2x )(%e ) + 2x - 2x +--R * +--R atanh(x) 2 +--R (%e ) +--R + +--R atanh(x) 6 atanh(x) 4 +--R -------- -------- +--R 4 2 2 4 2 2 +--R (4x - 4x )(%e ) + (- 4x + 4x )(%e ) +--R + +--R atanh(x) 2 +--R -------- +--R 4 2 2 4 2 +--R (- 4x + 4x )(%e ) + 4x - 4x +--R * +--R atanh(x) +--R %e +--R + +--R atanh(x) 6 atanh(x) 4 +--R -------- -------- +--R 4 2 2 4 2 2 +--R (2x - 2x )(%e ) + (- 2x + 2x )(%e ) +--R + +--R atanh(x) 2 +--R -------- +--R 4 2 2 4 2 +--R (- 2x + 2x )(%e ) + 2x - 2x +--R * +--R - x - 1 4 +--R log(-------) +--R x - 1 +--R ------------ +--R 4 +--R (%e ) +--R + +--R atanh(x) 6 atanh(x) 4 +--R -------- -------- +--R 4 2 2 4 2 2 +--R (- 2x + 2x )(%e ) + (2x - 2x )(%e ) +--R + +--R atanh(x) 2 +--R -------- +--R 4 2 2 4 2 +--R (2x - 2x )(%e ) - 2x + 2x +--R * +--R atanh(x) 2 +--R (%e ) +--R + +--R atanh(x) 6 atanh(x) 4 +--R -------- -------- +--R 4 2 2 4 2 2 +--R (- 4x + 4x )(%e ) + (4x - 4x )(%e ) +--R + +--R atanh(x) 2 +--R -------- +--R 4 2 2 4 2 +--R (4x - 4x )(%e ) - 4x + 4x +--R * +--R atanh(x) +--R %e +--R + +--R atanh(x) 6 atanh(x) 4 +--R -------- -------- +--R 4 2 2 4 2 2 +--R (- 2x + 2x )(%e ) + (2x - 2x )(%e ) +--R + +--R atanh(x) 2 +--R -------- +--R 4 2 2 4 2 +--R (2x - 2x )(%e ) - 2x + 2x +--R Type: Expression Integer +--E 75 + +--S 76 of 489 +t0215:= exp(1)^(1/2*atanh(x))/x^3 +--R +--R +--R atanh(x) +--R -------- +--R 2 +--R %e +--R (61) ---------- +--R 3 +--R x +--R Type: Expression Integer +--E 76 + +--S 77 of 489 +r0215:= -1/8/(1-exp(1)^(1/2*atanh(x)))^2+3/(8-8*exp(1)^(1/2*atanh(x)))+_ + 1/8/(1+exp(1)^(1/2*atanh(x)))^2-3/(8+8*exp(1)^(1/2*atanh(x)))-_ + 1/2*exp(1)^(1/2*atanh(x))/(1+exp(1)^atanh(x))^2+_ + 3*exp(1)^(1/2*atanh(x))/(4+4*exp(1)^atanh(x))-_ + 1/4*atan(exp(1)^(1/2*atanh(x)))+1/8*log(-1+exp(1)^(1/2*atanh(x)))-_ + 1/8*log(1+exp(1)^(1/2*atanh(x))) +--R +--R +--R (62) +--R atanh(x) 4 atanh(x) 2 +--R -------- -------- +--R 2 2 atanh(x) 2 +--R (- (%e ) + 2(%e ) - 1)(%e ) +--R + +--R atanh(x) 4 atanh(x) 2 atanh(x) 4 +--R -------- -------- -------- +--R 2 2 atanh(x) 2 +--R (- 2(%e ) + 4(%e ) - 2)%e - (%e ) +--R + +--R atanh(x) 2 +--R -------- +--R 2 +--R 2(%e ) - 1 +--R * +--R atanh(x) +--R -------- +--R 2 +--R log(%e + 1) +--R + +--R atanh(x) 4 atanh(x) 2 +--R -------- -------- +--R 2 2 atanh(x) 2 +--R ((%e ) - 2(%e ) + 1)(%e ) +--R + +--R atanh(x) 4 atanh(x) 2 atanh(x) 4 +--R -------- -------- -------- +--R 2 2 atanh(x) 2 +--R (2(%e ) - 4(%e ) + 2)%e + (%e ) +--R + +--R atanh(x) 2 +--R -------- +--R 2 +--R - 2(%e ) + 1 +--R * +--R atanh(x) +--R -------- +--R 2 +--R log(%e - 1) +--R + +--R atanh(x) 4 atanh(x) 2 +--R -------- -------- +--R 2 2 atanh(x) 2 +--R (- 2(%e ) + 4(%e ) - 2)(%e ) +--R + +--R atanh(x) 4 atanh(x) 2 atanh(x) 4 +--R -------- -------- -------- +--R 2 2 atanh(x) 2 +--R (- 4(%e ) + 8(%e ) - 4)%e - 2(%e ) +--R + +--R atanh(x) 2 +--R -------- +--R 2 +--R 4(%e ) - 2 +--R * +--R atanh(x) +--R -------- +--R 2 +--R atan(%e ) +--R + +--R atanh(x) 3 atanh(x) +--R -------- -------- +--R 2 2 atanh(x) 2 +--R (- 6(%e ) + 2%e )(%e ) +--R + +--R atanh(x) 5 atanh(x) 3 atanh(x) +--R -------- -------- -------- +--R 2 2 2 atanh(x) +--R (6(%e ) - 24(%e ) + 10%e )%e +--R + +--R atanh(x) 5 atanh(x) 3 atanh(x) +--R -------- -------- -------- +--R 2 2 2 +--R 2(%e ) - 10(%e ) + 4%e +--R / +--R atanh(x) 4 atanh(x) 2 +--R -------- -------- +--R 2 2 atanh(x) 2 +--R (8(%e ) - 16(%e ) + 8)(%e ) +--R + +--R atanh(x) 4 atanh(x) 2 atanh(x) 4 +--R -------- -------- -------- +--R 2 2 atanh(x) 2 +--R (16(%e ) - 32(%e ) + 16)%e + 8(%e ) +--R + +--R atanh(x) 2 +--R -------- +--R 2 +--R - 16(%e ) + 8 +--R Type: Expression Integer +--E 77 + +--S 78 of 489 +a0215:= integrate(t0215,x) +--R +--R +--R (63) +--R - x - 1 - x - 1 +--R log(-------) log(-------) +--R x - 1 x - 1 +--R ------------ ------------ +--R 2 4 2 4 +--R - x log(%e + 1) + x log(%e - 1) +--R + +--R - x - 1 - x - 1 +--R log(-------) log(-------) +--R x - 1 x - 1 +--R ------------ ------------ +--R 2 4 2 4 +--R - 2x atan(%e ) + (6x - 2x - 4)%e +--R / +--R 2 +--R 8x +--R Type: Union(Expression Integer,...) +--E 78 + +--S 79 of 489 +m0215:= a0215-r0215 +--R +--R +--R (64) +--R atanh(x) 4 atanh(x) 2 +--R -------- -------- +--R 2 2 2 2 2 atanh(x) 2 +--R (- x (%e ) + 2x (%e ) - x )(%e ) +--R + +--R atanh(x) 4 atanh(x) 2 +--R -------- -------- +--R 2 2 2 2 2 atanh(x) +--R (- 2x (%e ) + 4x (%e ) - 2x )%e +--R + +--R atanh(x) 4 atanh(x) 2 +--R -------- -------- +--R 2 2 2 2 2 +--R - x (%e ) + 2x (%e ) - x +--R * +--R - x - 1 +--R log(-------) +--R x - 1 +--R ------------ +--R 4 +--R log(%e + 1) +--R + +--R atanh(x) 4 atanh(x) 2 +--R -------- -------- +--R 2 2 2 2 2 atanh(x) 2 +--R (x (%e ) - 2x (%e ) + x )(%e ) +--R + +--R atanh(x) 4 atanh(x) 2 +--R -------- -------- +--R 2 2 2 2 2 atanh(x) +--R (2x (%e ) - 4x (%e ) + 2x )%e +--R + +--R atanh(x) 4 atanh(x) 2 +--R -------- -------- +--R 2 2 2 2 2 +--R x (%e ) - 2x (%e ) + x +--R * +--R - x - 1 +--R log(-------) +--R x - 1 +--R ------------ +--R 4 +--R log(%e - 1) +--R + +--R atanh(x) 4 atanh(x) 2 +--R -------- -------- +--R 2 2 2 2 2 atanh(x) 2 +--R (x (%e ) - 2x (%e ) + x )(%e ) +--R + +--R atanh(x) 4 atanh(x) 2 +--R -------- -------- +--R 2 2 2 2 2 atanh(x) +--R (2x (%e ) - 4x (%e ) + 2x )%e +--R + +--R atanh(x) 4 atanh(x) 2 +--R -------- -------- +--R 2 2 2 2 2 +--R x (%e ) - 2x (%e ) + x +--R * +--R atanh(x) +--R -------- +--R 2 +--R log(%e + 1) +--R + +--R atanh(x) 4 atanh(x) 2 +--R -------- -------- +--R 2 2 2 2 2 atanh(x) 2 +--R (- x (%e ) + 2x (%e ) - x )(%e ) +--R + +--R atanh(x) 4 atanh(x) 2 +--R -------- -------- +--R 2 2 2 2 2 atanh(x) +--R (- 2x (%e ) + 4x (%e ) - 2x )%e +--R + +--R atanh(x) 4 atanh(x) 2 +--R -------- -------- +--R 2 2 2 2 2 +--R - x (%e ) + 2x (%e ) - x +--R * +--R atanh(x) +--R -------- +--R 2 +--R log(%e - 1) +--R + +--R atanh(x) 4 atanh(x) 2 +--R -------- -------- +--R 2 2 2 2 2 atanh(x) 2 +--R (- 2x (%e ) + 4x (%e ) - 2x )(%e ) +--R + +--R atanh(x) 4 atanh(x) 2 +--R -------- -------- +--R 2 2 2 2 2 atanh(x) +--R (- 4x (%e ) + 8x (%e ) - 4x )%e +--R + +--R atanh(x) 4 atanh(x) 2 +--R -------- -------- +--R 2 2 2 2 2 +--R - 2x (%e ) + 4x (%e ) - 2x +--R * +--R - x - 1 +--R log(-------) +--R x - 1 +--R ------------ +--R 4 +--R atan(%e ) +--R + +--R atanh(x) 4 atanh(x) 2 +--R -------- -------- +--R 2 2 2 2 2 atanh(x) 2 +--R (2x (%e ) - 4x (%e ) + 2x )(%e ) +--R + +--R atanh(x) 4 atanh(x) 2 +--R -------- -------- +--R 2 2 2 2 2 atanh(x) +--R (4x (%e ) - 8x (%e ) + 4x )%e +--R + +--R atanh(x) 4 atanh(x) 2 +--R -------- -------- +--R 2 2 2 2 2 +--R 2x (%e ) - 4x (%e ) + 2x +--R * +--R atanh(x) +--R -------- +--R 2 +--R atan(%e ) +--R + +--R atanh(x) 4 atanh(x) 2 +--R -------- -------- +--R 2 2 2 2 +--R (6x - 2x - 4)(%e ) + (- 12x + 4x + 8)(%e ) +--R + +--R 2 +--R 6x - 2x - 4 +--R * +--R atanh(x) 2 +--R (%e ) +--R + +--R atanh(x) 4 atanh(x) 2 +--R -------- -------- +--R 2 2 2 2 +--R (12x - 4x - 8)(%e ) + (- 24x + 8x + 16)(%e ) +--R + +--R 2 +--R 12x - 4x - 8 +--R * +--R atanh(x) +--R %e +--R + +--R atanh(x) 4 atanh(x) 2 +--R -------- -------- +--R 2 2 2 2 2 +--R (6x - 2x - 4)(%e ) + (- 12x + 4x + 8)(%e ) + 6x +--R + +--R - 2x - 4 +--R * +--R - x - 1 +--R log(-------) +--R x - 1 +--R ------------ +--R 4 +--R %e +--R + +--R atanh(x) 3 atanh(x) +--R -------- -------- +--R 2 2 2 2 atanh(x) 2 +--R (6x (%e ) - 2x %e )(%e ) +--R + +--R atanh(x) 5 atanh(x) 3 atanh(x) +--R -------- -------- -------- +--R 2 2 2 2 2 2 atanh(x) +--R (- 6x (%e ) + 24x (%e ) - 10x %e )%e +--R + +--R atanh(x) 5 atanh(x) 3 atanh(x) +--R -------- -------- -------- +--R 2 2 2 2 2 2 +--R - 2x (%e ) + 10x (%e ) - 4x %e +--R / +--R atanh(x) 4 atanh(x) 2 +--R -------- -------- +--R 2 2 2 2 2 atanh(x) 2 +--R (8x (%e ) - 16x (%e ) + 8x )(%e ) +--R + +--R atanh(x) 4 atanh(x) 2 +--R -------- -------- +--R 2 2 2 2 2 atanh(x) +--R (16x (%e ) - 32x (%e ) + 16x )%e +--R + +--R atanh(x) 4 atanh(x) 2 +--R -------- -------- +--R 2 2 2 2 2 +--R 8x (%e ) - 16x (%e ) + 8x +--R Type: Expression Integer +--E 79 + +--S 80 of 489 +d0215:= D(m0215,x) +--R +--R +--R (65) +--R atanh(x) 8 atanh(x) 6 +--R -------- -------- +--R 3 2 2 3 2 2 +--R (- x + 9x - 8)(%e ) + (2x - 18x + 16)(%e ) +--R + +--R atanh(x) 2 +--R -------- +--R 3 2 2 3 2 +--R (- 2x + 18x - 16)(%e ) + x - 9x + 8 +--R * +--R atanh(x) 3 +--R (%e ) +--R + +--R atanh(x) 8 atanh(x) 6 +--R -------- -------- +--R 3 2 2 3 2 2 +--R (- 3x + 27x - 24)(%e ) + (6x - 54x + 48)(%e ) +--R + +--R atanh(x) 2 +--R -------- +--R 3 2 2 3 2 +--R (- 6x + 54x - 48)(%e ) + 3x - 27x + 24 +--R * +--R atanh(x) 2 +--R (%e ) +--R + +--R atanh(x) 8 atanh(x) 6 +--R -------- -------- +--R 3 2 2 3 2 2 +--R (- 3x + 27x - 24)(%e ) + (6x - 54x + 48)(%e ) +--R + +--R atanh(x) 2 +--R -------- +--R 3 2 2 3 2 +--R (- 6x + 54x - 48)(%e ) + 3x - 27x + 24 +--R * +--R atanh(x) +--R %e +--R + +--R atanh(x) 8 atanh(x) 6 +--R -------- -------- +--R 3 2 2 3 2 2 +--R (- x + 9x - 8)(%e ) + (2x - 18x + 16)(%e ) +--R + +--R atanh(x) 2 +--R -------- +--R 3 2 2 3 2 +--R (- 2x + 18x - 16)(%e ) + x - 9x + 8 +--R * +--R - x - 1 5 +--R log(-------) +--R x - 1 +--R ------------ +--R 4 +--R (%e ) +--R + +--R atanh(x) 7 atanh(x) 5 atanh(x) 3 +--R -------- -------- -------- +--R 3 2 3 2 3 2 +--R 3x (%e ) + 11x (%e ) + x (%e ) +--R + +--R atanh(x) +--R -------- +--R 3 2 +--R x %e +--R * +--R atanh(x) 3 +--R (%e ) +--R + +--R atanh(x) 9 atanh(x) 7 atanh(x) 5 +--R -------- -------- -------- +--R 3 2 3 2 3 2 +--R - 3x (%e ) + 15x (%e ) + 33x (%e ) +--R + +--R atanh(x) 3 atanh(x) +--R -------- -------- +--R 3 2 3 2 +--R - 3x (%e ) + 6x %e +--R * +--R atanh(x) 2 +--R (%e ) +--R + +--R atanh(x) 9 atanh(x) 7 atanh(x) 5 +--R -------- -------- -------- +--R 3 2 3 2 3 2 +--R 6x (%e ) - 3x (%e ) + 33x (%e ) +--R + +--R atanh(x) 3 atanh(x) +--R -------- -------- +--R 3 2 3 2 +--R 15x (%e ) - 3x %e +--R * +--R atanh(x) +--R %e +--R + +--R atanh(x) 9 atanh(x) 7 atanh(x) 5 +--R -------- -------- -------- +--R 3 2 3 2 3 2 +--R x (%e ) + x (%e ) + 11x (%e ) +--R + +--R atanh(x) 3 +--R -------- +--R 3 2 +--R 3x (%e ) +--R * +--R - x - 1 4 +--R log(-------) +--R x - 1 +--R ------------ +--R 4 +--R (%e ) +--R + +--R atanh(x) 8 atanh(x) 6 +--R -------- -------- +--R 3 2 2 3 2 2 +--R (- x - 9x + 8)(%e ) + (2x + 18x - 16)(%e ) +--R + +--R atanh(x) 2 +--R -------- +--R 3 2 2 3 2 +--R (- 2x - 18x + 16)(%e ) + x + 9x - 8 +--R * +--R atanh(x) 3 +--R (%e ) +--R + +--R atanh(x) 8 atanh(x) 6 +--R -------- -------- +--R 3 2 2 3 2 2 +--R (- 3x - 27x + 24)(%e ) + (6x + 54x - 48)(%e ) +--R + +--R atanh(x) 2 +--R -------- +--R 3 2 2 3 2 +--R (- 6x - 54x + 48)(%e ) + 3x + 27x - 24 +--R * +--R atanh(x) 2 +--R (%e ) +--R + +--R atanh(x) 8 atanh(x) 6 +--R -------- -------- +--R 3 2 2 3 2 2 +--R (- 3x - 27x + 24)(%e ) + (6x + 54x - 48)(%e ) +--R + +--R atanh(x) 2 +--R -------- +--R 3 2 2 3 2 +--R (- 6x - 54x + 48)(%e ) + 3x + 27x - 24 +--R * +--R atanh(x) +--R %e +--R + +--R atanh(x) 8 atanh(x) 6 +--R -------- -------- +--R 3 2 2 3 2 2 +--R (- x - 9x + 8)(%e ) + (2x + 18x - 16)(%e ) +--R + +--R atanh(x) 2 +--R -------- +--R 3 2 2 3 2 +--R (- 2x - 18x + 16)(%e ) + x + 9x - 8 +--R * +--R - x - 1 +--R log(-------) +--R x - 1 +--R ------------ +--R 4 +--R %e +--R + +--R atanh(x) 7 atanh(x) 5 atanh(x) 3 +--R -------- -------- -------- +--R 3 2 3 2 3 2 +--R - 3x (%e ) - 11x (%e ) - x (%e ) +--R + +--R atanh(x) +--R -------- +--R 3 2 +--R - x %e +--R * +--R atanh(x) 3 +--R (%e ) +--R + +--R atanh(x) 9 atanh(x) 7 atanh(x) 5 +--R -------- -------- -------- +--R 3 2 3 2 3 2 +--R 3x (%e ) - 15x (%e ) - 33x (%e ) +--R + +--R atanh(x) 3 atanh(x) +--R -------- -------- +--R 3 2 3 2 +--R 3x (%e ) - 6x %e +--R * +--R atanh(x) 2 +--R (%e ) +--R + +--R atanh(x) 9 atanh(x) 7 atanh(x) 5 +--R -------- -------- -------- +--R 3 2 3 2 3 2 +--R - 6x (%e ) + 3x (%e ) - 33x (%e ) +--R + +--R atanh(x) 3 atanh(x) +--R -------- -------- +--R 3 2 3 2 +--R - 15x (%e ) + 3x %e +--R * +--R atanh(x) +--R %e +--R + +--R atanh(x) 9 atanh(x) 7 atanh(x) 5 atanh(x) 3 +--R -------- -------- -------- -------- +--R 3 2 3 2 3 2 3 2 +--R - x (%e ) - x (%e ) - 11x (%e ) - 3x (%e ) +--R / +--R atanh(x) 8 atanh(x) 6 +--R -------- -------- +--R 5 3 2 5 3 2 +--R (8x - 8x )(%e ) + (- 16x + 16x )(%e ) +--R + +--R atanh(x) 2 +--R -------- +--R 5 3 2 5 3 +--R (16x - 16x )(%e ) - 8x + 8x +--R * +--R atanh(x) 3 +--R (%e ) +--R + +--R atanh(x) 8 atanh(x) 6 +--R -------- -------- +--R 5 3 2 5 3 2 +--R (24x - 24x )(%e ) + (- 48x + 48x )(%e ) +--R + +--R atanh(x) 2 +--R -------- +--R 5 3 2 5 3 +--R (48x - 48x )(%e ) - 24x + 24x +--R * +--R atanh(x) 2 +--R (%e ) +--R + +--R atanh(x) 8 atanh(x) 6 +--R -------- -------- +--R 5 3 2 5 3 2 +--R (24x - 24x )(%e ) + (- 48x + 48x )(%e ) +--R + +--R atanh(x) 2 +--R -------- +--R 5 3 2 5 3 +--R (48x - 48x )(%e ) - 24x + 24x +--R * +--R atanh(x) +--R %e +--R + +--R atanh(x) 8 atanh(x) 6 +--R -------- -------- +--R 5 3 2 5 3 2 +--R (8x - 8x )(%e ) + (- 16x + 16x )(%e ) +--R + +--R atanh(x) 2 +--R -------- +--R 5 3 2 5 3 +--R (16x - 16x )(%e ) - 8x + 8x +--R * +--R - x - 1 4 +--R log(-------) +--R x - 1 +--R ------------ +--R 4 +--R (%e ) +--R + +--R atanh(x) 8 atanh(x) 6 +--R -------- -------- +--R 5 3 2 5 3 2 +--R (- 8x + 8x )(%e ) + (16x - 16x )(%e ) +--R + +--R atanh(x) 2 +--R -------- +--R 5 3 2 5 3 +--R (- 16x + 16x )(%e ) + 8x - 8x +--R * +--R atanh(x) 3 +--R (%e ) +--R + +--R atanh(x) 8 atanh(x) 6 +--R -------- -------- +--R 5 3 2 5 3 2 +--R (- 24x + 24x )(%e ) + (48x - 48x )(%e ) +--R + +--R atanh(x) 2 +--R -------- +--R 5 3 2 5 3 +--R (- 48x + 48x )(%e ) + 24x - 24x +--R * +--R atanh(x) 2 +--R (%e ) +--R + +--R atanh(x) 8 atanh(x) 6 +--R -------- -------- +--R 5 3 2 5 3 2 +--R (- 24x + 24x )(%e ) + (48x - 48x )(%e ) +--R + +--R atanh(x) 2 +--R -------- +--R 5 3 2 5 3 +--R (- 48x + 48x )(%e ) + 24x - 24x +--R * +--R atanh(x) +--R %e +--R + +--R atanh(x) 8 atanh(x) 6 +--R -------- -------- +--R 5 3 2 5 3 2 +--R (- 8x + 8x )(%e ) + (16x - 16x )(%e ) +--R + +--R atanh(x) 2 +--R -------- +--R 5 3 2 5 3 +--R (- 16x + 16x )(%e ) + 8x - 8x +--R Type: Expression Integer +--E 80 + +--S 81 of 489 +t0216:= exp(1)^(1/3*atanh(x)) +--R +--R +--R atanh(x) +--R -------- +--R 3 +--R (66) %e +--R Type: Expression Integer +--E 81 + +--S 82 of 489 +r0216:= -(1-x)^(5/6)*(1+x)^(1/6)-2/3*atan((1-x)^(1/6)/(1+x)^(1/6))-_ + 1/3*atan(-3^(1/2)+2*(1-x)^(1/6)/(1+x)^(1/6))-_ + 1/3*atan(3^(1/2)+2*(1-x)^(1/6)/(1+x)^(1/6))-_ + 1/6*log(1+(1-x)^(1/3)/(1+x)^(1/3)-_ + 3^(1/2)*(1-x)^(1/6)/(1+x)^(1/6))*3^(1/2)+_ + 1/6*log(1+(1-x)^(1/3)/(1+x)^(1/3)+_ + 3^(1/2)*(1-x)^(1/6)/(1+x)^(1/6))*3^(1/2) +--R +--R +--R (67) +--R 3+-----+ 3+-------+ 6+-----+ +-+6+-------+3+-----+ +--R +-+ (\|x + 1 + \|- x + 1 )\|x + 1 + \|3 \|- x + 1 \|x + 1 +--R \|3 log(--------------------------------------------------------) +--R 3+-----+6+-----+ +--R \|x + 1 \|x + 1 +--R + +--R 3+-----+ 3+-------+ 6+-----+ +-+6+-------+3+-----+ +--R +-+ (\|x + 1 + \|- x + 1 )\|x + 1 - \|3 \|- x + 1 \|x + 1 +--R - \|3 log(--------------------------------------------------------) +--R 3+-----+6+-----+ +--R \|x + 1 \|x + 1 +--R + +--R +-+6+-----+ 6+-------+ +-+6+-----+ 6+-------+ +--R \|3 \|x + 1 + 2\|- x + 1 \|3 \|x + 1 - 2\|- x + 1 +--R - 2atan(--------------------------) + 2atan(--------------------------) +--R 6+-----+ 6+-----+ +--R \|x + 1 \|x + 1 +--R + +--R 6+-------+ +--R \|- x + 1 6+-------+5 6+-----+ +--R - 4atan(----------) - 6\|- x + 1 \|x + 1 +--R 6+-----+ +--R \|x + 1 +--R / +--R 6 +--R Type: Expression Integer +--E 82 + +--S 83 of 489 +a0216:= integrate(t0216,x) +--R +--R +--R (68) +--R 3 +--R atan(----) +--R +-+ +--R \|3 +--R cos(----------) +--R 2 +--R * +--R log +--R - x - 1 2 +--R 3 2 log(-------) +--R atan(----) x - 1 +--R +-+ ------------ +--R \|3 6 +--R sin(----------) + (%e ) +--R 2 +--R + +--R - x - 1 +--R 3 log(-------) 3 2 +--R atan(----) x - 1 atan(----) +--R +-+ ------------ +-+ +--R \|3 6 \|3 +--R 2cos(----------)%e + cos(----------) +--R 2 2 +--R + +--R - +--R 3 +--R atan(----) +--R +-+ +--R \|3 +--R cos(----------) +--R 2 +--R * +--R log +--R - x - 1 2 +--R 3 2 log(-------) +--R atan(----) x - 1 +--R +-+ ------------ +--R \|3 6 +--R sin(----------) + (%e ) +--R 2 +--R + +--R - x - 1 +--R 3 log(-------) 3 2 +--R atan(----) x - 1 atan(----) +--R +-+ ------------ +-+ +--R \|3 6 \|3 +--R - 2cos(----------)%e + cos(----------) +--R 2 2 +--R + +--R 3 +--R atan(----) +--R 3 +-+ +--R atan(----) \|3 +--R +-+ sin(----------) +--R \|3 2 +--R - 2sin(----------)atan(--------------------------------) +--R 2 - x - 1 +--R log(-------) 3 +--R x - 1 atan(----) +--R ------------ +-+ +--R 6 \|3 +--R %e - cos(----------) +--R 2 +--R + +--R 3 +--R atan(----) +--R 3 +-+ +--R atan(----) \|3 +--R +-+ sin(----------) +--R \|3 2 +--R - 2sin(----------)atan(--------------------------------) +--R 2 - x - 1 +--R log(-------) 3 +--R x - 1 atan(----) +--R ------------ +-+ +--R 6 \|3 +--R %e + cos(----------) +--R 2 +--R + +--R - x - 1 +--R log(-------) - x - 1 +--R x - 1 log(-------) +--R ------------ x - 1 +--R 6 ------------ +--R 2%e 6 +--R - atan(---------------------) + (3x - 3)%e +--R - x - 1 2 +--R log(-------) +--R x - 1 +--R ------------ +--R 6 +--R (%e ) - 1 +--R / +--R 3 +--R Type: Union(Expression Integer,...) +--E 83 + +--S 84 of 489 +m0216:= a0216-r0216 +--R +--R +--R (69) +--R 3 +--R atan(----) +--R +-+ +--R \|3 +--R 2cos(----------) +--R 2 +--R * +--R log +--R - x - 1 2 +--R 3 2 log(-------) +--R atan(----) x - 1 +--R +-+ ------------ +--R \|3 6 +--R sin(----------) + (%e ) +--R 2 +--R + +--R - x - 1 +--R 3 log(-------) 3 2 +--R atan(----) x - 1 atan(----) +--R +-+ ------------ +-+ +--R \|3 6 \|3 +--R 2cos(----------)%e + cos(----------) +--R 2 2 +--R + +--R - +--R 3 +--R atan(----) +--R +-+ +--R \|3 +--R 2cos(----------) +--R 2 +--R * +--R log +--R - x - 1 2 +--R 3 2 log(-------) +--R atan(----) x - 1 +--R +-+ ------------ +--R \|3 6 +--R sin(----------) + (%e ) +--R 2 +--R + +--R - x - 1 +--R 3 log(-------) 3 2 +--R atan(----) x - 1 atan(----) +--R +-+ ------------ +-+ +--R \|3 6 \|3 +--R - 2cos(----------)%e + cos(----------) +--R 2 2 +--R + +--R 3 +--R atan(----) +--R 3 +-+ +--R atan(----) \|3 +--R +-+ sin(----------) +--R \|3 2 +--R - 4sin(----------)atan(--------------------------------) +--R 2 - x - 1 +--R log(-------) 3 +--R x - 1 atan(----) +--R ------------ +-+ +--R 6 \|3 +--R %e - cos(----------) +--R 2 +--R + +--R 3 +--R atan(----) +--R 3 +-+ +--R atan(----) \|3 +--R +-+ sin(----------) +--R \|3 2 +--R - 4sin(----------)atan(--------------------------------) +--R 2 - x - 1 +--R log(-------) 3 +--R x - 1 atan(----) +--R ------------ +-+ +--R 6 \|3 +--R %e + cos(----------) +--R 2 +--R + +--R - x - 1 +--R log(-------) +--R x - 1 +--R ------------ +--R 6 +--R 2%e +--R - 2atan(---------------------) +--R - x - 1 2 +--R log(-------) +--R x - 1 +--R ------------ +--R 6 +--R (%e ) - 1 +--R + +--R 3+-----+ 3+-------+ 6+-----+ +-+6+-------+3+-----+ +--R +-+ (\|x + 1 + \|- x + 1 )\|x + 1 + \|3 \|- x + 1 \|x + 1 +--R - \|3 log(--------------------------------------------------------) +--R 3+-----+6+-----+ +--R \|x + 1 \|x + 1 +--R + +--R 3+-----+ 3+-------+ 6+-----+ +-+6+-------+3+-----+ +--R +-+ (\|x + 1 + \|- x + 1 )\|x + 1 - \|3 \|- x + 1 \|x + 1 +--R \|3 log(--------------------------------------------------------) +--R 3+-----+6+-----+ +--R \|x + 1 \|x + 1 +--R + +--R - x - 1 +--R log(-------) +--R x - 1 +--R ------------ +-+6+-----+ 6+-------+ +--R 6 \|3 \|x + 1 + 2\|- x + 1 +--R (6x - 6)%e + 2atan(--------------------------) +--R 6+-----+ +--R \|x + 1 +--R + +--R +-+6+-----+ 6+-------+ 6+-------+ +--R \|3 \|x + 1 - 2\|- x + 1 \|- x + 1 +--R - 2atan(--------------------------) + 4atan(----------) +--R 6+-----+ 6+-----+ +--R \|x + 1 \|x + 1 +--R + +--R 6+-------+5 6+-----+ +--R 6\|- x + 1 \|x + 1 +--R / +--R 6 +--R Type: Expression Integer +--E 84 + +--S 85 of 489 +d0216:= D(m0216,x) +--R +--R +--R (70) +--R 2 3+-------+6+-------+3 3+-----+2 6+-----+5 +--R (54x - 18x - 60)\|- x + 1 \|- x + 1 \|x + 1 \|x + 1 +--R + +--R 3 2 3+-------+6+-------+3+-----+2 +--R (- 18x - 12x + 26x + 20)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 3 2 3+-------+2 6+-------+3+-----+ +--R (- 36x - 24x + 52x + 40)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 4 3 2 6+-------+ +--R (18x - 6x - 38x + 6x + 20)\|- x + 1 +--R * +--R 6+-----+ +--R \|x + 1 +--R * +--R - x - 1 3 +--R log(-------) +--R x - 1 +--R ------------ +--R 6 +--R (%e ) +--R + +--R 3+-------+6+-------+4 3+-----+2 6+-----+4 +--R (9x + 9)\|- x + 1 \|- x + 1 \|x + 1 \|x + 1 +--R + +--R 3 2 3+-------+3+-----+2 +--R (18x + 15x - 18x - 15)\|- x + 1 \|x + 1 +--R + +--R 3 2 3+-------+2 3+-----+ 4 3 +--R (36x + 30x - 36x - 30)\|- x + 1 \|x + 1 - 18x + 3x +--R + +--R 2 +--R 33x - 3x - 15 +--R * +--R 6+-----+2 +--R \|x + 1 +--R + +--R 3 2 3+-------+6+-------+2 3+-----+2 +--R (- 54x - 48x + 54x + 48)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 2 3+-------+2 6+-------+2 3+-----+ +--R (- 6x - 18x - 12)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 3 2 6+-------+2 +--R (3x + 3x - 3x - 3)\|- x + 1 +--R * +--R - x - 1 2 +--R log(-------) +--R x - 1 +--R ------------ +--R 6 +--R (%e ) +--R + +--R 2 3+-------+6+-------+3 3+-----+2 6+-----+5 +--R (54x - 18x - 72)\|- x + 1 \|- x + 1 \|x + 1 \|x + 1 +--R + +--R 3 2 3+-------+6+-------+3+-----+2 +--R (- 18x - 12x + 30x + 24)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 3 2 3+-------+2 6+-------+3+-----+ +--R (- 36x - 24x + 60x + 48)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 4 3 2 6+-------+ +--R (18x - 6x - 42x + 6x + 24)\|- x + 1 +--R * +--R 6+-----+ +--R \|x + 1 +--R * +--R - x - 1 +--R log(-------) +--R x - 1 +--R ------------ +--R 6 +--R %e +--R + +--R 3+-------+6+-------+4 3+-----+2 6+-----+4 +--R (9x + 9)\|- x + 1 \|- x + 1 \|x + 1 \|x + 1 +--R + +--R 3 2 3+-------+3+-----+2 +--R (18x + 15x - 18x - 15)\|- x + 1 \|x + 1 +--R + +--R 3 2 3+-------+2 3+-----+ 4 3 2 +--R (36x + 30x - 36x - 30)\|- x + 1 \|x + 1 - 18x + 3x + 33x +--R + +--R - 3x - 15 +--R * +--R 6+-----+2 +--R \|x + 1 +--R + +--R 3 2 3+-------+6+-------+2 3+-----+2 +--R (- 54x - 48x + 54x + 48)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 2 3+-------+2 6+-------+2 3+-----+ +--R (- 6x - 18x - 12)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 3 2 6+-------+2 +--R (3x + 3x - 3x - 3)\|- x + 1 +--R * +--R 3 4 +--R atan(----) +--R +-+ +--R \|3 +--R sin(----------) +--R 2 +--R + +--R 2 3+-------+6+-------+3 3+-----+2 6+-----+5 +--R (108x - 36x - 96)\|- x + 1 \|- x + 1 \|x + 1 \|x + 1 +--R + +--R 3 2 3+-------+6+-------+3+-----+2 +--R (- 36x - 24x + 44x + 32)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 3 2 3+-------+2 6+-------+3+-----+ +--R (- 72x - 48x + 88x + 64)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 4 3 2 6+-------+ +--R (36x - 12x - 68x + 12x + 32)\|- x + 1 +--R * +--R 6+-----+ +--R \|x + 1 +--R * +--R - x - 1 5 +--R log(-------) +--R x - 1 +--R ------------ +--R 6 +--R (%e ) +--R + +--R 3+-------+6+-------+4 3+-----+2 6+-----+4 +--R (18x + 18)\|- x + 1 \|- x + 1 \|x + 1 \|x + 1 +--R + +--R 3 2 3+-------+3+-----+2 +--R (36x + 30x - 36x - 30)\|- x + 1 \|x + 1 +--R + +--R 3 2 3+-------+2 3+-----+ 4 3 +--R (72x + 60x - 72x - 60)\|- x + 1 \|x + 1 - 36x + 6x +--R + +--R 2 +--R 66x - 6x - 30 +--R * +--R 6+-----+2 +--R \|x + 1 +--R + +--R 3 2 3+-------+6+-------+2 3+-----+2 +--R (- 108x - 96x + 108x + 96)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 2 3+-------+2 6+-------+2 3+-----+ +--R (- 12x - 36x - 24)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 3 2 6+-------+2 +--R (6x + 6x - 6x - 6)\|- x + 1 +--R * +--R - x - 1 4 +--R log(-------) +--R x - 1 +--R ------------ +--R 6 +--R (%e ) +--R + +--R 2 3+-------+6+-------+3 3+-----+2 6+-----+5 +--R (108x - 36x - 120)\|- x + 1 \|- x + 1 \|x + 1 \|x + 1 +--R + +--R 3 2 3+-------+6+-------+3+-----+2 +--R (- 36x - 24x + 52x + 40)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 3 2 3+-------+2 6+-------+3+-----+ +--R (- 72x - 48x + 104x + 80)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 4 3 2 6+-------+ +--R (36x - 12x - 76x + 12x + 40)\|- x + 1 +--R * +--R 6+-----+ +--R \|x + 1 +--R * +--R 3 2 +--R atan(----) +--R +-+ +--R \|3 +--R cos(----------) +--R 2 +--R + +--R 2 3+-------+6+-------+3 3+-----+2 6+-----+5 +--R (108x - 36x - 120)\|- x + 1 \|- x + 1 \|x + 1 \|x + 1 +--R + +--R 3 2 3+-------+6+-------+3+-----+2 +--R (- 36x - 24x + 52x + 40)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 3 2 3+-------+2 6+-------+3+-----+ +--R (- 72x - 48x + 104x + 80)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 4 3 2 6+-------+ +--R (36x - 12x - 76x + 12x + 40)\|- x + 1 +--R * +--R 6+-----+ +--R \|x + 1 +--R * +--R - x - 1 3 +--R log(-------) +--R x - 1 +--R ------------ +--R 6 +--R (%e ) +--R + +--R 3+-------+6+-------+4 3+-----+2 6+-----+4 +--R (18x + 18)\|- x + 1 \|- x + 1 \|x + 1 \|x + 1 +--R + +--R 3 2 3+-------+3+-----+2 +--R (36x + 30x - 36x - 30)\|- x + 1 \|x + 1 +--R + +--R 3 2 3+-------+2 3+-----+ 4 3 +--R (72x + 60x - 72x - 60)\|- x + 1 \|x + 1 - 36x + 6x +--R + +--R 2 +--R 66x - 6x - 30 +--R * +--R 6+-----+2 +--R \|x + 1 +--R + +--R 3 2 3+-------+6+-------+2 3+-----+2 +--R (- 108x - 96x + 108x + 96)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 2 3+-------+2 6+-------+2 3+-----+ +--R (- 12x - 36x - 24)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 3 2 6+-------+2 +--R (6x + 6x - 6x - 6)\|- x + 1 +--R * +--R 3 2 +--R atan(----) +--R +-+ +--R \|3 +--R cos(----------) +--R 2 +--R + +--R 3+-------+6+-------+4 3+-----+2 6+-----+4 +--R (18x + 18)\|- x + 1 \|- x + 1 \|x + 1 \|x + 1 +--R + +--R 3 2 3+-------+3+-----+2 +--R (36x + 30x - 36x - 30)\|- x + 1 \|x + 1 +--R + +--R 3 2 3+-------+2 3+-----+ 4 3 +--R (72x + 60x - 72x - 60)\|- x + 1 \|x + 1 - 36x + 6x +--R + +--R 2 +--R 66x - 6x - 30 +--R * +--R 6+-----+2 +--R \|x + 1 +--R + +--R 3 2 3+-------+6+-------+2 3+-----+2 +--R (- 108x - 96x + 108x + 96)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 2 3+-------+2 6+-------+2 3+-----+ +--R (- 12x - 36x - 24)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 3 2 6+-------+2 +--R (6x + 6x - 6x - 6)\|- x + 1 +--R * +--R - x - 1 2 +--R log(-------) +--R x - 1 +--R ------------ +--R 6 +--R (%e ) +--R + +--R 2 3+-------+6+-------+3 3+-----+2 6+-----+5 +--R (108x - 36x - 144)\|- x + 1 \|- x + 1 \|x + 1 \|x + 1 +--R + +--R 3 2 3+-------+6+-------+3+-----+2 +--R (- 36x - 24x + 60x + 48)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 3 2 3+-------+2 6+-------+3+-----+ +--R (- 72x - 48x + 120x + 96)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 4 3 2 6+-------+ +--R (36x - 12x - 84x + 12x + 48)\|- x + 1 +--R * +--R 6+-----+ +--R \|x + 1 +--R * +--R - x - 1 +--R 3 2 log(-------) +--R atan(----) x - 1 +--R +-+ ------------ +--R \|3 6 +--R cos(----------) %e +--R 2 +--R + +--R 3+-------+6+-------+4 3+-----+2 6+-----+4 +--R (18x + 18)\|- x + 1 \|- x + 1 \|x + 1 \|x + 1 +--R + +--R 3 2 3+-------+3+-----+2 +--R (36x + 30x - 36x - 30)\|- x + 1 \|x + 1 +--R + +--R 3 2 3+-------+2 3+-----+ 4 3 +--R (72x + 60x - 72x - 60)\|- x + 1 \|x + 1 - 36x + 6x +--R + +--R 2 +--R 66x - 6x - 30 +--R * +--R 6+-----+2 +--R \|x + 1 +--R + +--R 3 2 3+-------+6+-------+2 3+-----+2 +--R (- 108x - 96x + 108x + 96)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 2 3+-------+2 6+-------+2 3+-----+ +--R (- 12x - 36x - 24)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 3 2 6+-------+2 +--R (6x + 6x - 6x - 6)\|- x + 1 +--R * +--R 3 2 +--R atan(----) +--R +-+ +--R \|3 +--R cos(----------) +--R 2 +--R * +--R 3 2 +--R atan(----) +--R +-+ +--R \|3 +--R sin(----------) +--R 2 +--R + +--R 2 3+-------+6+-------+3 3+-----+2 6+-----+5 +--R (54x - 18x - 36)\|- x + 1 \|- x + 1 \|x + 1 \|x + 1 +--R + +--R 3 2 3+-------+6+-------+3+-----+2 +--R (- 18x - 12x + 18x + 12)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 3 2 3+-------+2 6+-------+3+-----+ +--R (- 36x - 24x + 36x + 24)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 4 3 2 6+-------+ +--R (18x - 6x - 30x + 6x + 12)\|- x + 1 +--R * +--R 6+-----+ +--R \|x + 1 +--R * +--R - x - 1 7 +--R log(-------) +--R x - 1 +--R ------------ +--R 6 +--R (%e ) +--R + +--R 3+-------+6+-------+4 3+-----+2 6+-----+4 +--R (9x + 9)\|- x + 1 \|- x + 1 \|x + 1 \|x + 1 +--R + +--R 3 2 3+-------+3+-----+2 +--R (18x + 15x - 18x - 15)\|- x + 1 \|x + 1 +--R + +--R 3 2 3+-------+2 3+-----+ 4 3 2 +--R (36x + 30x - 36x - 30)\|- x + 1 \|x + 1 - 18x + 3x + 33x +--R + +--R - 3x - 15 +--R * +--R 6+-----+2 +--R \|x + 1 +--R + +--R 3 2 3+-------+6+-------+2 3+-----+2 +--R (- 54x - 48x + 54x + 48)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 2 3+-------+2 6+-------+2 3+-----+ +--R (- 6x - 18x - 12)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 3 2 6+-------+2 +--R (3x + 3x - 3x - 3)\|- x + 1 +--R * +--R - x - 1 6 +--R log(-------) +--R x - 1 +--R ------------ +--R 6 +--R (%e ) +--R + +--R 2 3+-------+6+-------+3 3+-----+2 6+-----+5 +--R (- 108x + 36x + 96)\|- x + 1 \|- x + 1 \|x + 1 \|x + 1 +--R + +--R 3 2 3+-------+6+-------+3+-----+2 +--R (36x + 24x - 44x - 32)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 3 2 3+-------+2 6+-------+3+-----+ +--R (72x + 48x - 88x - 64)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 4 3 2 6+-------+ +--R (- 36x + 12x + 68x - 12x - 32)\|- x + 1 +--R * +--R 6+-----+ +--R \|x + 1 +--R * +--R 3 2 +--R atan(----) +--R +-+ +--R \|3 +--R cos(----------) +--R 2 +--R + +--R 2 3+-------+6+-------+3 3+-----+2 6+-----+5 +--R (54x - 18x - 48)\|- x + 1 \|- x + 1 \|x + 1 \|x + 1 +--R + +--R 3 2 3+-------+6+-------+3+-----+2 +--R (- 18x - 12x + 22x + 16)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 3 2 3+-------+2 6+-------+3+-----+ +--R (- 36x - 24x + 44x + 32)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 4 3 2 6+-------+ +--R (18x - 6x - 34x + 6x + 16)\|- x + 1 +--R * +--R 6+-----+ +--R \|x + 1 +--R * +--R - x - 1 5 +--R log(-------) +--R x - 1 +--R ------------ +--R 6 +--R (%e ) +--R + +--R 3+-------+6+-------+4 3+-----+2 6+-----+4 +--R (- 18x - 18)\|- x + 1 \|- x + 1 \|x + 1 \|x + 1 +--R + +--R 3 2 3+-------+3+-----+2 +--R (- 36x - 30x + 36x + 30)\|- x + 1 \|x + 1 +--R + +--R 3 2 3+-------+2 3+-----+ 4 3 +--R (- 72x - 60x + 72x + 60)\|- x + 1 \|x + 1 + 36x - 6x +--R + +--R 2 +--R - 66x + 6x + 30 +--R * +--R 6+-----+2 +--R \|x + 1 +--R + +--R 3 2 3+-------+6+-------+2 3+-----+2 +--R (108x + 96x - 108x - 96)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 2 3+-------+2 6+-------+2 3+-----+ +--R (12x + 36x + 24)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 3 2 6+-------+2 +--R (- 6x - 6x + 6x + 6)\|- x + 1 +--R * +--R 3 2 +--R atan(----) +--R +-+ +--R \|3 +--R cos(----------) +--R 2 +--R + +--R 3+-------+6+-------+4 3+-----+2 6+-----+4 +--R (9x + 9)\|- x + 1 \|- x + 1 \|x + 1 \|x + 1 +--R + +--R 3 2 3+-------+3+-----+2 +--R (18x + 15x - 18x - 15)\|- x + 1 \|x + 1 +--R + +--R 3 2 3+-------+2 3+-----+ 4 3 2 +--R (36x + 30x - 36x - 30)\|- x + 1 \|x + 1 - 18x + 3x + 33x +--R + +--R - 3x - 15 +--R * +--R 6+-----+2 +--R \|x + 1 +--R + +--R 3 2 3+-------+6+-------+2 3+-----+2 +--R (- 54x - 48x + 54x + 48)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 2 3+-------+2 6+-------+2 3+-----+ +--R (- 6x - 18x - 12)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 3 2 6+-------+2 +--R (3x + 3x - 3x - 3)\|- x + 1 +--R * +--R - x - 1 4 +--R log(-------) +--R x - 1 +--R ------------ +--R 6 +--R (%e ) +--R + +--R 2 3+-------+6+-------+3 3+-----+2 6+-----+5 +--R (54x - 18x - 60)\|- x + 1 \|- x + 1 \|x + 1 \|x + 1 +--R + +--R 3 2 3+-------+6+-------+3+-----+2 +--R (- 18x - 12x + 26x + 20)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 3 2 3+-------+2 6+-------+3+-----+ +--R (- 36x - 24x + 52x + 40)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 4 3 2 6+-------+ +--R (18x - 6x - 38x + 6x + 20)\|- x + 1 +--R * +--R 6+-----+ +--R \|x + 1 +--R * +--R 3 4 +--R atan(----) +--R +-+ +--R \|3 +--R cos(----------) +--R 2 +--R + +--R 2 3+-------+6+-------+3 3+-----+2 6+-----+5 +--R (- 108x + 36x + 120)\|- x + 1 \|- x + 1 \|x + 1 \|x + 1 +--R + +--R 3 2 3+-------+6+-------+3+-----+2 +--R (36x + 24x - 52x - 40)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 3 2 3+-------+2 6+-------+3+-----+ +--R (72x + 48x - 104x - 80)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 4 3 2 6+-------+ +--R (- 36x + 12x + 76x - 12x - 40)\|- x + 1 +--R * +--R 6+-----+ +--R \|x + 1 +--R * +--R 3 2 +--R atan(----) +--R +-+ +--R \|3 +--R cos(----------) +--R 2 +--R * +--R - x - 1 3 +--R log(-------) +--R x - 1 +--R ------------ +--R 6 +--R (%e ) +--R + +--R 3+-------+6+-------+4 3+-----+2 6+-----+4 +--R (9x + 9)\|- x + 1 \|- x + 1 \|x + 1 \|x + 1 +--R + +--R 3 2 3+-------+3+-----+2 +--R (18x + 15x - 18x - 15)\|- x + 1 \|x + 1 +--R + +--R 3 2 3+-------+2 3+-----+ 4 3 +--R (36x + 30x - 36x - 30)\|- x + 1 \|x + 1 - 18x + 3x +--R + +--R 2 +--R 33x - 3x - 15 +--R * +--R 6+-----+2 +--R \|x + 1 +--R + +--R 3 2 3+-------+6+-------+2 3+-----+2 +--R (- 54x - 48x + 54x + 48)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 2 3+-------+2 6+-------+2 3+-----+ +--R (- 6x - 18x - 12)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 3 2 6+-------+2 +--R (3x + 3x - 3x - 3)\|- x + 1 +--R * +--R 3 4 +--R atan(----) +--R +-+ +--R \|3 +--R cos(----------) +--R 2 +--R + +--R 3+-------+6+-------+4 3+-----+2 6+-----+4 +--R (- 18x - 18)\|- x + 1 \|- x + 1 \|x + 1 \|x + 1 +--R + +--R 3 2 3+-------+3+-----+2 +--R (- 36x - 30x + 36x + 30)\|- x + 1 \|x + 1 +--R + +--R 3 2 3+-------+2 3+-----+ 4 3 +--R (- 72x - 60x + 72x + 60)\|- x + 1 \|x + 1 + 36x - 6x +--R + +--R 2 +--R - 66x + 6x + 30 +--R * +--R 6+-----+2 +--R \|x + 1 +--R + +--R 3 2 3+-------+6+-------+2 3+-----+2 +--R (108x + 96x - 108x - 96)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 2 3+-------+2 6+-------+2 3+-----+ +--R (12x + 36x + 24)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 3 2 6+-------+2 +--R (- 6x - 6x + 6x + 6)\|- x + 1 +--R * +--R 3 2 +--R atan(----) +--R +-+ +--R \|3 +--R cos(----------) +--R 2 +--R * +--R - x - 1 2 +--R log(-------) +--R x - 1 +--R ------------ +--R 6 +--R (%e ) +--R + +--R 2 3+-------+6+-------+3 3+-----+2 6+-----+5 +--R (54x - 18x - 72)\|- x + 1 \|- x + 1 \|x + 1 \|x + 1 +--R + +--R 3 2 3+-------+6+-------+3+-----+2 +--R (- 18x - 12x + 30x + 24)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 3 2 3+-------+2 6+-------+3+-----+ +--R (- 36x - 24x + 60x + 48)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 4 3 2 6+-------+ +--R (18x - 6x - 42x + 6x + 24)\|- x + 1 +--R * +--R 6+-----+ +--R \|x + 1 +--R * +--R - x - 1 +--R 3 4 log(-------) +--R atan(----) x - 1 +--R +-+ ------------ +--R \|3 6 +--R cos(----------) %e +--R 2 +--R + +--R 3+-------+6+-------+4 3+-----+2 6+-----+4 +--R (9x + 9)\|- x + 1 \|- x + 1 \|x + 1 \|x + 1 +--R + +--R 3 2 3+-------+3+-----+2 +--R (18x + 15x - 18x - 15)\|- x + 1 \|x + 1 +--R + +--R 3 2 3+-------+2 3+-----+ 4 3 2 +--R (36x + 30x - 36x - 30)\|- x + 1 \|x + 1 - 18x + 3x + 33x +--R + +--R - 3x - 15 +--R * +--R 6+-----+2 +--R \|x + 1 +--R + +--R 3 2 3+-------+6+-------+2 3+-----+2 +--R (- 54x - 48x + 54x + 48)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 2 3+-------+2 6+-------+2 3+-----+ +--R (- 6x - 18x - 12)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 3 2 6+-------+2 +--R (3x + 3x - 3x - 3)\|- x + 1 +--R * +--R 3 4 +--R atan(----) +--R +-+ +--R \|3 +--R cos(----------) +--R 2 +--R / +--R 2 3+-------+6+-------+3 3+-----+2 6+-----+5 +--R (54x - 54)\|- x + 1 \|- x + 1 \|x + 1 \|x + 1 +--R + +--R 3 2 3+-------+6+-------+3+-----+2 +--R (- 18x - 18x + 18x + 18)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 3 2 3+-------+2 6+-------+3+-----+ +--R (- 36x - 36x + 36x + 36)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 4 2 6+-------+ +--R (18x - 36x + 18)\|- x + 1 +--R * +--R 6+-----+ +--R \|x + 1 +--R * +--R - x - 1 2 +--R log(-------) +--R x - 1 +--R ------------ +--R 6 +--R (%e ) +--R + +--R 2 3+-------+6+-------+3 3+-----+2 6+-----+5 +--R (54x - 54)\|- x + 1 \|- x + 1 \|x + 1 \|x + 1 +--R + +--R 3 2 3+-------+6+-------+3+-----+2 +--R (- 18x - 18x + 18x + 18)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 3 2 3+-------+2 6+-------+3+-----+ +--R (- 36x - 36x + 36x + 36)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 4 2 6+-------+ +--R (18x - 36x + 18)\|- x + 1 +--R * +--R 6+-----+ +--R \|x + 1 +--R * +--R 3 4 +--R atan(----) +--R +-+ +--R \|3 +--R sin(----------) +--R 2 +--R + +--R 2 3+-------+6+-------+3 3+-----+2 6+-----+5 +--R (108x - 108)\|- x + 1 \|- x + 1 \|x + 1 \|x + 1 +--R + +--R 3 2 3+-------+6+-------+3+-----+2 +--R (- 36x - 36x + 36x + 36)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 3 2 3+-------+2 6+-------+3+-----+ +--R (- 72x - 72x + 72x + 72)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 4 2 6+-------+ +--R (36x - 72x + 36)\|- x + 1 +--R * +--R 6+-----+ +--R \|x + 1 +--R * +--R - x - 1 4 +--R log(-------) +--R x - 1 +--R ------------ +--R 6 +--R (%e ) +--R + +--R 2 3+-------+6+-------+3 3+-----+2 6+-----+5 +--R (108x - 108)\|- x + 1 \|- x + 1 \|x + 1 \|x + 1 +--R + +--R 3 2 3+-------+6+-------+3+-----+2 +--R (- 36x - 36x + 36x + 36)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 3 2 3+-------+2 6+-------+3+-----+ +--R (- 72x - 72x + 72x + 72)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 4 2 6+-------+ +--R (36x - 72x + 36)\|- x + 1 +--R * +--R 6+-----+ +--R \|x + 1 +--R * +--R 3 2 +--R atan(----) +--R +-+ +--R \|3 +--R cos(----------) +--R 2 +--R + +--R 2 3+-------+6+-------+3 3+-----+2 6+-----+5 +--R (108x - 108)\|- x + 1 \|- x + 1 \|x + 1 \|x + 1 +--R + +--R 3 2 3+-------+6+-------+3+-----+2 +--R (- 36x - 36x + 36x + 36)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 3 2 3+-------+2 6+-------+3+-----+ +--R (- 72x - 72x + 72x + 72)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 4 2 6+-------+ +--R (36x - 72x + 36)\|- x + 1 +--R * +--R 6+-----+ +--R \|x + 1 +--R * +--R - x - 1 2 +--R log(-------) +--R x - 1 +--R ------------ +--R 6 +--R (%e ) +--R + +--R 2 3+-------+6+-------+3 3+-----+2 6+-----+5 +--R (108x - 108)\|- x + 1 \|- x + 1 \|x + 1 \|x + 1 +--R + +--R 3 2 3+-------+6+-------+3+-----+2 +--R (- 36x - 36x + 36x + 36)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 3 2 3+-------+2 6+-------+3+-----+ +--R (- 72x - 72x + 72x + 72)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 4 2 6+-------+ +--R (36x - 72x + 36)\|- x + 1 +--R * +--R 6+-----+ +--R \|x + 1 +--R * +--R 3 2 +--R atan(----) +--R +-+ +--R \|3 +--R cos(----------) +--R 2 +--R * +--R 3 2 +--R atan(----) +--R +-+ +--R \|3 +--R sin(----------) +--R 2 +--R + +--R 2 3+-------+6+-------+3 3+-----+2 6+-----+5 +--R (54x - 54)\|- x + 1 \|- x + 1 \|x + 1 \|x + 1 +--R + +--R 3 2 3+-------+6+-------+3+-----+2 +--R (- 18x - 18x + 18x + 18)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 3 2 3+-------+2 6+-------+3+-----+ +--R (- 36x - 36x + 36x + 36)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 4 2 6+-------+ +--R (18x - 36x + 18)\|- x + 1 +--R * +--R 6+-----+ +--R \|x + 1 +--R * +--R - x - 1 6 +--R log(-------) +--R x - 1 +--R ------------ +--R 6 +--R (%e ) +--R + +--R 2 3+-------+6+-------+3 3+-----+2 6+-----+5 +--R (- 108x + 108)\|- x + 1 \|- x + 1 \|x + 1 \|x + 1 +--R + +--R 3 2 3+-------+6+-------+3+-----+2 +--R (36x + 36x - 36x - 36)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 3 2 3+-------+2 6+-------+3+-----+ +--R (72x + 72x - 72x - 72)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 4 2 6+-------+ +--R (- 36x + 72x - 36)\|- x + 1 +--R * +--R 6+-----+ +--R \|x + 1 +--R * +--R 3 2 +--R atan(----) +--R +-+ +--R \|3 +--R cos(----------) +--R 2 +--R + +--R 2 3+-------+6+-------+3 3+-----+2 6+-----+5 +--R (54x - 54)\|- x + 1 \|- x + 1 \|x + 1 \|x + 1 +--R + +--R 3 2 3+-------+6+-------+3+-----+2 +--R (- 18x - 18x + 18x + 18)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 3 2 3+-------+2 6+-------+3+-----+ +--R (- 36x - 36x + 36x + 36)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 4 2 6+-------+ +--R (18x - 36x + 18)\|- x + 1 +--R * +--R 6+-----+ +--R \|x + 1 +--R * +--R - x - 1 4 +--R log(-------) +--R x - 1 +--R ------------ +--R 6 +--R (%e ) +--R + +--R 2 3+-------+6+-------+3 3+-----+2 6+-----+5 +--R (54x - 54)\|- x + 1 \|- x + 1 \|x + 1 \|x + 1 +--R + +--R 3 2 3+-------+6+-------+3+-----+2 +--R (- 18x - 18x + 18x + 18)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 3 2 3+-------+2 6+-------+3+-----+ +--R (- 36x - 36x + 36x + 36)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 4 2 6+-------+ +--R (18x - 36x + 18)\|- x + 1 +--R * +--R 6+-----+ +--R \|x + 1 +--R * +--R 3 4 +--R atan(----) +--R +-+ +--R \|3 +--R cos(----------) +--R 2 +--R + +--R 2 3+-------+6+-------+3 3+-----+2 6+-----+5 +--R (- 108x + 108)\|- x + 1 \|- x + 1 \|x + 1 \|x + 1 +--R + +--R 3 2 3+-------+6+-------+3+-----+2 +--R (36x + 36x - 36x - 36)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 3 2 3+-------+2 6+-------+3+-----+ +--R (72x + 72x - 72x - 72)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 4 2 6+-------+ +--R (- 36x + 72x - 36)\|- x + 1 +--R * +--R 6+-----+ +--R \|x + 1 +--R * +--R 3 2 +--R atan(----) +--R +-+ +--R \|3 +--R cos(----------) +--R 2 +--R * +--R - x - 1 2 +--R log(-------) +--R x - 1 +--R ------------ +--R 6 +--R (%e ) +--R + +--R 2 3+-------+6+-------+3 3+-----+2 6+-----+5 +--R (54x - 54)\|- x + 1 \|- x + 1 \|x + 1 \|x + 1 +--R + +--R 3 2 3+-------+6+-------+3+-----+2 +--R (- 18x - 18x + 18x + 18)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 3 2 3+-------+2 6+-------+3+-----+ +--R (- 36x - 36x + 36x + 36)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 4 2 6+-------+ +--R (18x - 36x + 18)\|- x + 1 +--R * +--R 6+-----+ +--R \|x + 1 +--R * +--R 3 4 +--R atan(----) +--R +-+ +--R \|3 +--R cos(----------) +--R 2 +--R Type: Expression Integer +--E 85 + +--S 86 of 489 +t0217:= exp(1)^(2/3*atanh(x)) +--R +--R +--R 2atanh(x) +--R --------- +--R 3 +--R (71) %e +--R Type: Expression Integer +--E 86 + +--S 87 of 489 +r0217:= -(1-x)^(2/3)*(1+x)^(1/3)+_ + 2/3*atan(1/3*(1-2*(1-x)^(1/3)/(1+x)^(1/3))*3^(1/2))*3^(1/2)-_ + 1/3*log(1+(1-x)^(2/3)/(1+x)^(2/3)-(1-x)^(1/3)/(1+x)^(1/3))+_ + 2/3*log(1+(1-x)^(1/3)/(1+x)^(1/3)) +--R +--R +--R (72) +--R 3+-----+ 3+-------+ +--R \|x + 1 + \|- x + 1 +--R 2log(---------------------) +--R 3+-----+ +--R \|x + 1 +--R + +--R 3+-----+2 3+-------+3+-----+ 3+-------+2 +--R \|x + 1 - \|- x + 1 \|x + 1 + \|- x + 1 +--R - log(--------------------------------------------) +--R 3+-----+2 +--R \|x + 1 +--R + +--R +-+3+-----+ +-+3+-------+ +--R +-+ \|3 \|x + 1 - 2\|3 \|- x + 1 3+-------+2 3+-----+ +--R 2\|3 atan(------------------------------) - 3\|- x + 1 \|x + 1 +--R 3+-----+ +--R 3\|x + 1 +--R / +--R 3 +--R Type: Expression Integer +--E 87 + +--S 88 of 489 +a0217:= integrate(t0217,x) +--R +--R +--R (73) +--R - x - 1 2 - x - 1 +--R log(-------) log(-------) +--R x - 1 x - 1 +--R ------------ ------------ +--R +-+ 3 3 +--R - \|3 log((%e ) - %e + 1) +--R + +--R - x - 1 +--R - x - 1 log(-------) +--R log(-------) x - 1 +--R x - 1 ------------ +--R ------------ +-+ 3 +-+ +--R +-+ 3 2\|3 %e - \|3 +--R 2\|3 log(%e + 1) + 6atan(--------------------------) +--R 3 +--R + +--R - x - 1 +--R log(-------) +--R x - 1 +--R ------------ +--R +-+ 3 +--R (3x - 3)\|3 %e +--R / +--R +-+ +--R 3\|3 +--R Type: Union(Expression Integer,...) +--E 88 + +--S 89 of 489 +m0217:= a0217-r0217 +--R +--R +--R (74) +--R - x - 1 2 - x - 1 +--R log(-------) log(-------) +--R x - 1 x - 1 +--R ------------ ------------ +--R +-+ 3 3 +--R - \|3 log((%e ) - %e + 1) +--R + +--R - x - 1 +--R - x - 1 log(-------) +--R log(-------) x - 1 +--R x - 1 ------------ +--R ------------ +-+ 3 +-+ +--R +-+ 3 2\|3 %e - \|3 +--R 2\|3 log(%e + 1) + 6atan(--------------------------) +--R 3 +--R + +--R 3+-----+ 3+-------+ +--R +-+ \|x + 1 + \|- x + 1 +--R - 2\|3 log(---------------------) +--R 3+-----+ +--R \|x + 1 +--R + +--R 3+-----+2 3+-------+3+-----+ 3+-------+2 +--R +-+ \|x + 1 - \|- x + 1 \|x + 1 + \|- x + 1 +--R \|3 log(--------------------------------------------) +--R 3+-----+2 +--R \|x + 1 +--R + +--R - x - 1 +--R log(-------) +--R x - 1 +--R ------------ +-+3+-----+ +-+3+-------+ +--R +-+ 3 \|3 \|x + 1 - 2\|3 \|- x + 1 +--R (3x - 3)\|3 %e - 6atan(------------------------------) +--R 3+-----+ +--R 3\|x + 1 +--R + +--R +-+3+-------+2 3+-----+ +--R 3\|3 \|- x + 1 \|x + 1 +--R / +--R +-+ +--R 3\|3 +--R Type: Expression Integer +--E 89 + +--S 90 of 489 +d0217:= D(m0217,x) +--R +--R +--R (75) +--R 3 2 3+-----+2 +--R (3x - 5x + x + 1)\|x + 1 +--R + +--R 3 2 3+-------+3+-----+ +--R (- 3x - x + 3x + 1)\|- x + 1 \|x + 1 +--R + +--R 3 2 3+-------+2 +--R (3x + x - 3x - 1)\|- x + 1 +--R * +--R - x - 1 4 +--R log(-------) +--R x - 1 +--R ------------ +--R 3 +--R (%e ) +--R + +--R 3 2 3+-----+2 +--R (3x + 3x - 3x - 3)\|x + 1 +--R + +--R 3 2 3+-------+3+-----+ +--R (- 3x - 3x + 3x + 3)\|- x + 1 \|x + 1 +--R + +--R 3 2 3+-------+2 +--R (3x + 3x - 3x - 3)\|- x + 1 +--R * +--R - x - 1 3 +--R log(-------) +--R x - 1 +--R ------------ +--R 3 +--R (%e ) +--R + +--R 3 2 3+-----+2 +--R (3x - 5x - 3x + 5)\|x + 1 +--R + +--R 3 2 3+-------+3+-----+ +--R (- 3x - x + 7x + 5)\|- x + 1 \|x + 1 +--R + +--R 3 2 3+-------+2 +--R (3x + x - 7x - 5)\|- x + 1 +--R * +--R - x - 1 +--R log(-------) +--R x - 1 +--R ------------ +--R 3 +--R %e +--R + +--R 3 2 3+-----+2 3 2 3+-------+3+-----+ +--R (3x + 3x - 3x - 3)\|x + 1 + (- 3x - 3x + 3x + 3)\|- x + 1 \|x + 1 +--R + +--R 3 2 3+-------+2 +--R (3x + 3x - 3x - 3)\|- x + 1 +--R / +--R 3 2 3+-----+2 +--R (3x - 3x - 3x + 3)\|x + 1 +--R + +--R 3 2 3+-------+3+-----+ +--R (- 3x - 3x + 3x + 3)\|- x + 1 \|x + 1 +--R + +--R 3 2 3+-------+2 +--R (3x + 3x - 3x - 3)\|- x + 1 +--R * +--R - x - 1 3 +--R log(-------) +--R x - 1 +--R ------------ +--R 3 +--R (%e ) +--R + +--R 3 2 3+-----+2 3 2 3+-------+3+-----+ +--R (3x - 3x - 3x + 3)\|x + 1 + (- 3x - 3x + 3x + 3)\|- x + 1 \|x + 1 +--R + +--R 3 2 3+-------+2 +--R (3x + 3x - 3x - 3)\|- x + 1 +--R Type: Expression Integer +--E 90 + +--S 91 of 489 +t0218:= exp(1)^(1/4*atanh(x)) +--R +--R +--R atanh(x) +--R -------- +--R 4 +--R (76) %e +--R Type: Expression Integer +--E 91 + +--S 92 of 489 +r0218:= -(1-x)^(7/8)*(1+x)^(1/8)-_ + 1/2*atan(sec(1/8*%pi)*((1-x)^(1/8)/(1+x)^(1/8)-sin(1/8*%pi)))*_ + cos(1/8*%pi)-1/2*atan(sec(1/8*%pi)*((1-x)^(1/8)/(1+x)^(1/8)+_ + sin(1/8*%pi)))*cos(1/8*%pi)-1/4*cos(1/8*%pi)*_ + log(1+(1-x)^(1/4)/(1+x)^(1/4)-2*(1-x)^(1/8)*_ + cos(1/8*%pi)/(1+x)^(1/8))+1/4*cos(1/8*%pi)*_ + log(1+(1-x)^(1/4)/(1+x)^(1/4)+2*(1-x)^(1/8)*_ + cos(1/8*%pi)/(1+x)^(1/8))-1/2*atan(((1-x)^(1/8)/(1+x)^(1/8)-_ + cos(1/8*%pi))*csc(1/8*%pi))*sin(1/8*%pi)-_ + 1/2*atan(((1-x)^(1/8)/(1+x)^(1/8)+cos(1/8*%pi))*csc(1/8*%pi))*_ + sin(1/8*%pi)-1/4*log(1+(1-x)^(1/4)/(1+x)^(1/4)-2*(1-x)^(1/8)*_ + sin(1/8*%pi)/(1+x)^(1/8))*sin(1/8*%pi)+_ + 1/4*log(1+(1-x)^(1/4)/(1+x)^(1/4)+2*(1-x)^(1/8)*_ + sin(1/8*%pi)/(1+x)^(1/8))*sin(1/8*%pi) +--R +--R +--R (77) +--R %pi +--R sin(---) +--R 8 +--R * +--R 4+-----+ 4+-------+ 8+-----+ %pi 8+-------+4+-----+ +--R (\|x + 1 + \|- x + 1 )\|x + 1 + 2sin(---)\|- x + 1 \|x + 1 +--R 8 +--R log(-------------------------------------------------------------) +--R 4+-----+8+-----+ +--R \|x + 1 \|x + 1 +--R + +--R %pi +--R cos(---) +--R 8 +--R * +--R 4+-----+ 4+-------+ 8+-----+ %pi 8+-------+4+-----+ +--R (\|x + 1 + \|- x + 1 )\|x + 1 + 2cos(---)\|- x + 1 \|x + 1 +--R 8 +--R log(-------------------------------------------------------------) +--R 4+-----+8+-----+ +--R \|x + 1 \|x + 1 +--R + +--R - +--R %pi +--R cos(---) +--R 8 +--R * +--R 4+-----+ 4+-------+ 8+-----+ %pi 8+-------+4+-----+ +--R (\|x + 1 + \|- x + 1 )\|x + 1 - 2cos(---)\|- x + 1 \|x + 1 +--R 8 +--R log(-------------------------------------------------------------) +--R 4+-----+8+-----+ +--R \|x + 1 \|x + 1 +--R + +--R - +--R %pi +--R sin(---) +--R 8 +--R * +--R 4+-----+ 4+-------+ 8+-----+ %pi 8+-------+4+-----+ +--R (\|x + 1 + \|- x + 1 )\|x + 1 - 2sin(---)\|- x + 1 \|x + 1 +--R 8 +--R log(-------------------------------------------------------------) +--R 4+-----+8+-----+ +--R \|x + 1 \|x + 1 +--R + +--R %pi %pi 8+-----+ %pi 8+-------+ +--R sec(---)sin(---)\|x + 1 + sec(---)\|- x + 1 +--R %pi 8 8 8 +--R - 2cos(---)atan(---------------------------------------------) +--R 8 8+-----+ +--R \|x + 1 +--R + +--R %pi %pi 8+-----+ %pi 8+-------+ +--R sec(---)sin(---)\|x + 1 - sec(---)\|- x + 1 +--R %pi 8 8 8 +--R 2cos(---)atan(---------------------------------------------) +--R 8 8+-----+ +--R \|x + 1 +--R + +--R %pi %pi 8+-----+ %pi 8+-------+ +--R cos(---)csc(---)\|x + 1 + csc(---)\|- x + 1 +--R %pi 8 8 8 +--R - 2sin(---)atan(---------------------------------------------) +--R 8 8+-----+ +--R \|x + 1 +--R + +--R %pi %pi 8+-----+ %pi 8+-------+ +--R cos(---)csc(---)\|x + 1 - csc(---)\|- x + 1 +--R %pi 8 8 8 +--R 2sin(---)atan(---------------------------------------------) +--R 8 8+-----+ +--R \|x + 1 +--R + +--R 8+-------+7 8+-----+ +--R - 4\|- x + 1 \|x + 1 +--R / +--R 4 +--R Type: Expression Integer +--E 92 + +--S 93 of 489 +a0218:= integrate(t0218,x) +--R +--R +--R (78) +--R - x - 1 2 - x - 1 +--R log(-------) log(-------) +--R x - 1 x - 1 +--R ------------ ------------ +--R 8+---+ 8 8+---+ +-+ 8 8+---+2 +--R \|- 1 log((%e ) + \|- 1 \|2 %e + \|- 1 ) +--R + +--R - x - 1 2 - x - 1 +--R log(-------) log(-------) +--R x - 1 x - 1 +--R ------------ ------------ +--R 8+---+ 8 8+---+ +-+ 8 8+---+2 +--R - \|- 1 log((%e ) - \|- 1 \|2 %e + \|- 1 ) +--R + +--R - x - 1 +--R log(-------) +--R x - 1 +--R ------------ +--R 8+---+ +-+ 8 8+---+ +--R \|- 1 \|2 log(%e + \|- 1 ) +--R + +--R - x - 1 +--R log(-------) +--R x - 1 +--R ------------ +--R 8+---+ +-+ 8 8+---+ +--R - \|- 1 \|2 log(%e - \|- 1 ) +--R + +--R 8+---+ +--R 8+---+ +-+ \|- 1 +--R - 2\|- 1 \|2 atan(--------------) +--R - x - 1 +--R log(-------) +--R x - 1 +--R ------------ +--R 8 +--R %e +--R + +--R 8+---+ +--R 8+---+ \|- 1 +--R - 2\|- 1 atan(---------------------------) +--R - x - 1 +--R log(-------) +--R x - 1 +--R ------------ +--R +-+ 8 8+---+ +--R \|2 %e - \|- 1 +--R + +--R - x - 1 +--R log(-------) +--R x - 1 +--R 8+---+ ------------ +--R 8+---+ \|- 1 +-+ 8 +--R - 2\|- 1 atan(---------------------------) + (4x - 4)\|2 %e +--R - x - 1 +--R log(-------) +--R x - 1 +--R ------------ +--R +-+ 8 8+---+ +--R \|2 %e + \|- 1 +--R / +--R +-+ +--R 4\|2 +--R Type: Union(Expression Integer,...) +--E 93 + +--S 94 of 489 +m0218:= a0218-r0218 +--R +--R +--R (79) +--R - x - 1 2 - x - 1 +--R log(-------) log(-------) +--R x - 1 x - 1 +--R ------------ ------------ +--R 8+---+ 8 8+---+ +-+ 8 8+---+2 +--R \|- 1 log((%e ) + \|- 1 \|2 %e + \|- 1 ) +--R + +--R - x - 1 2 - x - 1 +--R log(-------) log(-------) +--R x - 1 x - 1 +--R ------------ ------------ +--R 8+---+ 8 8+---+ +-+ 8 8+---+2 +--R - \|- 1 log((%e ) - \|- 1 \|2 %e + \|- 1 ) +--R + +--R - x - 1 +--R log(-------) +--R x - 1 +--R ------------ +--R 8+---+ +-+ 8 8+---+ +--R \|- 1 \|2 log(%e + \|- 1 ) +--R + +--R - x - 1 +--R log(-------) +--R x - 1 +--R ------------ +--R 8+---+ +-+ 8 8+---+ +--R - \|- 1 \|2 log(%e - \|- 1 ) +--R + +--R 8+---+ +--R 8+---+ +-+ \|- 1 +--R - 2\|- 1 \|2 atan(--------------) +--R - x - 1 +--R log(-------) +--R x - 1 +--R ------------ +--R 8 +--R %e +--R + +--R 8+---+ +--R 8+---+ \|- 1 +--R - 2\|- 1 atan(---------------------------) +--R - x - 1 +--R log(-------) +--R x - 1 +--R ------------ +--R +-+ 8 8+---+ +--R \|2 %e - \|- 1 +--R + +--R 8+---+ +--R 8+---+ \|- 1 +--R - 2\|- 1 atan(---------------------------) +--R - x - 1 +--R log(-------) +--R x - 1 +--R ------------ +--R +-+ 8 8+---+ +--R \|2 %e + \|- 1 +--R + +--R - +--R +-+ %pi +--R \|2 sin(---) +--R 8 +--R * +--R 4+-----+ 4+-------+ 8+-----+ %pi 8+-------+4+-----+ +--R (\|x + 1 + \|- x + 1 )\|x + 1 + 2sin(---)\|- x + 1 \|x + 1 +--R 8 +--R log(-------------------------------------------------------------) +--R 4+-----+8+-----+ +--R \|x + 1 \|x + 1 +--R + +--R - +--R +-+ %pi +--R \|2 cos(---) +--R 8 +--R * +--R 4+-----+ 4+-------+ 8+-----+ %pi 8+-------+4+-----+ +--R (\|x + 1 + \|- x + 1 )\|x + 1 + 2cos(---)\|- x + 1 \|x + 1 +--R 8 +--R log(-------------------------------------------------------------) +--R 4+-----+8+-----+ +--R \|x + 1 \|x + 1 +--R + +--R +-+ %pi +--R \|2 cos(---) +--R 8 +--R * +--R 4+-----+ 4+-------+ 8+-----+ %pi 8+-------+4+-----+ +--R (\|x + 1 + \|- x + 1 )\|x + 1 - 2cos(---)\|- x + 1 \|x + 1 +--R 8 +--R log(-------------------------------------------------------------) +--R 4+-----+8+-----+ +--R \|x + 1 \|x + 1 +--R + +--R +-+ %pi +--R \|2 sin(---) +--R 8 +--R * +--R 4+-----+ 4+-------+ 8+-----+ %pi 8+-------+4+-----+ +--R (\|x + 1 + \|- x + 1 )\|x + 1 - 2sin(---)\|- x + 1 \|x + 1 +--R 8 +--R log(-------------------------------------------------------------) +--R 4+-----+8+-----+ +--R \|x + 1 \|x + 1 +--R + +--R - x - 1 +--R log(-------) +--R x - 1 +--R ------------ +--R +-+ 8 +--R (4x - 4)\|2 %e +--R + +--R %pi %pi 8+-----+ %pi 8+-------+ +--R sec(---)sin(---)\|x + 1 + sec(---)\|- x + 1 +--R +-+ %pi 8 8 8 +--R 2\|2 cos(---)atan(---------------------------------------------) +--R 8 8+-----+ +--R \|x + 1 +--R + +--R %pi %pi 8+-----+ %pi 8+-------+ +--R sec(---)sin(---)\|x + 1 - sec(---)\|- x + 1 +--R +-+ %pi 8 8 8 +--R - 2\|2 cos(---)atan(---------------------------------------------) +--R 8 8+-----+ +--R \|x + 1 +--R + +--R %pi %pi 8+-----+ %pi 8+-------+ +--R cos(---)csc(---)\|x + 1 + csc(---)\|- x + 1 +--R +-+ %pi 8 8 8 +--R 2\|2 sin(---)atan(---------------------------------------------) +--R 8 8+-----+ +--R \|x + 1 +--R + +--R %pi %pi 8+-----+ %pi 8+-------+ +--R cos(---)csc(---)\|x + 1 - csc(---)\|- x + 1 +--R +-+ %pi 8 8 8 +--R - 2\|2 sin(---)atan(---------------------------------------------) +--R 8 8+-----+ +--R \|x + 1 +--R + +--R +-+8+-------+7 8+-----+ +--R 4\|2 \|- x + 1 \|x + 1 +--R / +--R +-+ +--R 4\|2 +--R Type: Expression Integer +--E 94 + +--S 95 of 489 +--d0218:= D(m0218,x) +--E 95 + +--S 96 of 489 +t0219:= x^2*exp(1)^atanh(a+b*x)/(1-a^2-2*a*b*x-b^2*x^2) +--R +--R +--R 2 atanh(b x + a) +--R x %e +--R (80) - ---------------------- +--R 2 2 2 +--R b x + 2a b x + a - 1 +--R Type: Expression Integer +--E 96 + +--S 97 of 489 +r0219:= 2*exp(1)^atanh(a+b*x)/b^3-3*a*exp(1)^atanh(a+b*x)/b^3+_ + a^2*exp(1)^atanh(a+b*x)/b^3-exp(1)^atanh(a+b*x)*x/b^2-_ + asin(a+b*x)/b^3+2*a*asin(a+b*x)/b^3 +--R +--R +--R 2 atanh(b x + a) +--R (- b x + a - 3a + 2)%e + (2a - 1)asin(b x + a) +--R (81) ------------------------------------------------------------- +--R 3 +--R b +--R Type: Expression Integer +--E 97 + +--S 98 of 489 +a0219:= integrate(t0219,x) +--R +--R +--R (82) +--R - b x - a - 1 +--R log(-------------) +--R b x + a - 1 +--R ------------------ +--R 2 +--R (4a - 2)atan(%e ) +--R + +--R - b x - a - 1 +--R log(-------------) +--R b x + a - 1 +--R ------------------ +--R 2 2 +--R (- b x + a - 3a + 2)%e +--R / +--R 3 +--R b +--R Type: Union(Expression Integer,...) +--E 98 + +--S 99 of 489 +m0219:= a0219-r0219 +--R +--R +--R (83) +--R - b x - a - 1 +--R log(-------------) +--R b x + a - 1 +--R ------------------ +--R 2 +--R (4a - 2)atan(%e ) +--R + +--R - b x - a - 1 +--R log(-------------) +--R b x + a - 1 +--R ------------------ +--R 2 2 +--R (- b x + a - 3a + 2)%e +--R + +--R 2 atanh(b x + a) +--R (b x - a + 3a - 2)%e + (- 2a + 1)asin(b x + a) +--R / +--R 3 +--R b +--R Type: Expression Integer +--E 99 + +--S 100 of 489 +d0219:= D(m0219,x) +--R +--R +--R (84) +--R +------------------------+ +--R 2 2 2 | 2 2 2 +--R (- b x + (- 2a + 1)b x - 2a + 3a - 1)\|- b x - 2a b x - a + 1 +--R * +--R - b x - a - 1 3 +--R log(-------------) +--R b x + a - 1 +--R ------------------ +--R 2 +--R (%e ) +--R + +--R +------------------------+ +--R 2 2 2 | 2 2 2 +--R (b x + (2a - 1)b x + 2a - 3a + 1)\|- b x - 2a b x - a + 1 +--R * +--R atanh(b x + a) +--R %e +--R + +--R 2 2 2 3 2 +--R (- 2a + 1)b x + (- 4a + 2a)b x - 2a + a + 2a - 1 +--R * +--R - b x - a - 1 2 +--R log(-------------) +--R b x + a - 1 +--R ------------------ +--R 2 +--R (%e ) +--R + +--R +------------------------+ +--R 2 2 2 | 2 2 2 +--R (- b x + (- 2a + 1)b x - 2a - a + 1)\|- b x - 2a b x - a + 1 +--R * +--R - b x - a - 1 +--R log(-------------) +--R b x + a - 1 +--R ------------------ +--R 2 +--R %e +--R + +--R +------------------------+ +--R 2 2 2 | 2 2 2 +--R (b x + (2a - 1)b x + 2a - 3a + 1)\|- b x - 2a b x - a + 1 +--R * +--R atanh(b x + a) +--R %e +--R + +--R 2 2 2 3 2 +--R (- 2a + 1)b x + (- 4a + 2a)b x - 2a + a + 2a - 1 +--R / +--R +------------------------+ +--R 4 2 3 2 2 | 2 2 2 +--R (b x + 2a b x + (a - 1)b )\|- b x - 2a b x - a + 1 +--R * +--R - b x - a - 1 2 +--R log(-------------) +--R b x + a - 1 +--R ------------------ +--R 2 +--R (%e ) +--R + +--R +------------------------+ +--R 4 2 3 2 2 | 2 2 2 +--R (b x + 2a b x + (a - 1)b )\|- b x - 2a b x - a + 1 +--R Type: Expression Integer +--E 100 + +--S 101 of 489 +t0220:= x*exp(1)^atanh(a+b*x)/(1-a^2-2*a*b*x-b^2*x^2) +--R +--R +--R atanh(b x + a) +--R x %e +--R (85) - ---------------------- +--R 2 2 2 +--R b x + 2a b x + a - 1 +--R Type: Expression Integer +--E 101 + +--S 102 of 489 +r0220:= exp(1)^atanh(a+b*x)/b^2-a*exp(1)^atanh(a+b*x)/b^2-asin(a+b*x)/b^2 +--R +--R +--R atanh(b x + a) +--R (- a + 1)%e - asin(b x + a) +--R (86) ----------------------------------------- +--R 2 +--R b +--R Type: Expression Integer +--E 102 + +--S 103 of 489 +a0220:= integrate(t0220,x) +--R +--R +--R - b x - a - 1 - b x - a - 1 +--R log(-------------) log(-------------) +--R b x + a - 1 b x + a - 1 +--R ------------------ ------------------ +--R 2 2 +--R - 2atan(%e ) + (- a + 1)%e +--R (87) ------------------------------------------------------------- +--R 2 +--R b +--R Type: Union(Expression Integer,...) +--E 103 + +--S 104 of 489 +m0220:= a0220-r0220 +--R +--R +--R (88) +--R - b x - a - 1 - b x - a - 1 +--R log(-------------) log(-------------) +--R b x + a - 1 b x + a - 1 +--R ------------------ ------------------ +--R 2 2 +--R - 2atan(%e ) + (- a + 1)%e +--R + +--R atanh(b x + a) +--R (a - 1)%e + asin(b x + a) +--R / +--R 2 +--R b +--R Type: Expression Integer +--E 104 + +--S 105 of 489 +d0220:= D(m0220,x) +--R +--R +--R (89) +--R - b x - a - 1 3 +--R log(-------------) +--R b x + a - 1 +--R +------------------------+ ------------------ +--R | 2 2 2 2 +--R (a - 1)\|- b x - 2a b x - a + 1 (%e ) +--R + +--R +------------------------+ +--R | 2 2 2 atanh(b x + a) 2 2 +--R (- a + 1)\|- b x - 2a b x - a + 1 %e + b x + 2a b x +--R + +--R 2 +--R a - 1 +--R * +--R - b x - a - 1 2 +--R log(-------------) +--R b x + a - 1 +--R ------------------ +--R 2 +--R (%e ) +--R + +--R - b x - a - 1 +--R log(-------------) +--R b x + a - 1 +--R +------------------------+ ------------------ +--R | 2 2 2 2 +--R (a + 1)\|- b x - 2a b x - a + 1 %e +--R + +--R +------------------------+ +--R | 2 2 2 atanh(b x + a) 2 2 2 +--R (- a + 1)\|- b x - 2a b x - a + 1 %e + b x + 2a b x + a +--R + +--R - 1 +--R / +--R +------------------------+ +--R 3 2 2 2 | 2 2 2 +--R (b x + 2a b x + (a - 1)b)\|- b x - 2a b x - a + 1 +--R * +--R - b x - a - 1 2 +--R log(-------------) +--R b x + a - 1 +--R ------------------ +--R 2 +--R (%e ) +--R + +--R +------------------------+ +--R 3 2 2 2 | 2 2 2 +--R (b x + 2a b x + (a - 1)b)\|- b x - 2a b x - a + 1 +--R Type: Expression Integer +--E 105 + +--S 106 of 489 +t0221:= exp(1)^atanh(a+b*x)/x/(1-a^2-2*a*b*x-b^2*x^2) +--R +--R +--R atanh(b x + a) +--R %e +--R (90) - -------------------------- +--R 2 3 2 2 +--R b x + 2a b x + (a - 1)x +--R Type: Expression Integer +--E 106 + +--S 107 of 489 +r0221:= exp(1)^atanh(a+b*x)/(1-a)-2*atanh((-1+a)^(1/2)*_ + exp(1)^atanh(a+b*x)/(-1-a)^(1/2))/(-1-a)^(1/2)/(-1+a)^(3/2) +--R +--R +--R (91) +--R +-----+ atanh(b x + a) +--R \|a - 1 %e +-------+ +-----+ atanh(b x + a) +--R - 2atanh(------------------------) - \|- a - 1 \|a - 1 %e +--R +-------+ +--R \|- a - 1 +--R ----------------------------------------------------------------------- +--R +-------+ +-----+ +--R (a - 1)\|- a - 1 \|a - 1 +--R Type: Expression Integer +--E 107 + +--S 108 of 489 +a0221:= integrate(t0221,x) +--R +--R +--R (92) +--R [ +--R log +--R - b x - a - 1 +--R log(-------------) +--R b x + a - 1 +--R ------------------ +--R 2 3 2 2 +--R ((a - 1)b x + a - a - a + 1)%e +--R + +--R +--------+ +--R 2 | 2 +--R (- a b x - a + 1)\|- a + 1 +--R / +--R x +--R + +--R - b x - a - 1 +--R log(-------------) +--R b x + a - 1 +--R +--------+ ------------------ +--R | 2 2 +--R - \|- a + 1 %e +--R / +--R +--------+ +--R | 2 +--R (a - 1)\|- a + 1 +--R , +--R - b x - a - 1 +--R log(-------------) - b x - a - 1 +--R b x + a - 1 log(-------------) +--R +------+ ------------------ b x + a - 1 +--R | 2 2 +------+ ------------------ +--R \|a - 1 %e | 2 2 +--R 2atan(-----------------------------) - \|a - 1 %e +--R a + 1 +--R --------------------------------------------------------------------] +--R +------+ +--R | 2 +--R (a - 1)\|a - 1 +--R Type: Union(List Expression Integer,...) +--E 108 + +--S 109 of 489 +m0221a:= a0221.1-r0221 +--R +--R +--R (93) +--R +-------+ +-----+ +--R \|- a - 1 \|a - 1 +--R * +--R log +--R - b x - a - 1 +--R log(-------------) +--R b x + a - 1 +--R ------------------ +--R 2 3 2 2 +--R ((a - 1)b x + a - a - a + 1)%e +--R + +--R +--------+ +--R 2 | 2 +--R (- a b x - a + 1)\|- a + 1 +--R / +--R x +--R + +--R +--------+ +-----+ atanh(b x + a) +--R | 2 \|a - 1 %e +--R 2\|- a + 1 atanh(------------------------) +--R +-------+ +--R \|- a - 1 +--R + +--R - b x - a - 1 +--R log(-------------) +--R b x + a - 1 +--R +--------+ ------------------ +--R | 2 +-------+ +-----+ 2 +--R - \|- a + 1 \|- a - 1 \|a - 1 %e +--R + +--R +--------+ +--R | 2 +-------+ +-----+ atanh(b x + a) +--R \|- a + 1 \|- a - 1 \|a - 1 %e +--R / +--R +--------+ +--R | 2 +-------+ +-----+ +--R (a - 1)\|- a + 1 \|- a - 1 \|a - 1 +--R Type: Expression Integer +--E 109 + +--S 110 of 489 +d0221a:= D(m0221a,x) +--R +--R +--R (94) +--R 2 2 2 3 2 atanh(b x + a) 2 +--R ((a - 1)b x + (a - a - a + 1)b x)(%e ) +--R + +--R 2 2 2 3 2 +--R (a + 2a + 1)b x + (a + a - a - 1)b x +--R * +--R - b x - a - 1 2 +--R log(-------------) +--R b x + a - 1 +--R ------------------ +--R 2 +--R (%e ) +--R + +--R 2 2 2 3 2 atanh(b x + a) 3 +--R ((- a + 1)b x + (- a + a + a - 1)b x)(%e ) +--R + +--R +--------+ +--R 2 3 2 | 2 atanh(b x + a) 2 +--R ((a - a)b x + a - a - a + 1)\|- a + 1 (%e ) +--R + +--R 2 2 2 3 2 atanh(b x + a) +--R ((- a + 1)b x + (- a + a + a - 1)b x)%e +--R + +--R +--------+ +--R 2 3 2 | 2 +--R ((a + a)b x + a + a - a - 1)\|- a + 1 +--R * +--R - b x - a - 1 +--R log(-------------) +--R b x + a - 1 +--R ------------------ +--R 2 +--R %e +--R + +--R +--------+ +--R 2 2 2 | 2 atanh(b x + a) 3 +--R (a b x + (a - 1)b x)\|- a + 1 (%e ) +--R + +--R 2 2 2 3 4 2 atanh(b x + a) 2 +--R ((a - 1)b x + (2a - 2a)b x + a - 2a + 1)(%e ) +--R + +--R +--------+ +--R 2 2 2 | 2 atanh(b x + a) 2 2 2 +--R (a b x + (a - 1)b x)\|- a + 1 %e + (a + 2a + 1)b x +--R + +--R 3 2 4 3 +--R (2a + 4a + 2a)b x + a + 2a - 2a - 1 +--R / +--R 3 2 3 4 4 3 2 2 3 +--R (a - a - a + 1)b x + (3a - 4a - 2a + 4a - 1)b x +--R + +--R 5 4 3 2 2 +--R (3a - 5a - 2a + 6a - a - 1)b x +--R + +--R 6 5 4 3 2 +--R (a - 2a - a + 4a - a - 2a + 1)x +--R * +--R atanh(b x + a) 2 +--R (%e ) +--R + +--R 3 2 3 4 4 3 2 2 3 +--R (a + a - a - 1)b x + (3a + 2a - 4a - 2a + 1)b x +--R + +--R 5 4 3 2 2 6 4 2 +--R (3a + a - 6a - 2a + 3a + 1)b x + (a - 3a + 3a - 1)x +--R * +--R - b x - a - 1 +--R log(-------------) +--R b x + a - 1 +--R ------------------ +--R 2 +--R %e +--R + +--R 2 3 4 3 2 2 3 +--R (- a + a)b x + (- 3a + 3a + a - 1)b x +--R + +--R 4 3 2 2 5 4 3 2 +--R (- 3a + 3a + 3a - 3a)b x + (- a + a + 2a - 2a - a + 1)x +--R * +--R +--------+ +--R | 2 atanh(b x + a) 2 +--R \|- a + 1 (%e ) +--R + +--R 2 3 4 3 2 2 3 +--R (- a - a)b x + (- 3a - 3a + a + 1)b x +--R + +--R 4 3 2 2 5 4 3 2 +--R (- 3a - 3a + 3a + 3a)b x + (- a - a + 2a + 2a - a - 1)x +--R * +--R +--------+ +--R | 2 +--R \|- a + 1 +--R Type: Expression Integer +--E 110 + +--S 111 of 489 +m0221b:= a0221.2-r0221 +--R +--R +--R (95) +--R +------+ +-----+ atanh(b x + a) +--R | 2 \|a - 1 %e +--R 2\|a - 1 atanh(------------------------) +--R +-------+ +--R \|- a - 1 +--R + +--R - b x - a - 1 +--R log(-------------) +--R b x + a - 1 +--R +------+ ------------------ +--R | 2 2 +--R +-------+ +-----+ \|a - 1 %e +--R 2\|- a - 1 \|a - 1 atan(-----------------------------) +--R a + 1 +--R + +--R - b x - a - 1 +--R log(-------------) +--R b x + a - 1 +--R +------+ ------------------ +--R +-------+ +-----+ | 2 2 +--R - \|- a - 1 \|a - 1 \|a - 1 %e +--R + +--R +------+ +--R +-------+ +-----+ | 2 atanh(b x + a) +--R \|- a - 1 \|a - 1 \|a - 1 %e +--R / +--R +------+ +--R +-------+ +-----+ | 2 +--R (a - 1)\|- a - 1 \|a - 1 \|a - 1 +--R Type: Expression Integer +--E 111 + +--S 112 of 489 +d0221b:= D(m0221b,x) +--R +--R +--R (96) +--R - b x - a - 1 3 +--R log(-------------) +--R b x + a - 1 +--R ------------------ +--R atanh(b x + a) 2 2 +--R ((a - 1)b (%e ) + (a + 1)b)(%e ) +--R + +--R atanh(b x + a) 3 atanh(b x + a) +--R ((- a + 1)b (%e ) + (- a + 1)b %e ) +--R * +--R - b x - a - 1 2 +--R log(-------------) +--R b x + a - 1 +--R ------------------ +--R 2 +--R (%e ) +--R + +--R - b x - a - 1 +--R log(-------------) +--R b x + a - 1 +--R ------------------ +--R atanh(b x + a) 2 2 +--R ((a - 1)b (%e ) + (a + 1)b)%e +--R + +--R atanh(b x + a) 3 atanh(b x + a) +--R (- a - 1)b (%e ) + (- a - 1)b %e +--R / +--R 2 2 2 3 2 4 3 +--R ((a - 2a + 1)b x + (2a - 4a + 2a)b x + a - 2a + 2a - 1) +--R * +--R atanh(b x + a) 2 +--R (%e ) +--R + +--R 2 2 2 3 4 2 +--R (a - 1)b x + (2a - 2a)b x + a - 2a + 1 +--R * +--R - b x - a - 1 2 +--R log(-------------) +--R b x + a - 1 +--R ------------------ +--R 2 +--R (%e ) +--R + +--R 2 2 2 3 4 2 atanh(b x + a) 2 +--R ((a - 1)b x + (2a - 2a)b x + a - 2a + 1)(%e ) +--R + +--R 2 2 2 3 2 4 3 +--R (a + 2a + 1)b x + (2a + 4a + 2a)b x + a + 2a - 2a - 1 +--R Type: Expression Integer +--E 112 + +--S 113 of 489 +t0222:= exp(1)^atanh(a+b*x)/x^2/(1-a^2-2*a*b*x-b^2*x^2) +--R +--R +--R atanh(b x + a) +--R %e +--R (97) - --------------------------- +--R 2 4 3 2 2 +--R b x + 2a b x + (a - 1)x +--R Type: Expression Integer +--E 113 + +--S 114 of 489 +r0222:= b*exp(1)^atanh(a+b*x)/(1-a)^2+_ + 2*b*exp(1)^atanh(a+b*x)/(1-a)^2/(1+a)/(1+a+(-1+a)*(-1+2/(1-a-b*x)))+_ + 2*b*atanh((-1+a)^(1/2)*exp(1)^atanh(a+b*x)/_ + (-1-a)^(1/2))/(-1-a)^(3/2)/(-1+a)^(5/2)+_ + 4*b*atanh((-1+a)^(1/2)*exp(1)^atanh(a+b*x)/(-1-a)^(1/2))/_ + (-1-a)^(1/2)/(-1+a)^(5/2) +--R +--R +--R (98) +--R +-----+ atanh(b x + a) +--R \|a - 1 %e +--R (4a + 2)b x atanh(------------------------) +--R +-------+ +--R \|- a - 1 +--R + +--R +-------+ +-----+ atanh(b x + a) +--R ((a + 2)b x + a - 1)\|- a - 1 \|a - 1 %e +--R / +--R 3 2 +-------+ +-----+ +--R (a - a - a + 1)x\|- a - 1 \|a - 1 +--R Type: Expression Integer +--E 114 + +--S 115 of 489 +a0222:= integrate(t0222,x) +--R +--R +--R (99) +--R [ +--R (2a + 1)b x +--R * +--R log +--R - b x - a - 1 +--R log(-------------) +--R b x + a - 1 +--R ------------------ +--R 2 3 2 2 +--R ((- a + 1)b x - a + a + a - 1)%e +--R + +--R +--------+ +--R 2 | 2 +--R (- a b x - a + 1)\|- a + 1 +--R / +--R x +--R + +--R - b x - a - 1 +--R log(-------------) +--R b x + a - 1 +--R +--------+ ------------------ +--R | 2 2 +--R ((a + 2)b x + a - 1)\|- a + 1 %e +--R / +--R +--------+ +--R 3 2 | 2 +--R (a - a - a + 1)x\|- a + 1 +--R , +--R +--R - b x - a - 1 +--R log(-------------) +--R b x + a - 1 +--R +------+ ------------------ +--R | 2 2 +--R \|a - 1 %e +--R (- 4a - 2)b x atan(-----------------------------) +--R a + 1 +--R + +--R - b x - a - 1 +--R log(-------------) +--R b x + a - 1 +--R +------+ ------------------ +--R | 2 2 +--R ((a + 2)b x + a - 1)\|a - 1 %e +--R / +--R +------+ +--R 3 2 | 2 +--R (a - a - a + 1)x\|a - 1 +--R ] +--R Type: Union(List Expression Integer,...) +--E 115 + +--S 116 of 489 +m0222a:= a0222.1-r0222 +--R +--R +--R (100) +--R +-------+ +-----+ +--R (2a + 1)b x\|- a - 1 \|a - 1 +--R * +--R log +--R - b x - a - 1 +--R log(-------------) +--R b x + a - 1 +--R ------------------ +--R 2 3 2 2 +--R ((- a + 1)b x - a + a + a - 1)%e +--R + +--R +--------+ +--R 2 | 2 +--R (- a b x - a + 1)\|- a + 1 +--R / +--R x +--R + +--R +--------+ +-----+ atanh(b x + a) +--R | 2 \|a - 1 %e +--R (- 4a - 2)b x\|- a + 1 atanh(------------------------) +--R +-------+ +--R \|- a - 1 +--R + +--R - b x - a - 1 +--R log(-------------) +--R b x + a - 1 +--R +--------+ ------------------ +--R | 2 +-------+ +-----+ 2 +--R ((a + 2)b x + a - 1)\|- a + 1 \|- a - 1 \|a - 1 %e +--R + +--R +--------+ +--R | 2 +-------+ +-----+ atanh(b x + a) +--R ((- a - 2)b x - a + 1)\|- a + 1 \|- a - 1 \|a - 1 %e +--R / +--R +--------+ +--R 3 2 | 2 +-------+ +-----+ +--R (a - a - a + 1)x\|- a + 1 \|- a - 1 \|a - 1 +--R Type: Expression Integer +--E 116 + +--S 117 of 489 +d0222a:= D(m0222a,x) +--R +--R +--R (101) +--R 3 2 3 3 4 3 2 2 2 +--R (- 2a - a + 2a + 1)b x + (- 4a + 2a + 6a - 2a - 2)b x +--R + +--R 5 4 3 2 6 5 4 3 2 +--R (- 3a + 4a + 4a - 6a - a + 2)b x - a + 2a + a - 4a + a +--R + +--R 2a - 1 +--R * +--R atanh(b x + a) 2 +--R (%e ) +--R + +--R 3 2 3 3 4 3 2 2 2 +--R (- 2a - 5a - 4a - 1)b x + (- 4a - 6a + 2a + 6a + 2)b x +--R + +--R 5 4 3 2 6 4 2 +--R (- 3a - 2a + 6a + 4a - 3a - 2)b x - a + 3a - 3a + 1 +--R * +--R - b x - a - 1 2 +--R log(-------------) +--R b x + a - 1 +--R ------------------ +--R 2 +--R (%e ) +--R + +--R 3 2 3 3 4 3 2 2 2 +--R (2a + a - 2a - 1)b x + (4a - 2a - 6a + 2a + 2)b x +--R + +--R 5 4 3 2 6 5 4 3 2 +--R (3a - 4a - 4a + 6a + a - 2)b x + a - 2a - a + 4a - a +--R + +--R - 2a + 1 +--R * +--R atanh(b x + a) 3 +--R (%e ) +--R + +--R +--------+ +--R 4 3 2 5 4 3 2 | 2 +--R ((- a + a + a - a)b x - a + a + 2a - 2a - a + 1)\|- a + 1 +--R * +--R atanh(b x + a) 2 +--R (%e ) +--R + +--R 3 2 3 3 4 3 2 2 2 +--R (2a + a - 2a - 1)b x + (4a + 2a - 4a - 2a)b x +--R + +--R 5 4 3 2 6 4 2 +--R (3a + 2a - 6a - 4a + 3a + 2)b x + a - 3a + 3a - 1 +--R * +--R atanh(b x + a) +--R %e +--R + +--R +--------+ +--R 4 3 2 5 4 3 2 | 2 +--R ((- a - a + a + a)b x - a - a + 2a + 2a - a - 1)\|- a + 1 +--R * +--R - b x - a - 1 +--R log(-------------) +--R b x + a - 1 +--R ------------------ +--R 2 +--R %e +--R + +--R 2 3 3 3 2 2 4 3 2 +--R (2a + a)b x + (4a - 3a - 1)b x + (3a - 2a - 4a + 2a + 1)b x +--R + +--R 5 4 3 2 +--R a - a - 2a + 2a + a - 1 +--R * +--R +--------+ +--R | 2 atanh(b x + a) 3 +--R \|- a + 1 (%e ) +--R + +--R 3 2 3 3 4 3 2 2 2 +--R (- 2a - a + 2a + 1)b x + (- 4a - 2a + 4a + 2a)b x +--R + +--R 5 4 3 2 +--R (- 2a - a + 4a + 2a - 2a - 1)b x +--R * +--R atanh(b x + a) 2 +--R (%e ) +--R + +--R 2 3 3 3 2 2 2 +--R (2a + a)b x + (4a + 4a - a - 1)b x +--R + +--R 4 3 2 5 4 3 2 +--R (3a + 4a - 2a - 4a - 1)b x + a + a - 2a - 2a + a + 1 +--R * +--R +--------+ +--R | 2 atanh(b x + a) +--R \|- a + 1 %e +--R + +--R 3 2 3 3 4 3 2 2 2 +--R (- 2a - 5a - 4a - 1)b x + (- 4a - 10a - 8a - 2a)b x +--R + +--R 5 4 3 2 +--R (- 2a - 5a - 2a + 4a + 4a + 1)b x +--R / +--R 5 4 3 2 3 5 +--R (a - a - 2a + 2a + a - 1)b x +--R + +--R 6 5 4 3 2 2 4 +--R (3a - 4a - 5a + 8a + a - 4a + 1)b x +--R + +--R 7 6 5 4 3 2 3 +--R (3a - 5a - 5a + 11a + a - 7a + a + 1)b x +--R + +--R 8 7 6 5 3 2 2 +--R (a - 2a - 2a + 6a - 6a + 2a + 2a - 1)x +--R * +--R atanh(b x + a) 2 +--R (%e ) +--R + +--R 5 4 3 2 3 5 +--R (a + a - 2a - 2a + a + 1)b x +--R + +--R 6 5 4 3 2 2 4 +--R (3a + 2a - 7a - 4a + 5a + 2a - 1)b x +--R + +--R 7 6 5 4 3 2 3 +--R (3a + a - 9a - 3a + 9a + 3a - 3a - 1)b x +--R + +--R 8 6 4 2 2 +--R (a - 4a + 6a - 4a + 1)x +--R * +--R - b x - a - 1 +--R log(-------------) +--R b x + a - 1 +--R ------------------ +--R 2 +--R %e +--R + +--R 4 3 2 3 5 5 4 3 2 2 4 +--R (a - a - a + a)b x + (3a - 3a - 4a + 4a + a - 1)b x +--R + +--R 6 5 4 3 2 3 +--R (3a - 3a - 6a + 6a + 3a - 3a)b x +--R + +--R 7 6 5 4 3 2 2 +--R (a - a - 3a + 3a + 3a - 3a - a + 1)x +--R * +--R +--------+ +--R | 2 atanh(b x + a) 2 +--R \|- a + 1 (%e ) +--R + +--R 4 3 2 3 5 5 4 3 2 2 4 +--R (a + a - a - a)b x + (3a + 3a - 4a - 4a + a + 1)b x +--R + +--R 6 5 4 3 2 3 +--R (3a + 3a - 6a - 6a + 3a + 3a)b x +--R + +--R 7 6 5 4 3 2 2 +--R (a + a - 3a - 3a + 3a + 3a - a - 1)x +--R * +--R +--------+ +--R | 2 +--R \|- a + 1 +--R Type: Expression Integer +--E 117 + +--S 118 of 489 +m0222b:= a0222.2-r0222 +--R +--R +--R (102) +--R +------+ +-----+ atanh(b x + a) +--R | 2 \|a - 1 %e +--R (- 4a - 2)b x\|a - 1 atanh(------------------------) +--R +-------+ +--R \|- a - 1 +--R + +--R - b x - a - 1 +--R log(-------------) +--R b x + a - 1 +--R +------+ ------------------ +--R | 2 2 +--R +-------+ +-----+ \|a - 1 %e +--R (- 4a - 2)b x\|- a - 1 \|a - 1 atan(-----------------------------) +--R a + 1 +--R + +--R - b x - a - 1 +--R log(-------------) +--R b x + a - 1 +--R +------+ ------------------ +--R +-------+ +-----+ | 2 2 +--R ((a + 2)b x + a - 1)\|- a - 1 \|a - 1 \|a - 1 %e +--R + +--R +------+ +--R +-------+ +-----+ | 2 atanh(b x + a) +--R ((- a - 2)b x - a + 1)\|- a - 1 \|a - 1 \|a - 1 %e +--R / +--R +------+ +--R 3 2 +-------+ +-----+ | 2 +--R (a - a - a + 1)x\|- a - 1 \|a - 1 \|a - 1 +--R Type: Expression Integer +--E 118 + +--S 119 of 489 +d0222b:= D(m0222b,x) +--R +--R +--R (103) +--R 2 2 2 3 2 4 3 +--R ((- 2a + a + 1)b x + (- 2a + 3a - 1)b x - a + 2a - 2a + 1) +--R * +--R atanh(b x + a) 2 +--R (%e ) +--R + +--R 2 2 2 3 2 4 2 +--R (- 2a - 3a - 1)b x + (- 2a - a + 2a + 1)b x - a + 2a - 1 +--R * +--R - b x - a - 1 3 +--R log(-------------) +--R b x + a - 1 +--R ------------------ +--R 2 +--R (%e ) +--R + +--R 2 2 2 3 2 4 3 +--R ((2a - a - 1)b x + (2a - 3a + 1)b x + a - 2a + 2a - 1) +--R * +--R atanh(b x + a) 3 +--R (%e ) +--R + +--R 2 2 2 3 2 4 2 +--R ((2a - a - 1)b x + (2a + a - 2a - 1)b x + a - 2a + 1) +--R * +--R atanh(b x + a) +--R %e +--R * +--R - b x - a - 1 2 +--R log(-------------) +--R b x + a - 1 +--R ------------------ +--R 2 +--R (%e ) +--R + +--R 2 2 2 3 2 4 2 +--R ((- 2a + a + 1)b x + (- 2a - a + 2a + 1)b x - a + 2a - 1) +--R * +--R atanh(b x + a) 2 +--R (%e ) +--R + +--R 2 2 2 3 2 4 3 +--R (- 2a - 3a - 1)b x + (- 2a - 5a - 4a - 1)b x - a - 2a + 2a + 1 +--R * +--R - b x - a - 1 +--R log(-------------) +--R b x + a - 1 +--R ------------------ +--R 2 +--R %e +--R + +--R 2 2 2 3 2 4 2 +--R ((2a + 3a + 1)b x + (2a + a - 2a - 1)b x + a - 2a + 1) +--R * +--R atanh(b x + a) 3 +--R (%e ) +--R + +--R 2 2 2 3 2 4 3 +--R ((2a + 3a + 1)b x + (2a + 5a + 4a + 1)b x + a + 2a - 2a - 1) +--R * +--R atanh(b x + a) +--R %e +--R / +--R 4 3 2 4 5 4 2 3 +--R (a - 2a + 2a - 1)b x + (2a - 4a + 4a - 2a)b x +--R + +--R 6 5 4 3 2 2 +--R (a - 2a - a + 4a - a - 2a + 1)x +--R * +--R atanh(b x + a) 2 +--R (%e ) +--R + +--R 4 2 2 4 5 3 3 6 4 2 2 +--R (a - 2a + 1)b x + (2a - 4a + 2a)b x + (a - 3a + 3a - 1)x +--R * +--R - b x - a - 1 2 +--R log(-------------) +--R b x + a - 1 +--R ------------------ +--R 2 +--R (%e ) +--R + +--R 4 2 2 4 5 3 3 6 4 2 2 +--R ((a - 2a + 1)b x + (2a - 4a + 2a)b x + (a - 3a + 3a - 1)x ) +--R * +--R atanh(b x + a) 2 +--R (%e ) +--R + +--R 4 3 2 4 5 4 2 3 +--R (a + 2a - 2a - 1)b x + (2a + 4a - 4a - 2a)b x +--R + +--R 6 5 4 3 2 2 +--R (a + 2a - a - 4a - a + 2a + 1)x +--R Type: Expression Integer +--E 119 + +--S 120 of 489 +t0223:= exp(1)^atanh(x)*(1-x)^(1/2) +--R +--R +--R +-------+ atanh(x) +--R (104) \|- x + 1 %e +--R Type: Expression Integer +--E 120 + +--S 121 of 489 +r0223:= 2/3*(1+x)^(3/2) +--R +--R +--R +-----+ +--R (2x + 2)\|x + 1 +--R (105) ---------------- +--R 3 +--R Type: Expression Integer +--E 121 + +--S 122 of 489 +a0223:= integrate(t0223,x) +--R +--R +--R - x - 1 +--R log(-------) +--R x - 1 +--R ------------ +--R +-------+ 2 +--R (2x + 2)\|- x + 1 %e +--R (106) -------------------------------- +--R 3 +--R Type: Union(Expression Integer,...) +--E 122 + +--S 123 of 489 +m0223:= a0223-r0223 +--R +--R +--R - x - 1 +--R log(-------) +--R x - 1 +--R ------------ +--R +-------+ 2 +-----+ +--R (2x + 2)\|- x + 1 %e + (- 2x - 2)\|x + 1 +--R (107) ----------------------------------------------------- +--R 3 +--R Type: Expression Integer +--E 123 + +--S 124 of 489 +d0223:= D(m0223,x) +--R +--R +--R - x - 1 +--R log(-------) +--R x - 1 +--R ------------ +--R +-----+ 2 +-------+ +--R (- x + 1)\|x + 1 %e + (- x - 1)\|- x + 1 +--R (108) ----------------------------------------------------- +--R +-------+ +-----+ +--R \|- x + 1 \|x + 1 +--R Type: Expression Integer +--E 124 + +--S 125 of 489 +t0224:= exp(1)^atanh(x)/(1-x)^(1/2) +--R +--R +--R atanh(x) +--R %e +--R (109) ---------- +--R +-------+ +--R \|- x + 1 +--R Type: Expression Integer +--E 125 + +--S 126 of 489 +r0224:= -2*(1+x)^(1/2)+2*2^(1/2)*atanh(1/2*(1+x)^(1/2)*2^(1/2)) +--R +--R +--R +-+ +-----+ +--R +-+ \|2 \|x + 1 +-----+ +--R (110) 2\|2 atanh(------------) - 2\|x + 1 +--R 2 +--R Type: Expression Integer +--E 126 + +--S 127 of 489 +--a0224:= integrate(t0224,x) +--E 127 + +--S 128 of 489 +--m0224:= a0224-r0224 +--E 128 + +--S 129 of 489 +--d0224:= D(m0224,x) +--E 129 + +--S 130 of 489 +t0225:= exp(1)^atanh(x)/(1-x)^(3/2) +--R +--R +--R atanh(x) +--R %e +--R (111) - ----------------- +--R +-------+ +--R (x - 1)\|- x + 1 +--R Type: Expression Integer +--E 130 + +--S 131 of 489 +r0225:= (1+x)^(1/2)/(1-x)-1/2*2^(1/2)*atanh(1/2*(1+x)^(1/2)*2^(1/2)) +--R +--R +--R +-+ +-----+ +--R +-+ \|2 \|x + 1 +-----+ +--R (- x + 1)\|2 atanh(------------) - 2\|x + 1 +--R 2 +--R (112) -------------------------------------------- +--R 2x - 2 +--R Type: Expression Integer +--E 131 + +--S 132 of 489 +--a0225:= integrate(t0225,x) +--E 132 + +--S 133 of 489 +--m0225:= a0225-r0225 +--E 133 + +--S 134 of 489 +--d0225:= D(m0225,x) +--E 134 + +--S 135 of 489 +t0226:= exp(1)^atanh(x)*(1+x)^(3/2) +--R +--R +--R +-----+ atanh(x) +--R (113) (x + 1)\|x + 1 %e +--R Type: Expression Integer +--E 135 + +--S 136 of 489 +r0226:= -86/15*(1-x)^(1/2)-28/15*(1-x)^(1/2)*x-2/5*(1-x)^(1/2)*x^2 +--R +--R +--R 2 +-------+ +--R (- 6x - 28x - 86)\|- x + 1 +--R (114) ---------------------------- +--R 15 +--R Type: Expression Integer +--E 136 + +--S 137 of 489 +a0226:= integrate(t0226,x) +--R +--R +--R - x - 1 +--R log(-------) +--R x - 1 +--R ------------ +--R 3 2 +-----+ 2 +--R (18x + 66x + 174x - 258)\|x + 1 %e + 430x + 430 +--R (115) ------------------------------------------------------------- +--R 45x + 45 +--R Type: Union(Expression Integer,...) +--E 137 + +--S 138 of 489 +m0226:= a0226-r0226 +--R +--R +--R (116) +--R - x - 1 +--R log(-------) +--R x - 1 +--R ------------ +--R 3 2 +-----+ 2 +--R (18x + 66x + 174x - 258)\|x + 1 %e +--R + +--R 3 2 +-------+ +--R (18x + 102x + 342x + 258)\|- x + 1 + 430x + 430 +--R / +--R 45x + 45 +--R Type: Expression Integer +--E 138 + +--S 139 of 489 +d0226:= D(m0226,x) +--R +--R +--R - x - 1 +--R log(-------) +--R x - 1 +--R ------------ +--R 2 +-------+ 2 2 +-----+ +--R (x + 2x + 1)\|- x + 1 %e + (- x - 2x - 1)\|x + 1 +--R (117) --------------------------------------------------------------- +--R +-------+ +-----+ +--R \|- x + 1 \|x + 1 +--R Type: Expression Integer +--E 139 + +--S 140 of 489 +t0227:= exp(1)^atanh(x)/(1+x)^(1/2) +--R +--R +--R atanh(x) +--R %e +--R (118) ---------- +--R +-----+ +--R \|x + 1 +--R Type: Expression Integer +--E 140 + +--S 141 of 489 +r0227:= -2*(1-x)^(1/2) +--R +--R +--R +-------+ +--R (119) - 2\|- x + 1 +--R Type: Expression Integer +--E 141 + +--S 142 of 489 +a0227:= integrate(t0227,x) +--R +--R +--R - x - 1 +--R log(-------) +--R x - 1 +--R ------------ +--R +-----+ 2 +--R (6x - 6)\|x + 1 %e - 10x - 10 +--R (120) ----------------------------------------- +--R 3x + 3 +--R Type: Union(Expression Integer,...) +--E 142 + +--S 143 of 489 +m0227:= a0227-r0227 +--R +--R +--R - x - 1 +--R log(-------) +--R x - 1 +--R ------------ +--R +-----+ 2 +-------+ +--R (6x - 6)\|x + 1 %e + (6x + 6)\|- x + 1 - 10x - 10 +--R (121) -------------------------------------------------------------- +--R 3x + 3 +--R Type: Expression Integer +--E 143 + +--S 144 of 489 +d0227:= D(m0227,x) +--R +--R +--R - x - 1 +--R log(-------) +--R x - 1 +--R ------------ +--R +-------+ 2 +-----+ +--R \|- x + 1 %e - \|x + 1 +--R (122) ----------------------------------- +--R +-------+ +-----+ +--R \|- x + 1 \|x + 1 +--R Type: Expression Integer +--E 144 + +--S 145 of 489 +t0228:= exp(1)^atanh(x)/(1+x)^(3/2) +--R +--R +--R atanh(x) +--R %e +--R (123) --------------- +--R +-----+ +--R (x + 1)\|x + 1 +--R Type: Expression Integer +--E 145 + +--S 146 of 489 +r0228:= -2^(1/2)*atanh(1/2*(1-x)^(1/2)*2^(1/2)) +--R +--R +--R +-+ +-------+ +--R +-+ \|2 \|- x + 1 +--R (124) - \|2 atanh(--------------) +--R 2 +--R Type: Expression Integer +--E 146 + +--S 147 of 489 +--a0228:= integrate(t0228,x) +--E 147 + +--S 148 of 489 +--m0228:= a0228-r0228 +--E 148 + +--S 149 of 489 +--d0228:= D(m0228,x) +--E 149 + +--S 150 of 489 +t0229:= x*exp(1)^atanh(x)/(1-x) +--R +--R +--R atanh(x) +--R x %e +--R (125) - ------------ +--R x - 1 +--R Type: Expression Integer +--E 150 + +--S 151 of 489 +r0229:= -(-3+x)*(1+x)^(1/2)/(1-x)^(1/2)-2*asin(x) +--R +--R +--R +-----+ +-------+ +--R (- x + 3)\|x + 1 - 2asin(x)\|- x + 1 +--R (126) -------------------------------------- +--R +-------+ +--R \|- x + 1 +--R Type: Expression Integer +--E 151 + +--S 152 of 489 +a0229:= integrate(t0229,x) +--R +--R +--R - x - 1 - x - 1 +--R log(-------) log(-------) +--R x - 1 x - 1 +--R ------------ ------------ +--R 2 2 +--R (127) - 4atan(%e ) + (- x + 3)%e +--R Type: Union(Expression Integer,...) +--E 152 + +--S 153 of 489 +m0229:= a0229-r0229 +--R +--R +--R (128) +--R - x - 1 - x - 1 +--R log(-------) log(-------) +--R x - 1 x - 1 +--R ------------ ------------ +--R +-------+ 2 +-------+ 2 +--R - 4\|- x + 1 atan(%e ) + (- x + 3)\|- x + 1 %e +--R + +--R +-----+ +-------+ +--R (x - 3)\|x + 1 + 2asin(x)\|- x + 1 +--R / +--R +-------+ +--R \|- x + 1 +--R Type: Expression Integer +--E 153 + +--S 154 of 489 +d0229:= D(m0229,x) +--R +--R +--R (129) +--R - x - 1 3 +--R log(-------) +--R x - 1 +--R +--------+ ------------ +--R 2 | 2 +-------+ +-----+ 2 +--R (- x + x - 2)\|- x + 1 \|- x + 1 \|x + 1 (%e ) +--R + +--R - x - 1 2 +--R log(-------) +--R x - 1 +--R +--------+ ------------ +--R 2 +-------+ +-----+ 3 | 2 2 +--R ((2x - 2)\|- x + 1 \|x + 1 + (x + x + 2)\|- x + 1 )(%e ) +--R + +--R - x - 1 +--R log(-------) +--R x - 1 +--R +--------+ ------------ +--R 2 | 2 +-------+ +-----+ 2 +--R (- x + x + 2)\|- x + 1 \|- x + 1 \|x + 1 %e +--R + +--R +--------+ +--R 2 +-------+ +-----+ 3 | 2 +--R (2x - 2)\|- x + 1 \|x + 1 + (x + x + 2)\|- x + 1 +--R / +--R - x - 1 2 +--R log(-------) +--R x - 1 +--R +--------+ ------------ +--R 2 | 2 +-------+ +-----+ 2 +--R (x - 1)\|- x + 1 \|- x + 1 \|x + 1 (%e ) +--R + +--R +--------+ +--R 2 | 2 +-------+ +-----+ +--R (x - 1)\|- x + 1 \|- x + 1 \|x + 1 +--R Type: Expression Integer +--E 154 + +--S 155 of 489 +t0230:= x*exp(1)^atanh(x)/(1-x)^(1/2) +--R +--R +--R atanh(x) +--R x %e +--R (130) ------------ +--R +-------+ +--R \|- x + 1 +--R Type: Expression Integer +--E 155 + +--S 156 of 489 +r0230:= -2*(1+x)^(1/2)-2/3*(1+x)^(3/2)+2*2^(1/2)*atanh(1/2*(1+x)^(1/2)*2^(1/2)) +--R +--R +--R +-+ +-----+ +--R +-+ \|2 \|x + 1 +-----+ +--R 6\|2 atanh(------------) + (- 2x - 8)\|x + 1 +--R 2 +--R (131) --------------------------------------------- +--R 3 +--R Type: Expression Integer +--E 156 + +--S 157 of 489 +--a0230:= integrate(t0230,x) +--E 157 + +--S 158 of 489 +--m0230:= a0230-r0230 +--E 158 + +--S 159 of 489 +--d0230:= D(m0230,x) +--E 159 + +--S 160 of 489 +t0231:= x*exp(1)^atanh(x)/(1-x)^(3/2) +--R +--R +--R atanh(x) +--R x %e +--R (132) - ----------------- +--R +-------+ +--R (x - 1)\|- x + 1 +--R Type: Expression Integer +--E 160 + +--S 161 of 489 +r0231:= 2*(1+x)^(1/2)+(1+x)^(1/2)/(1-x)-_ + 5/2*2^(1/2)*atanh(1/2*(1+x)^(1/2)*2^(1/2)) +--R +--R +--R +-+ +-----+ +--R +-+ \|2 \|x + 1 +-----+ +--R (- 5x + 5)\|2 atanh(------------) + (4x - 6)\|x + 1 +--R 2 +--R (133) ---------------------------------------------------- +--R 2x - 2 +--R Type: Expression Integer +--E 161 + +--S 162 of 489 +--a0231:= integrate(t0231,x) +--E 162 + +--S 163 of 489 +--m0231:= a0231-r0231 +--E 163 + +--S 164 of 489 +--d0231:= D(m0231,x) +--E 164 + +--S 165 of 489 +t0232:= x*exp(1)^atanh(x)*(1+x)^(3/2) +--R +--R +--R 2 +-----+ atanh(x) +--R (134) (x + x)\|x + 1 %e +--R Type: Expression Integer +--E 165 + +--S 166 of 489 +r0232:= -8*(1-x)^(1/2)+16/3*(1-x)^(3/2)-2*(1-x)^(5/2)+2/7*(1-x)^(7/2) +--R +--R +--R 3 2 +-------+ +--R (- 6x - 24x - 46x - 92)\|- x + 1 +--R (135) ----------------------------------- +--R 21 +--R Type: Expression Integer +--E 166 + +--S 167 of 489 +a0232:= integrate(t0232,x) +--R +--R +--R - x - 1 +--R log(-------) +--R x - 1 +--R ------------ +--R 4 3 2 +-----+ 2 +--R (6x + 18x + 22x + 46x - 92)\|x + 1 %e +--R (136) ---------------------------------------------------- +--R 21x + 21 +--R Type: Union(Expression Integer,...) +--E 167 + +--S 168 of 489 +m0232:= a0232-r0232 +--R +--R +--R (137) +--R - x - 1 +--R log(-------) +--R x - 1 +--R ------------ +--R 4 3 2 +-----+ 2 +--R (6x + 18x + 22x + 46x - 92)\|x + 1 %e +--R + +--R 4 3 2 +-------+ +--R (6x + 30x + 70x + 138x + 92)\|- x + 1 +--R / +--R 21x + 21 +--R Type: Expression Integer +--E 168 + +--S 169 of 489 +d0232:= D(m0232,x) +--R +--R +--R - x - 1 +--R log(-------) +--R x - 1 +--R ------------ +--R 3 2 +-------+ 2 3 2 +-----+ +--R (x + 2x + x)\|- x + 1 %e + (- x - 2x - x)\|x + 1 +--R (138) ----------------------------------------------------------------- +--R +-------+ +-----+ +--R \|- x + 1 \|x + 1 +--R Type: Expression Integer +--E 169 + +--S 170 of 489 +t0233:= x*exp(1)^atanh(x)/(1+x)^(3/2) +--R +--R +--R atanh(x) +--R x %e +--R (139) --------------- +--R +-----+ +--R (x + 1)\|x + 1 +--R Type: Expression Integer +--E 170 + +--S 171 of 489 +r0233:= -2*(1-x)^(1/2)+2^(1/2)*atanh(1/2*(1-x)^(1/2)*2^(1/2)) +--R +--R +--R +-+ +-------+ +--R +-+ \|2 \|- x + 1 +-------+ +--R (140) \|2 atanh(--------------) - 2\|- x + 1 +--R 2 +--R Type: Expression Integer +--E 171 + +--S 172 of 489 +--a0233:= integrate(t0233,x) +--E 172 + +--S 173 of 489 +--m0233:= a0233-r0233 +--E 173 + +--S 174 of 489 +--d0233:= D(m0233,x) +--E 174 + +--S 175 of 489 +t0234:= sin(x)*exp(1)^atanh(x)*(1-x)^(1/2) +--R +--R +--R +-------+ atanh(x) +--R (141) sin(x)\|- x + 1 %e +--R Type: Expression Integer +--E 175 + +--S 176 of 489 +r0234:= -(1+x)^(1/2)*cos(x)+1/2*2^(1/2)*%pi^(1/2)*cos(1)*_ + FresnelC(2^(1/2)/%pi^(1/2)*(1+x)^(1/2))+1/2*2^(1/2)*_ + %pi^(1/2)*FresnelS(2^(1/2)/%pi^(1/2)*(1+x)^(1/2))*sin(1) +--R +--R There are no library operations named FresnelC +--R Use HyperDoc Browse or issue +--R )what op FresnelC +--R to learn if there is any operation containing " FresnelC " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R FresnelC with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 176 + +--S 177 of 489 +a0234:= integrate(t0234,x) +--R +--R +--R x +--R ++ +--------+ atanh(%I) +--R (142) | sin(%I)\|- %I + 1 %e d%I +--R ++ +--R Type: Union(Expression Integer,...) +--E 177 + +--S 178 of 489 +--m0234:= a0234-r0234 +--E 178 + +--S 179 of 489 +--d0234:= D(m0234,x) +--E 179 + +--S 180 of 489 +t0235:= sin(x)*exp(1)^atanh(x)*(1-x)^(3/2) +--R +--R +--R +-------+ atanh(x) +--R (143) (- x + 1)sin(x)\|- x + 1 %e +--R Type: Expression Integer +--E 180 + +--S 181 of 489 +r0235:= -2*(1+x)^(1/2)*cos(x)+(1+x)^(3/2)*cos(x)+1/4*2^(1/2)*_ + %pi^(1/2)*FresnelC(2^(1/2)/%pi^(1/2)*(1+x)^(1/2))*(4*cos(1)-_ + 3*sin(1))+1/4*2^(1/2)*%pi^(1/2)*_ + FresnelS(2^(1/2)/%pi^(1/2)*(1+x)^(1/2))*(3*cos(1)+4*sin(1))-_ + 3/2*(1+x)^(1/2)*sin(x) +--R +--R There are no library operations named FresnelC +--R Use HyperDoc Browse or issue +--R )what op FresnelC +--R to learn if there is any operation containing " FresnelC " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R FresnelC with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 181 + +--S 182 of 489 +a0235:= integrate(t0235,x) +--R +--R +--R x +--R ++ +--------+ atanh(%I) +--R (144) | (- %I + 1)sin(%I)\|- %I + 1 %e d%I +--R ++ +--R Type: Union(Expression Integer,...) +--E 182 + +--S 183 of 489 +--m0235:= a0235-r0235 +--E 183 + +--S 184 of 489 +--d0235:= D(m0235,x) +--E 184 + +--S 185 of 489 +t0236:= sin(x)*exp(1)^atanh(x)*(1+x)^(1/2) +--R +--R +--R +-----+ atanh(x) +--R (145) sin(x)\|x + 1 %e +--R Type: Expression Integer +--E 185 + +--S 186 of 489 +r0236:= (1-x)^(1/2)*cos(x)+1/2*2^(1/2)*%pi^(1/2)*_ + FresnelS(2^(1/2)/%pi^(1/2)*(1-x)^(1/2))*_ + (4*cos(1)-sin(1))-1/2*2^(1/2)*%pi^(1/2)*_ + FresnelC(2^(1/2)/%pi^(1/2)*(1-x)^(1/2))*(cos(1)+4*sin(1)) +--R +--R There are no library operations named FresnelS +--R Use HyperDoc Browse or issue +--R )what op FresnelS +--R to learn if there is any operation containing " FresnelS " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R FresnelS with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 186 + +--S 187 of 489 +a0236:= integrate(t0236,x) +--R +--R +--R x +--R ++ +------+ atanh(%I) +--R (146) | sin(%I)\|%I + 1 %e d%I +--R ++ +--R Type: Union(Expression Integer,...) +--E 187 + +--S 188 of 489 +--m0236:= a0236-r0236 +--E 188 + +--S 189 of 489 +--d0236:= D(m0236,x) +--E 189 + +--S 190 of 489 +t0237:= sin(x)*exp(1)^atanh(x)*(1+x)^(3/2) +--R +--R +--R +-----+ atanh(x) +--R (147) (x + 1)sin(x)\|x + 1 %e +--R Type: Expression Integer +--E 190 + +--S 191 of 489 +r0237:= 4*(1-x)^(1/2)*cos(x)-(1-x)^(3/2)*cos(x)+1/4*2^(1/2)*%pi^(1/2)*_ + FresnelS(2^(1/2)/%pi^(1/2)*(1-x)^(1/2))*(13*cos(1)-8*sin(1))-_ + 1/4*2^(1/2)*%pi^(1/2)*FresnelC(2^(1/2)/%pi^(1/2)*(1-x)^(1/2))*_ + (8*cos(1)+13*sin(1))-3/2*(1-x)^(1/2)*sin(x) +--R +--R There are no library operations named FresnelS +--R Use HyperDoc Browse or issue +--R )what op FresnelS +--R to learn if there is any operation containing " FresnelS " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R FresnelS with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 191 + +--S 192 of 489 +a0237:= integrate(t0237,x) +--R +--R +--R x +--R ++ +------+ atanh(%I) +--R (148) | (%I + 1)sin(%I)\|%I + 1 %e d%I +--R ++ +--R Type: Union(Expression Integer,...) +--E 192 + +--S 193 of 489 +--m0237:= a0237-r0237 +--E 193 + +--S 194 of 489 +--d0237:= D(m0237,x) +--E 194 + +--S 195 of 489 +t0238:= sin(x)*exp(1)^atanh(x)/(1+x)^(1/2) +--R +--R +--R atanh(x) +--R sin(x)%e +--R (149) ---------------- +--R +-----+ +--R \|x + 1 +--R Type: Expression Integer +--E 195 + +--S 196 of 489 +r0238:= 2^(1/2)*%pi^(1/2)*(FresnelS(2^(1/2)/%pi^(1/2)*(1-x)^(1/2))*cos(1)-_ + FresnelC(2^(1/2)/%pi^(1/2)*(1-x)^(1/2))*sin(1)) +--R +--R There are no library operations named FresnelS +--R Use HyperDoc Browse or issue +--R )what op FresnelS +--R to learn if there is any operation containing " FresnelS " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R FresnelS with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 196 + +--S 197 of 489 +a0238:= integrate(t0238,x) +--R +--R +--R x atanh(%I) +--R ++ sin(%I)%e +--R (150) | ------------------ d%I +--R ++ +------+ +--R \|%I + 1 +--R Type: Union(Expression Integer,...) +--E 197 + +--S 198 of 489 +--m0238:= a0238-r0238 +--E 198 + +--S 199 of 489 +--d0238:= D(m0238,x) +--E 199 + +--S 200 of 489 +t0239:= x*sin(x)*exp(1)^atanh(x)*(1-x)^(1/2) +--R +--R +--R +-------+ atanh(x) +--R (151) x sin(x)\|- x + 1 %e +--R Type: Expression Integer +--E 200 + +--S 201 of 489 +r0239:= (1+x)^(1/2)*cos(x)-(1+x)^(3/2)*cos(x)-1/4*2^(1/2)*%pi^(1/2)*_ + FresnelC(2^(1/2)/%pi^(1/2)*(1+x)^(1/2))*(2*cos(1)-3*sin(1))-_ + 1/4*2^(1/2)*%pi^(1/2)*FresnelS(2^(1/2)/%pi^(1/2)*(1+x)^(1/2))*_ + (3*cos(1)+2*sin(1))+3/2*(1+x)^(1/2)*sin(x) +--R +--R There are no library operations named FresnelC +--R Use HyperDoc Browse or issue +--R )what op FresnelC +--R to learn if there is any operation containing " FresnelC " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R FresnelC with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 201 + +--S 202 of 489 +a0239:= integrate(t0239,x) +--R +--R +--R x +--R ++ +--------+ atanh(%I) +--R (152) | %I sin(%I)\|- %I + 1 %e d%I +--R ++ +--R Type: Union(Expression Integer,...) +--E 202 + +--S 203 of 489 +--m0239:= a0239-r0239 +--E 203 + +--S 204 of 489 +--d0239:= D(m0239,x) +--E 204 + +--S 205 of 489 +t0240:= x*sin(x)*exp(1)^atanh(x)*(1-x)^(3/2) +--R +--R +--R 2 +-------+ atanh(x) +--R (153) (- x + x)sin(x)\|- x + 1 %e +--R Type: Expression Integer +--E 205 + +--S 206 of 489 +r0240:= -7/4*(1+x)^(1/2)*cos(x)-3*(1+x)^(3/2)*cos(x)+(1+x)^(5/2)*cos(x)-_ + 1/8*2^(1/2)*%pi^(1/2)*FresnelS(2^(1/2)/%pi^(1/2)*(1+x)^(1/2))*_ + (18*cos(1)-7*sin(1))+1/8*2^(1/2)*%pi^(1/2)*_ + FresnelC(2^(1/2)/%pi^(1/2)*(1+x)^(1/2))*(7*cos(1)+18*sin(1))+_ + 9/2*(1+x)^(1/2)*sin(x)-5/2*(1+x)^(3/2)*sin(x) +--R +--R There are no library operations named FresnelS +--R Use HyperDoc Browse or issue +--R )what op FresnelS +--R to learn if there is any operation containing " FresnelS " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R FresnelS with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 206 + +--S 207 of 489 +a0240:= integrate(t0240,x) +--R +--R +--R x +--R ++ 2 +--------+ atanh(%I) +--R (154) | (- %I + %I)sin(%I)\|- %I + 1 %e d%I +--R ++ +--R Type: Union(Expression Integer,...) +--E 207 + +--S 208 of 489 +--m0240:= a0240-r0240 +--E 208 + +--S 209 of 489 +--d0240:= D(m0240,x) +--E 209 + +--S 210 of 489 +t0241:= x*sin(x)*exp(1)^atanh(x)*(1+x)^(1/2) +--R +--R +--R +-----+ atanh(x) +--R (155) x sin(x)\|x + 1 %e +--R Type: Expression Integer +--E 210 + +--S 211 of 489 +r0241:= 3*(1-x)^(1/2)*cos(x)-(1-x)^(3/2)*cos(x)+1/4*2^(1/2)*%pi^(1/2)*_ + FresnelS(2^(1/2)/%pi^(1/2)*(1-x)^(1/2))*(5*cos(1)-6*sin(1))-_ + 1/4*2^(1/2)*%pi^(1/2)*FresnelC(2^(1/2)/%pi^(1/2)*(1-x)^(1/2))*_ + (6*cos(1)+5*sin(1))-3/2*(1-x)^(1/2)*sin(x) +--R +--R There are no library operations named FresnelS +--R Use HyperDoc Browse or issue +--R )what op FresnelS +--R to learn if there is any operation containing " FresnelS " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R FresnelS with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 211 + +--S 212 of 489 +a0241:= integrate(t0241,x) +--R +--R +--R x +--R ++ +------+ atanh(%I) +--R (156) | %I sin(%I)\|%I + 1 %e d%I +--R ++ +--R Type: Union(Expression Integer,...) +--E 212 + +--S 213 of 489 +--m0241:= a0241-r0241 +--E 213 + +--S 214 of 489 +--d0241:= D(m0241,x) +--E 214 + +--S 215 of 489 +t0242:= x*sin(x)*exp(1)^atanh(x)*(1+x)^(3/2) +--R +--R +--R 2 +-----+ atanh(x) +--R (157) (x + x)sin(x)\|x + 1 %e +--R Type: Expression Integer +--E 215 + +--S 216 of 489 +r0242:= 17/4*(1-x)^(1/2)*cos(x)-5*(1-x)^(3/2)*cos(x)+(1-x)^(5/2)*cos(x)+_ + 1/8*2^(1/2)*%pi^(1/2)*FresnelS(2^(1/2)/%pi^(1/2)*(1-x)^(1/2))*_ + (2*cos(1)-17*sin(1))-1/8*2^(1/2)*%pi^(1/2)*_ + FresnelC(2^(1/2)/%pi^(1/2)*(1-x)^(1/2))*(17*cos(1)+2*sin(1))-_ + 15/2*(1-x)^(1/2)*sin(x)+5/2*(1-x)^(3/2)*sin(x) +--R +--R There are no library operations named FresnelS +--R Use HyperDoc Browse or issue +--R )what op FresnelS +--R to learn if there is any operation containing " FresnelS " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R FresnelS with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 216 + +--S 217 of 489 +a0242:= integrate(t0242,x) +--R +--R +--R x +--R ++ 2 +------+ atanh(%I) +--R (158) | (%I + %I)sin(%I)\|%I + 1 %e d%I +--R ++ +--R Type: Union(Expression Integer,...) +--E 217 + +--S 218 of 489 +--m0242:= a0242-r0242 +--E 218 + +--S 219 of 489 +--d0242:= D(m0242,x) +--E 219 + +--S 220 of 489 +t0243:= x*sin(x)*exp(1)^atanh(x)/(1+x)^(1/2) +--R +--R +--R atanh(x) +--R x sin(x)%e +--R (159) ------------------ +--R +-----+ +--R \|x + 1 +--R Type: Expression Integer +--E 220 + +--S 221 of 489 +r0243:= (1-x)^(1/2)*cos(x)+1/2*2^(1/2)*%pi^(1/2)*_ + FresnelS(2^(1/2)/%pi^(1/2)*(1-x)^(1/2))*(2*cos(1)-sin(1))-_ + 1/2*2^(1/2)*%pi^(1/2)*FresnelC(2^(1/2)/%pi^(1/2)*(1-x)^(1/2))*_ + (cos(1)+2*sin(1)) +--R +--R There are no library operations named FresnelS +--R Use HyperDoc Browse or issue +--R )what op FresnelS +--R to learn if there is any operation containing " FresnelS " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R FresnelS with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 221 + +--S 222 of 489 +a0243:= integrate(t0243,x) +--R +--R +--R x atanh(%I) +--R ++ %I sin(%I)%e +--R (160) | --------------------- d%I +--R ++ +------+ +--R \|%I + 1 +--R Type: Union(Expression Integer,...) +--E 222 + +--S 223 of 489 +--m0243:= a0243-r0243 +--E 223 + +--S 224 of 489 +--d0243:= D(m0243,x) +--E 224 + +--S 225 of 489 +t0244:= exp(1)^atanh(x)/(1-x^2)^(3/2) +--R +--R +--R atanh(x) +--R %e +--R (161) - ------------------- +--R +--------+ +--R 2 | 2 +--R (x - 1)\|- x + 1 +--R Type: Expression Integer +--E 225 + +--S 226 of 489 +r0244:= 1/(2-2*x)+1/2*atanh(x) +--R +--R +--R (x - 1)atanh(x) - 1 +--R (162) ------------------- +--R 2x - 2 +--R Type: Expression Integer +--E 226 + +--S 227 of 489 +a0244:= integrate(t0244,x) +--R +--R +--R (163) +--R - x - 1 +--R log(-------) +--R x - 1 +--R +--------+ ------------ +--R 2 | 2 2 2 +--R 2 (x + 1)\|- x + 1 %e - 2x - 2x +--R (- x + 1)log(--------------------------------------------) +--R 3 2 +--R x + x - x - 1 +--R + +--R - x - 1 +--R log(-------) +--R x - 1 +--R +--------+ ------------ +--R | 2 2 +--R - 2x\|- x + 1 %e +--R / +--R 2 +--R 4x - 4 +--R Type: Union(Expression Integer,...) +--E 227 + +--S 228 of 489 +m0244:= a0244-r0244 +--R +--R +--R (164) +--R - x - 1 +--R log(-------) +--R x - 1 +--R +--------+ ------------ +--R 2 | 2 2 2 +--R 2 (x + 1)\|- x + 1 %e - 2x - 2x +--R (- x + 1)log(--------------------------------------------) +--R 3 2 +--R x + x - x - 1 +--R + +--R - x - 1 +--R log(-------) +--R x - 1 +--R +--------+ ------------ +--R | 2 2 2 +--R - 2x\|- x + 1 %e + (- 2x + 2)atanh(x) + 2x + 2 +--R / +--R 2 +--R 4x - 4 +--R Type: Expression Integer +--E 228 + +--S 229 of 489 +d0244:= D(m0244,x) +--R +--R +--R (165) +--R - x - 1 2 +--R log(-------) +--R x - 1 +--R ------------ +--R 3 2 2 +--R (- x + x - x + 1)(%e ) +--R + +--R - x - 1 +--R log(-------) +--R x - 1 +--R +--------+ ------------ +--R | 2 2 3 2 +--R (- 2x - 2)\|- x + 1 %e - x + x + 3x + 1 +--R / +--R - x - 1 +--R log(-------) +--R x - 1 +--R +--------+ ------------ +--R 4 3 2 | 2 2 4 3 2 +--R (2x - 4x + 4x - 4x + 2)\|- x + 1 %e - 4x + 4x + 4x - 4x +--R Type: Expression Integer +--E 229 + +--S 230 of 489 +t0245:= exp(1)^atanh(x)*(a-a*x^2)^(7/2) +--R +--R +--R +----------+ +--R 3 6 3 4 3 2 3 | 2 atanh(x) +--R (166) (- a x + 3a x - 3a x + a )\|- a x + a %e +--R Type: Expression Integer +--E 230 + +--S 231 of 489 +r0245:= -1/280*(-a*(-1+x^2))^(1/2)*(1+x)^5*_ + a^3*(-93+185*x-135*x^2+35*x^3)/(1-x^2)^(1/2) +--R +--R +--R (167) +--R 3 8 3 7 3 6 3 5 3 4 3 3 3 2 +--R - 35a x - 40a x + 140a x + 168a x - 210a x - 280a x + 140a x +--R + +--R 3 3 +--R 280a x + 93a +--R * +--R +----------+ +--R | 2 +--R \|- a x + a +--R / +--R +--------+ +--R | 2 +--R 280\|- x + 1 +--R Type: Expression Integer +--E 231 + +--S 232 of 489 +a0245:= integrate(t0245,x) +--R +--R +--R (168) +--R 3 8 3 7 3 6 3 5 3 4 3 3 3 2 +--R - 35a x - 40a x + 140a x + 168a x - 210a x - 280a x + 140a x +--R + +--R 3 +--R 280a x +--R * +--R - x - 1 +--R log(-------) +--R x - 1 +--R +----------+ ------------ +--R | 2 2 +--R \|- a x + a %e +--R / +--R 280x + 280 +--R Type: Union(Expression Integer,...) +--E 232 + +--S 233 of 489 +m0245:= a0245-r0245 +--R +--R +--R (169) +--R 3 8 3 7 3 6 3 5 3 4 3 3 3 2 +--R - 35a x - 40a x + 140a x + 168a x - 210a x - 280a x + 140a x +--R + +--R 3 +--R 280a x +--R * +--R - x - 1 +--R log(-------) +--R x - 1 +--R +----------+ +--------+ ------------ +--R | 2 | 2 2 +--R \|- a x + a \|- x + 1 %e +--R + +--R 3 9 3 8 3 7 3 6 3 5 3 4 3 3 +--R 35a x + 75a x - 100a x - 308a x + 42a x + 490a x + 140a x +--R + +--R 3 2 3 3 +--R - 420a x - 373a x - 93a +--R * +--R +----------+ +--R | 2 +--R \|- a x + a +--R / +--R +--------+ +--R | 2 +--R (280x + 280)\|- x + 1 +--R Type: Expression Integer +--E 233 + +--S 234 of 489 +d0245:= D(m0245,x) +--R +--R +--R (170) +--R - x - 1 +--R log(-------) +--R x - 1 +--R +--------+ ------------ +--R 4 8 4 6 4 4 4 2 4 | 2 2 4 9 +--R (a x - 4a x + 6a x - 4a x + a )\|- x + 1 %e - a x +--R + +--R 4 8 4 7 4 6 4 5 4 4 4 3 4 2 4 4 +--R - a x + 4a x + 4a x - 6a x - 6a x + 4a x + 4a x - a x - a +--R / +--R +----------+ +--------+ +--R | 2 | 2 +--R \|- a x + a \|- x + 1 +--R Type: Expression Integer +--E 234 + +--S 235 of 489 +t0246:= exp(1)^atanh(x)/(a-a*x^2)^(3/2) +--R +--R +--R atanh(x) +--R %e +--R (171) - ----------------------- +--R +----------+ +--R 2 | 2 +--R (a x - a)\|- a x + a +--R Type: Expression Integer +--E 235 + +--S 236 of 489 +r0246:= 1/2*(1-x^2)^(3/2)*(1/(1-x)+atanh(x))/(a-a*x^2)^(3/2) +--R +--R +--R +--------+ +--R | 2 +--R ((x - 1)atanh(x) - 1)\|- x + 1 +--R (172) -------------------------------- +--R +----------+ +--R | 2 +--R (2a x - 2a)\|- a x + a +--R Type: Expression Integer +--E 236 + +--S 237 of 489 +--a0246:= integrate(t0246,x) +--E 237 + +--S 238 of 489 +--m0246:= a0246-r0246 +--E 238 + +--S 239 of 489 +--d0246:= D(m0246,x) +--E 239 + +--S 240 of 489 +t0247:= exp(1)^atanh(x)/(a-a*x^2)^(5/2) +--R +--R +--R atanh(x) +--R %e +--R (173) -------------------------------- +--R +----------+ +--R 2 4 2 2 2 | 2 +--R (a x - 2a x + a )\|- a x + a +--R Type: Expression Integer +--E 240 + +--S 241 of 489 +r0247:= 1/8*(1-x^2)^(5/2)*(1/(1-x)^2+2/(1-x)-_ + 1/(1+x)+3*atanh(x))/(a-a*x^2)^(5/2) +--R +--R +--R +--------+ +--R 3 2 2 | 2 +--R ((3x - 3x - 3x + 3)atanh(x) - 3x + 3x + 2)\|- x + 1 +--R (174) -------------------------------------------------------- +--R +----------+ +--R 2 3 2 2 2 2 | 2 +--R (8a x - 8a x - 8a x + 8a )\|- a x + a +--R Type: Expression Integer +--E 241 + +--S 242 of 489 +--a0247:= integrate(t0247,x) +--E 242 + +--S 243 of 489 +--m0247:= a0247-r0247 +--E 243 + +--S 244 of 489 +--d0247:= D(m0247,x) +--E 244 + +--S 245 of 489 +t0248:= exp(1)^atanh(x)/(a-a*x^2)^(7/2) +--R +--R +--R atanh(x) +--R %e +--R (175) - ---------------------------------------- +--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 245 + +--S 246 of 489 +r0248:= 1/96*(1-x^2)^(7/2)*(4/(1-x)^3+9/(1-x)^2+_ + 18/(1-x)-3/(1+x)^2-12/(1+x)+30*atanh(x))/(a-a*x^2)^(7/2) +--R +--R +--R (176) +--R 5 4 3 2 4 3 2 +--R (15x - 15x - 30x + 30x + 15x - 15)atanh(x) - 15x + 15x + 25x +--R + +--R - 25x - 8 +--R * +--R +--------+ +--R | 2 +--R \|- x + 1 +--R / +--R +----------+ +--R 3 5 3 4 3 3 3 2 3 3 | 2 +--R (48a x - 48a x - 96a x + 96a x + 48a x - 48a )\|- a x + a +--R Type: Expression Integer +--E 246 + +--S 247 of 489 +--a0248:= integrate(t0248,x) +--E 247 + +--S 248 of 489 +--m0248:= a0248-r0248 +--E 248 + +--S 249 of 489 +--d0248:= D(m0248,x) +--E 249 + +--S 250 of 489 +t0249:= exp(1)^atanh(x)/(1-1/x^2)^(5/2) +--R +--R +--R 4 atanh(x) +--R x %e +--R (177) ----------------------- +--R +------+ +--R | 2 +--R 4 2 |x - 1 +--R (x - 2x + 1) |------ +--R | 2 +--R \| x +--R Type: Expression Integer +--E 250 + +--S 251 of 489 +r0249:= 1/16*(1-x^2)^(5/2)*(2/(1-x)^2-16/(1-x)-_ + 16*x+2/(1+x)-23*log(1-x)+7*log(1+x))/(1-1/x^2)^(5/2)/x^5 +--R +--R +--R (178) +--R 3 2 3 2 +--R (7x - 7x - 7x + 7)log(x + 1) + (- 23x + 23x + 23x - 23)log(- x + 1) +--R + +--R 4 3 2 +--R - 16x + 16x + 34x - 18x - 12 +--R * +--R +--------+ +--R | 2 +--R \|- x + 1 +--R / +--R +------+ +--R | 2 +--R 4 3 2 |x - 1 +--R (16x - 16x - 16x + 16x) |------ +--R | 2 +--R \| x +--R Type: Expression Integer +--E 251 + +--S 252 of 489 +--a0249:= integrate(t0249,x) +--E 252 + +--S 253 of 489 +--m0249:= a0249-r0249 +--E 253 + +--S 254 of 489 +--d0249:= D(m0249,x) +--E 254 + +--S 255 of 489 +t0250:= x*exp(1)^acoth(x) +--R +--R +--R acoth(x) +--R (179) x %e +--R Type: Expression Integer +--E 255 + +--S 256 of 489 +r0250:= (1-1/x^2)^(1/2)*x+1/2*(1-1/x^2)^(1/2)*x^2+1/2*atanh((1-1/x^2)^(1/2)) +--R +--R +--R +------+ +------+ +--R | 2 | 2 +--R |x - 1 2 |x - 1 +--R atanh( |------ ) + (x + 2x) |------ +--R | 2 | 2 +--R \| x \| x +--R (180) ------------------------------------- +--R 2 +--R Type: Expression Integer +--E 256 + +--S 257 of 489 +a0250:= integrate(t0250,x) +--R +--R +--R (181) +--R x + 1 x + 1 x + 1 +--R log(-----) log(-----) log(-----) +--R x - 1 x - 1 x - 1 +--R ---------- ---------- ---------- +--R 2 2 2 2 +--R log(%e + 1) - log(%e - 1) + (x + x - 2)%e +--R ------------------------------------------------------------------------ +--R 2 +--R Type: Union(Expression Integer,...) +--E 257 + +--S 258 of 489 +m0250:= a0250-r0250 +--R +--R +--R (182) +--R x + 1 x + 1 x + 1 +--R log(-----) log(-----) log(-----) +--R x - 1 x - 1 x - 1 +--R ---------- ---------- ---------- +--R 2 2 2 2 +--R log(%e + 1) - log(%e - 1) + (x + x - 2)%e +--R + +--R +------+ +------+ +--R | 2 | 2 +--R |x - 1 2 |x - 1 +--R - atanh( |------ ) + (- x - 2x) |------ +--R | 2 | 2 +--R \| x \| x +--R / +--R 2 +--R Type: Expression Integer +--E 258 + +--S 259 of 489 +d0250:= D(m0250,x) +--R +--R +--R (183) +--R x + 1 3 +--R log(-----) +--R +------+ x - 1 +--R | 2 ---------- +--R 3 |x - 1 2 +--R (2x - 3x + 1) |------ (%e ) +--R | 2 +--R \| x +--R + +--R x + 1 2 +--R log(-----) +--R x - 1 +--R ---------- +--R 3 2 2 +--R (- 2x - 2x + 2x + 2)(%e ) +--R + +--R x + 1 +--R log(-----) +--R +------+ x - 1 +--R | 2 ---------- +--R 3 |x - 1 2 3 2 +--R (- 2x + 3x + 1) |------ %e + 2x + 2x - 2x - 2 +--R | 2 +--R \| x +--R / +--R x + 1 2 +--R log(-----) +--R +------+ x - 1 +------+ +--R | 2 ---------- | 2 +--R 2 |x - 1 2 2 |x - 1 +--R (2x - 2) |------ (%e ) + (- 2x + 2) |------ +--R | 2 | 2 +--R \| x \| x +--R Type: Expression Integer +--E 259 + +--S 260 of 489 +t0251:= exp(1)^acoth(x) +--R +--R +--R acoth(x) +--R (184) %e +--R Type: Expression Integer +--E 260 + +--S 261 of 489 +r0251:= (1-1/x^2)^(1/2)*x+atanh((1-1/x^2)^(1/2)) +--R +--R +--R +------+ +------+ +--R | 2 | 2 +--R |x - 1 |x - 1 +--R (185) atanh( |------ ) + x |------ +--R | 2 | 2 +--R \| x \| x +--R Type: Expression Integer +--E 261 + +--S 262 of 489 +a0251:= integrate(t0251,x) +--R +--R +--R x + 1 x + 1 x + 1 +--R log(-----) log(-----) log(-----) +--R x - 1 x - 1 x - 1 +--R ---------- ---------- ---------- +--R 2 2 2 +--R (186) log(%e + 1) - log(%e - 1) + (x - 1)%e +--R Type: Union(Expression Integer,...) +--E 262 + +--S 263 of 489 +m0251:= a0251-r0251 +--R +--R +--R (187) +--R x + 1 x + 1 x + 1 +--R log(-----) log(-----) log(-----) +--R x - 1 x - 1 x - 1 +--R ---------- ---------- ---------- +--R 2 2 2 +--R log(%e + 1) - log(%e - 1) + (x - 1)%e +--R + +--R +------+ +------+ +--R | 2 | 2 +--R |x - 1 |x - 1 +--R - atanh( |------ ) - x |------ +--R | 2 | 2 +--R \| x \| x +--R Type: Expression Integer +--E 263 + +--S 264 of 489 +d0251:= D(m0251,x) +--R +--R +--R (188) +--R x + 1 3 x + 1 2 +--R log(-----) log(-----) +--R +------+ x - 1 x - 1 +--R | 2 ---------- ---------- +--R 3 2 |x - 1 2 3 2 2 +--R (x - x ) |------ (%e ) + (- x - x + x + 1)(%e ) +--R | 2 +--R \| x +--R + +--R x + 1 +--R log(-----) +--R +------+ x - 1 +--R | 2 ---------- +--R 3 2 |x - 1 2 3 2 +--R (- x + x + 2x) |------ %e + x + x - x - 1 +--R | 2 +--R \| x +--R / +--R x + 1 2 +--R log(-----) +--R +------+ x - 1 +------+ +--R | 2 ---------- | 2 +--R 3 |x - 1 2 3 |x - 1 +--R (x - x) |------ (%e ) + (- x + x) |------ +--R | 2 | 2 +--R \| x \| x +--R Type: Expression Integer +--E 264 + +--S 265 of 489 +t0252:= exp(1)^acoth(x)/x +--R +--R +--R acoth(x) +--R %e +--R (189) ---------- +--R x +--R Type: Expression Integer +--E 265 + +--S 266 of 489 +r0252:= -acsc(x)+atanh((1-1/x^2)^(1/2)) +--R +--R +--R +------+ +--R | 2 +--R |x - 1 +--R (190) atanh( |------ ) - acsc(x) +--R | 2 +--R \| x +--R Type: Expression Integer +--E 266 + +--S 267 of 489 +a0252:= integrate(t0252,x) +--R +--R +--R x + 1 x + 1 x + 1 +--R log(-----) log(-----) log(-----) +--R x - 1 x - 1 x - 1 +--R ---------- ---------- ---------- +--R 2 2 2 +--R (191) log(%e + 1) - log(%e - 1) - 2atan(%e ) +--R Type: Union(Expression Integer,...) +--E 267 + +--S 268 of 489 +m0252:= a0252-r0252 +--R +--R +--R (192) +--R x + 1 x + 1 x + 1 +--R log(-----) log(-----) log(-----) +--R x - 1 x - 1 x - 1 +--R ---------- ---------- ---------- +--R 2 2 2 +--R log(%e + 1) - log(%e - 1) - 2atan(%e ) +--R + +--R +------+ +--R | 2 +--R |x - 1 +--R - atanh( |------ ) + acsc(x) +--R | 2 +--R \| x +--R Type: Expression Integer +--E 268 + +--S 269 of 489 +d0252:= D(m0252,x) +--R +--R +--R (193) +--R x + 1 4 +--R log(-----) +--R +------+ x - 1 +--R +------+ | 2 ---------- +--R 2 | 2 2 |x - 1 2 +--R ((- x + 1)\|x - 1 + (- x + 1) |------ )(%e ) +--R | 2 +--R \| x +--R + +--R x + 1 3 +--R log(-----) +--R +------+ x - 1 +------+ +--R | 2 +------+ ---------- +------+ | 2 +--R |x - 1 | 2 2 2 | 2 2 |x - 1 +--R 4x |------ \|x - 1 (%e ) + (x - 1)\|x - 1 + (x - 1) |------ +--R | 2 | 2 +--R \| x \| x +--R / +--R x + 1 4 +--R log(-----) +--R +------+ x - 1 +------+ +--R | 2 +------+ ---------- | 2 +------+ +--R 3 |x - 1 | 2 2 3 |x - 1 | 2 +--R (x - x) |------ \|x - 1 (%e ) + (- x + x) |------ \|x - 1 +--R | 2 | 2 +--R \| x \| x +--R Type: Expression Integer +--E 269 + +--S 270 of 489 +t0253:= exp(1)^acoth(x)/x^2 +--R +--R +--R acoth(x) +--R %e +--R (194) ---------- +--R 2 +--R x +--R Type: Expression Integer +--E 270 + +--S 271 of 489 +r0253:= (1-1/x^2)^(1/2)-acsc(x) +--R +--R +--R +------+ +--R | 2 +--R |x - 1 +--R (195) |------ - acsc(x) +--R | 2 +--R \| x +--R Type: Expression Integer +--E 271 + +--S 272 of 489 +a0253:= integrate(t0253,x) +--R +--R +--R x + 1 x + 1 +--R log(-----) log(-----) +--R x - 1 x - 1 +--R ---------- ---------- +--R 2 2 +--R - 2x atan(%e ) + (x - 1)%e +--R (196) --------------------------------------------- +--R x +--R Type: Union(Expression Integer,...) +--E 272 + +--S 273 of 489 +m0253:= a0253-r0253 +--R +--R +--R (197) +--R x + 1 x + 1 +--R log(-----) log(-----) +--R x - 1 x - 1 +------+ +--R ---------- ---------- | 2 +--R 2 2 |x - 1 +--R - 2x atan(%e ) + (x - 1)%e - x |------ + x acsc(x) +--R | 2 +--R \| x +--R ---------------------------------------------------------------------- +--R x +--R Type: Expression Integer +--E 273 + +--S 274 of 489 +d0253:= D(m0253,x) +--R +--R +--R (198) +--R x + 1 3 +--R log(-----) +--R +------+ x - 1 +--R | 2 +------+ ---------- +--R 2 |x - 1 | 2 2 +--R (x - x) |------ \|x - 1 (%e ) +--R | 2 +--R \| x +--R + +--R x + 1 2 +--R log(-----) +--R +------+ x - 1 +--R +------+ | 2 ---------- +--R 2 | 2 4 2 |x - 1 2 +--R ((- x + 1)\|x - 1 + (- x + x ) |------ )(%e ) +--R | 2 +--R \| x +--R + +--R x + 1 +--R log(-----) +--R +------+ x - 1 +--R | 2 +------+ ---------- +------+ +--R 3 2 |x - 1 | 2 2 2 | 2 +--R (2x + x - x) |------ \|x - 1 %e + (- x + 1)\|x - 1 +--R | 2 +--R \| x +--R + +--R +------+ +--R | 2 +--R 4 2 |x - 1 +--R (- x + x ) |------ +--R | 2 +--R \| x +--R / +--R x + 1 2 +--R log(-----) +--R +------+ x - 1 +------+ +--R | 2 +------+ ---------- | 2 +------+ +--R 5 3 |x - 1 | 2 2 5 3 |x - 1 | 2 +--R (x - x ) |------ \|x - 1 (%e ) + (x - x ) |------ \|x - 1 +--R | 2 | 2 +--R \| x \| x +--R Type: Expression Integer +--E 274 + +--S 275 of 489 +t0254:= exp(1)^acoth(x)/x^3 +--R +--R +--R acoth(x) +--R %e +--R (199) ---------- +--R 3 +--R x +--R Type: Expression Integer +--E 275 + +--S 276 of 489 +r0254:= (1-1/x^2)^(1/2)+1/2*(1-1/x^2)^(1/2)/x-1/2*acsc(x) +--R +--R +--R +------+ +--R | 2 +--R |x - 1 +--R (2x + 1) |------ - x acsc(x) +--R | 2 +--R \| x +--R (200) ----------------------------- +--R 2x +--R Type: Expression Integer +--E 276 + +--S 277 of 489 +a0254:= integrate(t0254,x) +--R +--R +--R x + 1 x + 1 +--R log(-----) log(-----) +--R x - 1 x - 1 +--R ---------- ---------- +--R 2 2 2 2 +--R - 2x atan(%e ) + (2x - x - 1)%e +--R (201) --------------------------------------------------- +--R 2 +--R 2x +--R Type: Union(Expression Integer,...) +--E 277 + +--S 278 of 489 +m0254:= a0254-r0254 +--R +--R +--R (202) +--R x + 1 x + 1 +--R log(-----) log(-----) +--R x - 1 x - 1 +--R ---------- ---------- +--R 2 2 2 2 +--R - 2x atan(%e ) + (2x - x - 1)%e +--R + +--R +------+ +--R | 2 +--R 2 |x - 1 2 +--R (- 2x - x) |------ + x acsc(x) +--R | 2 +--R \| x +--R / +--R 2 +--R 2x +--R Type: Expression Integer +--E 278 + +--S 279 of 489 +d0254:= D(m0254,x) +--R +--R +--R (203) +--R x + 1 3 +--R log(-----) +--R +------+ x - 1 +--R | 2 +------+ ---------- +--R 4 3 |x - 1 | 2 2 +--R (- x + 3x - 2x) |------ \|x - 1 (%e ) +--R | 2 +--R \| x +--R + +--R +------+ +--R +------+ | 2 +--R 4 3 2 | 2 5 3 |x - 1 +--R ((x - 2x - 3x + 2x + 2)\|x - 1 + (- x + x ) |------ ) +--R | 2 +--R \| x +--R * +--R x + 1 2 +--R log(-----) +--R x - 1 +--R ---------- +--R 2 +--R (%e ) +--R + +--R x + 1 +--R log(-----) +--R +------+ x - 1 +--R | 2 +------+ ---------- +--R 4 3 |x - 1 | 2 2 +--R (x + 3x - 2x) |------ \|x - 1 %e +--R | 2 +--R \| x +--R + +--R +------+ +--R +------+ | 2 +--R 4 3 2 | 2 5 3 |x - 1 +--R (x - 2x - 3x + 2x + 2)\|x - 1 + (- x + x ) |------ +--R | 2 +--R \| x +--R / +--R x + 1 2 +--R log(-----) +--R +------+ x - 1 +--R | 2 +------+ ---------- +--R 6 4 |x - 1 | 2 2 +--R (2x - 2x ) |------ \|x - 1 (%e ) +--R | 2 +--R \| x +--R + +--R +------+ +--R | 2 +------+ +--R 6 4 |x - 1 | 2 +--R (2x - 2x ) |------ \|x - 1 +--R | 2 +--R \| x +--R Type: Expression Integer +--E 279 + +--S 280 of 489 +t0255:= x^2*exp(1)^(3*acoth(x)) +--R +--R +--R 2 3acoth(x) +--R (204) x %e +--R Type: Expression Integer +--E 280 + +--S 281 of 489 +r0255:= 1/6*(-33*x+26*x^2-52+9*x^3+2*x^4+33*_ + atanh(((-1+x^2)/x^2)^(1/2))*((-1+x^2)/x^2)^(1/2)*x)/_ + x/((-1+x^2)/x^2)^(1/2) +--R +--R +--R +------+ +------+ +--R | 2 | 2 +--R |x - 1 |x - 1 4 3 2 +--R 33x |------ atanh( |------ ) + 2x + 9x + 26x - 33x - 52 +--R | 2 | 2 +--R \| x \| x +--R (205) ---------------------------------------------------------- +--R +------+ +--R | 2 +--R |x - 1 +--R 6x |------ +--R | 2 +--R \| x +--R Type: Expression Integer +--E 281 + +--S 282 of 489 +a0255:= integrate(t0255,x) +--R +--R +--R (206) +--R +-----+ +-----+ +-----+ +--R |x + 1 |x + 1 3 2 |x + 1 +--R 33log( |----- + 1) - 33log( |----- - 1) + (2x + 7x + 19x - 52) |----- +--R \|x - 1 \|x - 1 \|x - 1 +--R -------------------------------------------------------------------------- +--R 6 +--R Type: Union(Expression Integer,...) +--E 282 + +--S 283 of 489 +m0255:= a0255-r0255 +--R +--R +--R (207) +--R +------+ +------+ +--R | 2 +-----+ | 2 +-----+ +--R |x - 1 |x + 1 |x - 1 |x + 1 +--R 33x |------ log( |----- + 1) - 33x |------ log( |----- - 1) +--R | 2 \|x - 1 | 2 \|x - 1 +--R \| x \| x +--R + +--R +------+ +------+ +--R | 2 | 2 +--R |x - 1 |x - 1 +--R - 33x |------ atanh( |------ ) +--R | 2 | 2 +--R \| x \| x +--R + +--R +------+ +--R | 2 +-----+ +--R 4 3 2 |x - 1 |x + 1 4 3 2 +--R (2x + 7x + 19x - 52x) |------ |----- - 2x - 9x - 26x + 33x + 52 +--R | 2 \|x - 1 +--R \| x +--R / +--R +------+ +--R | 2 +--R |x - 1 +--R 6x |------ +--R | 2 +--R \| x +--R Type: Expression Integer +--E 283 + +--S 284 of 489 +d0255:= D(m0255,x) +--R +--R +--R +------+ +--R +-----+ | 2 +--R 4 3 2 |x + 1 4 3 2 |x - 1 +--R (- x - x + x + x) |----- + (x + 2x + x ) |------ +--R \|x - 1 | 2 +--R \| x +--R (208) ------------------------------------------------------- +--R +------+ +--R | 2 +-----+ +--R 2 |x - 1 |x + 1 +--R (x - 2x + 1) |------ |----- +--R | 2 \|x - 1 +--R \| x +--R Type: Expression Integer +--E 284 + +--S 285 of 489 +t0256:= x*exp(1)^(3*acoth(x)) +--R +--R +--R 3acoth(x) +--R (209) x %e +--R Type: Expression Integer +--E 285 + +--S 286 of 489 +r0256:= 1/2*(-9*x-14+6*x^2+x^3+9*_ + atanh(((-1+x^2)/x^2)^(1/2))*((-1+x^2)/x^2)^(1/2)*x)/_ + ((-1+x^2)/x^2)^(1/2)/x +--R +--R +--R +------+ +------+ +--R | 2 | 2 +--R |x - 1 |x - 1 3 2 +--R 9x |------ atanh( |------ ) + x + 6x - 9x - 14 +--R | 2 | 2 +--R \| x \| x +--R (210) ------------------------------------------------ +--R +------+ +--R | 2 +--R |x - 1 +--R 2x |------ +--R | 2 +--R \| x +--R Type: Expression Integer +--E 286 + +--S 287 of 489 +a0256:= integrate(t0256,x) +--R +--R +--R +-----+ +-----+ +-----+ +--R |x + 1 |x + 1 2 |x + 1 +--R 9log( |----- + 1) - 9log( |----- - 1) + (x + 5x - 14) |----- +--R \|x - 1 \|x - 1 \|x - 1 +--R (211) ---------------------------------------------------------------- +--R 2 +--R Type: Union(Expression Integer,...) +--E 287 + +--S 288 of 489 +m0256:= a0256-r0256 +--R +--R +--R (212) +--R +------+ +------+ +--R | 2 +-----+ | 2 +-----+ +--R |x - 1 |x + 1 |x - 1 |x + 1 +--R 9x |------ log( |----- + 1) - 9x |------ log( |----- - 1) +--R | 2 \|x - 1 | 2 \|x - 1 +--R \| x \| x +--R + +--R +------+ +------+ +------+ +--R | 2 | 2 | 2 +-----+ +--R |x - 1 |x - 1 3 2 |x - 1 |x + 1 3 +--R - 9x |------ atanh( |------ ) + (x + 5x - 14x) |------ |----- - x +--R | 2 | 2 | 2 \|x - 1 +--R \| x \| x \| x +--R + +--R 2 +--R - 6x + 9x + 14 +--R / +--R +------+ +--R | 2 +--R |x - 1 +--R 2x |------ +--R | 2 +--R \| x +--R Type: Expression Integer +--E 288 + +--S 289 of 489 +d0256:= D(m0256,x) +--R +--R +--R +------+ +--R +-----+ | 2 +--R 3 2 |x + 1 3 2 |x - 1 +--R (- x - x + x + 1) |----- + (x + 2x + x) |------ +--R \|x - 1 | 2 +--R \| x +--R (213) ----------------------------------------------------- +--R +------+ +--R | 2 +-----+ +--R 2 |x - 1 |x + 1 +--R (x - 2x + 1) |------ |----- +--R | 2 \|x - 1 +--R \| x +--R Type: Expression Integer +--E 289 + +--S 290 of 489 +t0257:= exp(1)^(3*acoth(x)) +--R +--R +--R 3acoth(x) +--R (214) %e +--R Type: Expression Integer +--E 290 + +--S 291 of 489 +r0257:= (-4*x-5+x^2+3*atanh(((-1+x^2)/x^2)^(1/2))*((-1+x^2)/x^2)^(1/2)*x)/_ + ((-1+x^2)/x^2)^(1/2)/x +--R +--R +--R +------+ +------+ +--R | 2 | 2 +--R |x - 1 |x - 1 2 +--R 3x |------ atanh( |------ ) + x - 4x - 5 +--R | 2 | 2 +--R \| x \| x +--R (215) ----------------------------------------- +--R +------+ +--R | 2 +--R |x - 1 +--R x |------ +--R | 2 +--R \| x +--R Type: Expression Integer +--E 291 + +--S 292 of 489 +a0257:= integrate(t0257,x) +--R +--R +--R +-----+ +-----+ +-----+ +--R |x + 1 |x + 1 |x + 1 +--R (216) 3log( |----- + 1) - 3log( |----- - 1) + (x - 5) |----- +--R \|x - 1 \|x - 1 \|x - 1 +--R Type: Union(Expression Integer,...) +--E 292 + +--S 293 of 489 +m0257:= a0257-r0257 +--R +--R +--R (217) +--R +------+ +------+ +--R | 2 +-----+ | 2 +-----+ +--R |x - 1 |x + 1 |x - 1 |x + 1 +--R 3x |------ log( |----- + 1) - 3x |------ log( |----- - 1) +--R | 2 \|x - 1 | 2 \|x - 1 +--R \| x \| x +--R + +--R +------+ +------+ +------+ +--R | 2 | 2 | 2 +-----+ +--R |x - 1 |x - 1 2 |x - 1 |x + 1 2 +--R - 3x |------ atanh( |------ ) + (x - 5x) |------ |----- - x + 4x + 5 +--R | 2 | 2 | 2 \|x - 1 +--R \| x \| x \| x +--R / +--R +------+ +--R | 2 +--R |x - 1 +--R x |------ +--R | 2 +--R \| x +--R Type: Expression Integer +--E 293 + +--S 294 of 489 +d0257:= D(m0257,x) +--R +--R +--R +------+ +--R +-----+ | 2 +--R 3 2 |x + 1 3 2 |x - 1 +--R (- x - x + x + 1) |----- + (x + 2x + x) |------ +--R \|x - 1 | 2 +--R \| x +--R (218) ----------------------------------------------------- +--R +------+ +--R | 2 +-----+ +--R 3 2 |x - 1 |x + 1 +--R (x - 2x + x) |------ |----- +--R | 2 \|x - 1 +--R \| x +--R Type: Expression Integer +--E 294 + +--S 295 of 489 +t0258:= exp(1)^(3*acoth(x))/x +--R +--R +--R 3acoth(x) +--R %e +--R (219) ----------- +--R x +--R Type: Expression Integer +--E 295 + +--S 296 of 489 +r0258:= -4/(1-1/x^2)^(1/2)-4/(1-1/x^2)^(1/2)/x+acsc(x)+atanh((1-1/x^2)^(1/2)) +--R +--R +--R +------+ +------+ +------+ +--R | 2 | 2 | 2 +--R |x - 1 |x - 1 |x - 1 +--R x |------ atanh( |------ ) + x acsc(x) |------ - 4x - 4 +--R | 2 | 2 | 2 +--R \| x \| x \| x +--R (220) -------------------------------------------------------- +--R +------+ +--R | 2 +--R |x - 1 +--R x |------ +--R | 2 +--R \| x +--R Type: Expression Integer +--E 296 + +--S 297 of 489 +a0258:= integrate(t0258,x) +--R +--R +--R +-----+ +-----+ +-----+ +-----+ +--R |x + 1 |x + 1 |x + 1 |x + 1 +--R (221) log( |----- + 1) - log( |----- - 1) + 2atan( |----- ) - 4 |----- +--R \|x - 1 \|x - 1 \|x - 1 \|x - 1 +--R Type: Union(Expression Integer,...) +--E 297 + +--S 298 of 489 +m0258:= a0258-r0258 +--R +--R +--R (222) +--R +------+ +------+ +--R | 2 +-----+ | 2 +-----+ +--R |x - 1 |x + 1 |x - 1 |x + 1 +--R x |------ log( |----- + 1) - x |------ log( |----- - 1) +--R | 2 \|x - 1 | 2 \|x - 1 +--R \| x \| x +--R + +--R +------+ +------+ +------+ +--R | 2 | 2 | 2 +-----+ +--R |x - 1 |x - 1 |x - 1 |x + 1 +--R - x |------ atanh( |------ ) + 2x |------ atan( |----- ) +--R | 2 | 2 | 2 \|x - 1 +--R \| x \| x \| x +--R + +--R +------+ +------+ +--R | 2 +-----+ | 2 +--R |x - 1 |x + 1 |x - 1 +--R - 4x |------ |----- - x acsc(x) |------ + 4x + 4 +--R | 2 \|x - 1 | 2 +--R \| x \| x +--R / +--R +------+ +--R | 2 +--R |x - 1 +--R x |------ +--R | 2 +--R \| x +--R Type: Expression Integer +--E 298 + +--S 299 of 489 +d0258:= D(m0258,x) +--R +--R +--R (223) +--R +------+ +--R +-----+ | 2 +------+ +--R 2 |x + 1 2 |x - 1 | 2 +--R ((- x - 2x + 3) |----- + (x + 2x + 1) |------ )\|x - 1 +--R \|x - 1 | 2 +--R \| x +--R + +--R +------+ +--R | 2 +-----+ +--R 2 |x - 1 |x + 1 +--R (x - 2x + 1) |------ |----- +--R | 2 \|x - 1 +--R \| x +--R / +--R +------+ +--R | 2 +-----+ +------+ +--R 3 2 |x - 1 |x + 1 | 2 +--R (x - 2x + x) |------ |----- \|x - 1 +--R | 2 \|x - 1 +--R \| x +--R Type: Expression Integer +--E 299 + +--S 300 of 489 +t0259:= exp(1)^(3*acoth(x))/x^2 +--R +--R +--R 3acoth(x) +--R %e +--R (224) ----------- +--R 2 +--R x +--R Type: Expression Integer +--E 300 + +--S 301 of 489 +r0259:= (-5*x^2+1-4*x+3*acsc(x)*_ + ((-1+x^2)/x^2)^(1/2)*x^2)/((-1+x^2)/x^2)^(1/2)/x^2 +--R +--R +--R +------+ +--R | 2 +--R 2 |x - 1 2 +--R 3x acsc(x) |------ - 5x - 4x + 1 +--R | 2 +--R \| x +--R (225) ---------------------------------- +--R +------+ +--R | 2 +--R 2 |x - 1 +--R x |------ +--R | 2 +--R \| x +--R Type: Expression Integer +--E 301 + +--S 302 of 489 +a0259:= integrate(t0259,x) +--R +--R +--R +-----+ +-----+ +--R |x + 1 |x + 1 +--R 6x atan( |----- ) + (- 5x + 1) |----- +--R \|x - 1 \|x - 1 +--R (226) -------------------------------------- +--R x +--R Type: Union(Expression Integer,...) +--E 302 + +--S 303 of 489 +m0259:= a0259-r0259 +--R +--R +--R (227) +--R +------+ +------+ +--R | 2 +-----+ | 2 +-----+ +--R 2 |x - 1 |x + 1 2 |x - 1 |x + 1 +--R 6x |------ atan( |----- ) + (- 5x + x) |------ |----- +--R | 2 \|x - 1 | 2 \|x - 1 +--R \| x \| x +--R + +--R +------+ +--R | 2 +--R 2 |x - 1 2 +--R - 3x acsc(x) |------ + 5x + 4x - 1 +--R | 2 +--R \| x +--R / +--R +------+ +--R | 2 +--R 2 |x - 1 +--R x |------ +--R | 2 +--R \| x +--R Type: Expression Integer +--E 303 + +--S 304 of 489 +d0259:= D(m0259,x) +--R +--R +--R (228) +--R +------+ +--R +-----+ | 2 +------+ +--R 3 2 |x + 1 3 2 |x - 1 | 2 +--R ((- 4x + 5x - 2x + 1) |----- + (x + 2x + x) |------ )\|x - 1 +--R \|x - 1 | 2 +--R \| x +--R + +--R +------+ +--R | 2 +-----+ +--R 4 3 2 |x - 1 |x + 1 +--R (3x - 6x + 3x ) |------ |----- +--R | 2 \|x - 1 +--R \| x +--R / +--R +------+ +--R | 2 +-----+ +------+ +--R 5 4 3 |x - 1 |x + 1 | 2 +--R (x - 2x + x ) |------ |----- \|x - 1 +--R | 2 \|x - 1 +--R \| x +--R Type: Expression Integer +--E 304 + +--S 305 of 489 +t0260:= exp(1)^(3*acoth(x))/x^3 +--R +--R +--R 3acoth(x) +--R %e +--R (229) ----------- +--R 3 +--R x +--R Type: Expression Integer +--E 305 + +--S 306 of 489 +r0260:= -7*((-1+x^2)/x^2)^(1/2)-_ + 4*((-1+x^2)/x^2)^(1/2)/(-1+x)-1/2*((-1+x^2)/x^2)^(1/2)/x+9/2*acsc(x) +--R +--R +--R +------+ +--R | 2 +--R 2 |x - 1 2 +--R (- 14x + 5x + 1) |------ + (9x - 9x)acsc(x) +--R | 2 +--R \| x +--R (230) ---------------------------------------------- +--R 2 +--R 2x - 2x +--R Type: Expression Integer +--E 306 + +--S 307 of 489 +a0260:= integrate(t0260,x) +--R +--R +--R +-----+ +-----+ +--R 2 |x + 1 2 |x + 1 +--R 18x atan( |----- ) + (- 14x + 5x + 1) |----- +--R \|x - 1 \|x - 1 +--R (231) ---------------------------------------------- +--R 2 +--R 2x +--R Type: Union(Expression Integer,...) +--E 307 + +--S 308 of 489 +m0260:= a0260-r0260 +--R +--R +--R (232) +--R +-----+ +-----+ +--R 3 2 |x + 1 3 2 |x + 1 +--R (18x - 18x )atan( |----- ) + (- 14x + 19x - 4x - 1) |----- +--R \|x - 1 \|x - 1 +--R + +--R +------+ +--R | 2 +--R 3 2 |x - 1 3 2 +--R (14x - 5x - x) |------ + (- 9x + 9x )acsc(x) +--R | 2 +--R \| x +--R / +--R 3 2 +--R 2x - 2x +--R Type: Expression Integer +--E 308 + +--S 309 of 489 +d0260:= D(m0260,x) +--R +--R +--R (233) +--R +------+ +--R +-----+ | 2 +--R 4 3 2 |x + 1 3 2 |x - 1 +--R ((- 9x + 16x - 11x + 2x + 2) |----- + (2x + 4x + 2x) |------ ) +--R \|x - 1 | 2 +--R \| x +--R * +--R +------+ +--R | 2 +--R \|x - 1 +--R + +--R +------+ +--R | 2 +-----+ +--R 5 4 3 |x - 1 |x + 1 +--R (9x - 18x + 9x ) |------ |----- +--R | 2 \|x - 1 +--R \| x +--R / +--R +------+ +--R | 2 +-----+ +------+ +--R 6 5 4 |x - 1 |x + 1 | 2 +--R (2x - 4x + 2x ) |------ |----- \|x - 1 +--R | 2 \|x - 1 +--R \| x +--R Type: Expression Integer +--E 309 + +--S 310 of 489 +t0261:= x^2*exp(1)^(1/2*acoth(x)) +--R +--R +--R acoth(x) +--R -------- +--R 2 2 +--R (234) x %e +--R Type: Expression Integer +--E 310 + +--S 311 of 489 +r0261:= -1/6*(16*x^3+4*x^2+2*x-22+18*atan(1/((-1+x)/(1+x))^(1/4))*_ + ((-1+x)/(1+x))^(1/4)+9*log((((-1+x)/(1+x))^(1/4)+1)/_ + ((-1+x)/(1+x))^(1/4))*((-1+x)/(1+x))^(1/4)-_ + 9*log(-(((-1+x)/(1+x))^(1/4)-1)/((-1+x)/(1+x))^(1/4))*_ + ((-1+x)/(1+x))^(1/4))*((-1+x)/(1+x))^(3/4)/_ + (((-1+x)/(1+x))^(1/2)+1)^3/(((-1+x)/(1+x))^(1/4)+1)^3/_ + (((-1+x)/(1+x))^(1/4)-1)^3/(-1+x)/(1+x)^2 +--R +--R +--R (235) +--R +-----+ +-----+ +--R |x - 1 |x - 1 +--R 4|----- + 1 - 4|----- + 1 +--R \|x + 1 \|x + 1 1 +--R - 9log(------------) + 9log(--------------) - 18atan(--------) +--R +-----+ +-----+ +-----+ +--R |x - 1 |x - 1 |x - 1 +--R 4|----- 4|----- 4|----- +--R \|x + 1 \|x + 1 \|x + 1 +--R + +--R +-----+3 +--R 3 2 |x - 1 +--R (- 16x - 36x - 42x - 22) 4|----- +--R \|x + 1 +--R / +--R +-----+ +-----+2 +--R 3 2 |x - 1 3 2 |x - 1 +--R ((96x + 192x + 120x + 24) |----- + 96x + 96x - 24x - 24) 4|----- +--R \|x + 1 \|x + 1 +--R + +--R +-----+ +--R 3 2 |x - 1 3 +--R (- 96x - 96x + 24x + 24) |----- - 96x + 72x - 24 +--R \|x + 1 +--R Type: Expression Integer +--E 311 + +--S 312 of 489 +a0261:= integrate(t0261,x) +--R +--R +--R (236) +--R x + 1 x + 1 x + 1 +--R log(-----) log(-----) log(-----) +--R x - 1 x - 1 x - 1 +--R ---------- ---------- ---------- +--R 4 4 4 +--R 9log(%e + 1) - 9log(%e - 1) + 18atan(%e ) +--R + +--R x + 1 +--R log(-----) +--R x - 1 +--R ---------- +--R 3 2 4 +--R (16x + 4x + 2x - 22)%e +--R / +--R 48 +--R Type: Union(Expression Integer,...) +--E 312 + +--S 313 of 489 +m0261:= a0261-r0261 +--R +--R +--R (237) +--R +-----+ +-----+2 +--R 3 2 |x - 1 3 2 |x - 1 +--R ((36x + 72x + 45x + 9) |----- + 36x + 36x - 9x - 9) 4|----- +--R \|x + 1 \|x + 1 +--R + +--R +-----+ +--R 3 2 |x - 1 3 +--R (- 36x - 36x + 9x + 9) |----- - 36x + 27x - 9 +--R \|x + 1 +--R * +--R x + 1 +--R log(-----) +--R x - 1 +--R ---------- +--R 4 +--R log(%e + 1) +--R + +--R +-----+ +-----+2 +--R 3 2 |x - 1 3 2 |x - 1 +--R ((- 36x - 72x - 45x - 9) |----- - 36x - 36x + 9x + 9) 4|----- +--R \|x + 1 \|x + 1 +--R + +--R +-----+ +--R 3 2 |x - 1 3 +--R (36x + 36x - 9x - 9) |----- + 36x - 27x + 9 +--R \|x + 1 +--R * +--R x + 1 +--R log(-----) +--R x - 1 +--R ---------- +--R 4 +--R log(%e - 1) +--R + +--R +-----+ +-----+2 +--R 3 2 |x - 1 3 2 |x - 1 +--R ((72x + 144x + 90x + 18) |----- + 72x + 72x - 18x - 18) 4|----- +--R \|x + 1 \|x + 1 +--R + +--R +-----+ +--R 3 2 |x - 1 3 +--R (- 72x - 72x + 18x + 18) |----- - 72x + 54x - 18 +--R \|x + 1 +--R * +--R x + 1 +--R log(-----) +--R x - 1 +--R ---------- +--R 4 +--R atan(%e ) +--R + +--R +-----+ +-----+ +--R |x - 1 |x - 1 +--R 4|----- + 1 - 4|----- + 1 +--R \|x + 1 \|x + 1 +--R 18log(------------) - 18log(--------------) +--R +-----+ +-----+ +--R |x - 1 |x - 1 +--R 4|----- 4|----- +--R \|x + 1 \|x + 1 +--R + +--R +-----+ +--R 6 5 4 3 2 |x - 1 6 +--R (64x + 144x + 120x - 36x - 162x - 108x - 22) |----- + 64x +--R \|x + 1 +--R + +--R 5 4 3 2 +--R 80x + 8x - 100x - 94x + 20x + 22 +--R * +--R +-----+2 +--R |x - 1 +--R 4|----- +--R \|x + 1 +--R + +--R +-----+ +--R 6 5 4 3 2 |x - 1 6 5 +--R (- 64x - 80x - 8x + 100x + 94x - 20x - 22) |----- - 64x - 16x +--R \|x + 1 +--R + +--R 4 3 2 +--R 40x + 84x + 2x - 68x + 22 +--R * +--R x + 1 +--R log(-----) +--R x - 1 +--R ---------- +--R 4 +--R %e +--R + +--R +-----+3 +--R 1 3 2 |x - 1 +--R 36atan(--------) + (32x + 72x + 84x + 44) 4|----- +--R +-----+ \|x + 1 +--R |x - 1 +--R 4|----- +--R \|x + 1 +--R / +--R +-----+ +-----+2 +--R 3 2 |x - 1 3 2 |x - 1 +--R ((192x + 384x + 240x + 48) |----- + 192x + 192x - 48x - 48) 4|----- +--R \|x + 1 \|x + 1 +--R + +--R +-----+ +--R 3 2 |x - 1 3 +--R (- 192x - 192x + 48x + 48) |----- - 192x + 144x - 48 +--R \|x + 1 +--R Type: Expression Integer +--E 313 + +--S 314 of 489 +d0261:= D(m0261,x) +--R +--R +--R (238) +--R +-----+ +-----+2 +--R 4 2 |x - 1 4 3 2 |x - 1 +--R ((36x - 45x + 9) |----- + 36x - 36x - 27x + 27x) 4|----- +--R \|x + 1 \|x + 1 +--R + +--R +-----+ +--R 4 3 2 |x - 1 4 3 2 +--R (- 36x + 36x + 27x - 27x) |----- - 36x + 72x - 27x - 18x + 9 +--R \|x + 1 +--R * +--R x + 1 4 +--R log(-----) +--R x - 1 +--R ---------- +--R 4 +--R (%e ) +--R + +--R +-----+ +-----+2 +--R 4 2 |x - 1 4 3 2 |x - 1 +--R ((- 36x + 45x - 9) |----- - 36x + 36x + 27x - 27x) 4|----- +--R \|x + 1 \|x + 1 +--R + +--R +-----+ +--R 4 3 2 |x - 1 4 3 2 +--R (36x - 36x - 27x + 27x) |----- + 36x - 72x + 27x + 18x - 9 +--R \|x + 1 +--R * +--R +-----+ +--R |x - 1 +--R 4|----- + 1 +--R \|x + 1 +--R log(------------) +--R +-----+ +--R |x - 1 +--R 4|----- +--R \|x + 1 +--R + +--R +-----+ +-----+2 +--R 4 2 |x - 1 4 3 2 |x - 1 +--R ((- 36x + 45x - 9) |----- - 36x + 36x + 27x - 27x) 4|----- +--R \|x + 1 \|x + 1 +--R + +--R +-----+ +--R 4 3 2 |x - 1 4 3 2 +--R (36x - 36x - 27x + 27x) |----- + 36x - 72x + 27x + 18x - 9 +--R \|x + 1 +--R * +--R x + 1 4 +--R log(-----) +--R x - 1 +--R ---------- +--R 4 +--R (%e ) +--R + +--R +-----+ +-----+2 +--R 4 2 |x - 1 4 3 2 |x - 1 +--R ((36x - 45x + 9) |----- + 36x - 36x - 27x + 27x) 4|----- +--R \|x + 1 \|x + 1 +--R + +--R +-----+ +--R 4 3 2 |x - 1 4 3 2 +--R (- 36x + 36x + 27x - 27x) |----- - 36x + 72x - 27x - 18x + 9 +--R \|x + 1 +--R * +--R +-----+ +--R |x - 1 +--R - 4|----- + 1 +--R \|x + 1 +--R log(--------------) +--R +-----+ +--R |x - 1 +--R 4|----- +--R \|x + 1 +--R + +--R 10 8 7 6 5 4 3 2 +--R (512x - 1280x - 96x + 1152x + 144x - 432x - 54x + 54x ) +--R * +--R +-----+ +--R |x - 1 +--R |----- +--R \|x + 1 +--R + +--R 10 9 8 7 6 5 4 3 +--R 512x - 512x - 1024x + 928x + 800x - 608x - 288x + 174x +--R + +--R 2 +--R 36x - 18x +--R * +--R +-----+2 +--R |x - 1 +--R 4|----- +--R \|x + 1 +--R + +--R 10 9 8 7 6 5 4 3 +--R - 512x + 512x + 1024x - 928x - 800x + 608x + 288x - 174x +--R + +--R 2 +--R - 36x + 18x +--R * +--R +-----+ +--R |x - 1 +--R |----- +--R \|x + 1 +--R + +--R 10 9 8 7 6 5 4 3 +--R - 512x + 1024x + 256x - 1440x + 192x + 816x - 208x - 202x +--R + +--R 2 +--R 62x + 18x - 6 +--R * +--R x + 1 5 +--R log(-----) +--R x - 1 +--R ---------- +--R 4 +--R (%e ) +--R + +--R +-----+ +-----+2 +--R 4 2 |x - 1 4 3 2 |x - 1 +--R ((72x - 90x + 18) |----- + 72x - 72x - 54x + 54x) 4|----- +--R \|x + 1 \|x + 1 +--R + +--R +-----+ +--R 4 3 2 |x - 1 4 3 2 +--R (- 72x + 72x + 54x - 54x) |----- - 72x + 144x - 54x - 36x +--R \|x + 1 +--R + +--R 18 +--R * +--R 1 +--R atan(--------) +--R +-----+ +--R |x - 1 +--R 4|----- +--R \|x + 1 +--R + +--R +-----+ +--R 6 5 4 3 2 |x - 1 6 5 +--R (- 16x - 56x + 60x + 122x - 44x - 66x) |----- - 16x - 40x +--R \|x + 1 +--R + +--R 4 3 2 +--R 92x + 42x - 98x - 2x + 22 +--R * +--R +-----+3 +--R |x - 1 +--R 4|----- +--R \|x + 1 +--R + +--R +-----+ +--R 6 5 4 3 2 |x - 1 6 +--R (16x + 40x - 124x - 42x + 130x + 2x - 22) |----- + 16x +--R \|x + 1 +--R + +--R 5 4 3 2 +--R 24x - 140x + 78x + 88x - 66x +--R * +--R +-----+ +--R |x - 1 +--R 4|----- +--R \|x + 1 +--R * +--R x + 1 4 +--R log(-----) +--R x - 1 +--R ---------- +--R 4 +--R (%e ) +--R + +--R 10 8 7 6 5 4 3 +--R - 512x + 1280x + 96x - 960x - 144x + 144x + 54x +--R + +--R 2 +--R 54x +--R * +--R +-----+ +--R |x - 1 +--R |----- +--R \|x + 1 +--R + +--R 10 9 8 7 6 5 4 3 +--R - 512x + 512x + 1024x - 928x - 608x + 416x + 96x + 18x +--R + +--R - 18x +--R * +--R +-----+2 +--R |x - 1 +--R 4|----- +--R \|x + 1 +--R + +--R 10 9 8 7 6 5 4 3 +--R 512x - 512x - 1024x + 928x + 608x - 416x - 96x - 18x +--R + +--R 18x +--R * +--R +-----+ +--R |x - 1 +--R |----- +--R \|x + 1 +--R + +--R 10 9 8 7 6 5 4 3 +--R 512x - 1024x - 256x + 1440x - 384x - 432x + 112x + 10x +--R + +--R 2 +--R 22x + 6x - 6 +--R * +--R x + 1 +--R log(-----) +--R x - 1 +--R ---------- +--R 4 +--R %e +--R + +--R +-----+ +-----+2 +--R 4 2 |x - 1 4 3 2 |x - 1 +--R ((- 72x + 90x - 18) |----- - 72x + 72x + 54x - 54x) 4|----- +--R \|x + 1 \|x + 1 +--R + +--R +-----+ +--R 4 3 2 |x - 1 4 3 2 +--R (72x - 72x - 54x + 54x) |----- + 72x - 144x + 54x + 36x - 18 +--R \|x + 1 +--R * +--R 1 +--R atan(--------) +--R +-----+ +--R |x - 1 +--R 4|----- +--R \|x + 1 +--R + +--R +-----+ +--R 6 5 4 3 2 |x - 1 6 5 +--R (16x + 56x - 60x - 122x + 44x + 66x) |----- + 16x + 40x +--R \|x + 1 +--R + +--R 4 3 2 +--R - 92x - 42x + 98x + 2x - 22 +--R * +--R +-----+3 +--R |x - 1 +--R 4|----- +--R \|x + 1 +--R + +--R +-----+ +--R 6 5 4 3 2 |x - 1 6 +--R (- 16x - 40x + 124x + 42x - 130x - 2x + 22) |----- - 16x +--R \|x + 1 +--R + +--R 5 4 3 2 +--R - 24x + 140x - 78x - 88x + 66x +--R * +--R +-----+ +--R |x - 1 +--R 4|----- +--R \|x + 1 +--R / +--R +-----+ +--R 8 6 4 2 |x - 1 8 7 +--R (512x - 1280x + 1056x - 288x ) |----- + 512x - 512x +--R \|x + 1 +--R + +--R 6 5 4 3 2 +--R - 1024x + 1024x + 608x - 608x - 96x + 96x +--R * +--R +-----+2 +--R |x - 1 +--R 4|----- +--R \|x + 1 +--R + +--R 8 7 6 5 4 3 2 +--R (- 512x + 512x + 1024x - 1024x - 608x + 608x + 96x - 96x) +--R * +--R +-----+ +--R |x - 1 +--R |----- +--R \|x + 1 +--R + +--R 8 7 6 5 4 3 2 +--R - 512x + 1024x + 256x - 1536x + 480x + 576x - 256x - 64x + 32 +--R * +--R x + 1 4 +--R log(-----) +--R x - 1 +--R ---------- +--R 4 +--R (%e ) +--R + +--R +-----+ +--R 8 6 4 2 |x - 1 8 7 6 +--R (- 512x + 1280x - 1056x + 288x ) |----- - 512x + 512x + 1024x +--R \|x + 1 +--R + +--R 5 4 3 2 +--R - 1024x - 608x + 608x + 96x - 96x +--R * +--R +-----+2 +--R |x - 1 +--R 4|----- +--R \|x + 1 +--R + +--R +-----+ +--R 8 7 6 5 4 3 2 |x - 1 +--R (512x - 512x - 1024x + 1024x + 608x - 608x - 96x + 96x) |----- +--R \|x + 1 +--R + +--R 8 7 6 5 4 3 2 +--R 512x - 1024x - 256x + 1536x - 480x - 576x + 256x + 64x - 32 +--R Type: Expression Integer +--E 314 + +--S 315 of 489 +t0262:= x*exp(1)^(1/2*acoth(x)) +--R +--R +--R acoth(x) +--R -------- +--R 2 +--R (239) x %e +--R Type: Expression Integer +--E 315 + +--S 316 of 489 +r0262:= 1/8/(1-exp(1)^(1/2*acoth(x)))^2-3/(8-8*exp(1)^(1/2*acoth(x)))-_ + 1/8/(1+exp(1)^(1/2*acoth(x)))^2+3/(8+8*exp(1)^(1/2*acoth(x)))+_ + 1/2*exp(1)^(1/2*acoth(x))/(1+exp(1)^acoth(x))^2-_ + 3*exp(1)^(1/2*acoth(x))/(4+4*exp(1)^acoth(x))+_ + 1/4*atan(exp(1)^(1/2*acoth(x)))-1/8*log(-1+exp(1)^(1/2*acoth(x)))+_ + 1/8*log(1+exp(1)^(1/2*acoth(x))) +--R +--R +--R (240) +--R acoth(x) 4 acoth(x) 2 +--R -------- -------- +--R 2 2 acoth(x) 2 +--R ((%e ) - 2(%e ) + 1)(%e ) +--R + +--R acoth(x) 4 acoth(x) 2 acoth(x) 4 +--R -------- -------- -------- +--R 2 2 acoth(x) 2 +--R (2(%e ) - 4(%e ) + 2)%e + (%e ) +--R + +--R acoth(x) 2 +--R -------- +--R 2 +--R - 2(%e ) + 1 +--R * +--R acoth(x) +--R -------- +--R 2 +--R log(%e + 1) +--R + +--R acoth(x) 4 acoth(x) 2 +--R -------- -------- +--R 2 2 acoth(x) 2 +--R (- (%e ) + 2(%e ) - 1)(%e ) +--R + +--R acoth(x) 4 acoth(x) 2 acoth(x) 4 +--R -------- -------- -------- +--R 2 2 acoth(x) 2 +--R (- 2(%e ) + 4(%e ) - 2)%e - (%e ) +--R + +--R acoth(x) 2 +--R -------- +--R 2 +--R 2(%e ) - 1 +--R * +--R acoth(x) +--R -------- +--R 2 +--R log(%e - 1) +--R + +--R acoth(x) 4 acoth(x) 2 +--R -------- -------- +--R 2 2 acoth(x) 2 +--R (2(%e ) - 4(%e ) + 2)(%e ) +--R + +--R acoth(x) 4 acoth(x) 2 acoth(x) 4 +--R -------- -------- -------- +--R 2 2 acoth(x) 2 +--R (4(%e ) - 8(%e ) + 4)%e + 2(%e ) +--R + +--R acoth(x) 2 +--R -------- +--R 2 +--R - 4(%e ) + 2 +--R * +--R acoth(x) +--R -------- +--R 2 +--R atan(%e ) +--R + +--R acoth(x) 3 acoth(x) +--R -------- -------- +--R 2 2 acoth(x) 2 +--R (6(%e ) - 2%e )(%e ) +--R + +--R acoth(x) 5 acoth(x) 3 acoth(x) +--R -------- -------- -------- +--R 2 2 2 acoth(x) +--R (- 6(%e ) + 24(%e ) - 10%e )%e +--R + +--R acoth(x) 5 acoth(x) 3 acoth(x) +--R -------- -------- -------- +--R 2 2 2 +--R - 2(%e ) + 10(%e ) - 4%e +--R / +--R acoth(x) 4 acoth(x) 2 +--R -------- -------- +--R 2 2 acoth(x) 2 +--R (8(%e ) - 16(%e ) + 8)(%e ) +--R + +--R acoth(x) 4 acoth(x) 2 acoth(x) 4 +--R -------- -------- -------- +--R 2 2 acoth(x) 2 +--R (16(%e ) - 32(%e ) + 16)%e + 8(%e ) +--R + +--R acoth(x) 2 +--R -------- +--R 2 +--R - 16(%e ) + 8 +--R Type: Expression Integer +--E 316 + +--S 317 of 489 +a0262:= integrate(t0262,x) +--R +--R +--R (241) +--R x + 1 x + 1 x + 1 +--R log(-----) log(-----) log(-----) +--R x - 1 x - 1 x - 1 +--R ---------- ---------- ---------- +--R 4 4 4 +--R log(%e + 1) - log(%e - 1) + 2atan(%e ) +--R + +--R x + 1 +--R log(-----) +--R x - 1 +--R ---------- +--R 2 4 +--R (4x + 2x - 6)%e +--R / +--R 8 +--R Type: Union(Expression Integer,...) +--E 317 + +--S 318 of 489 +m0262:= a0262-r0262 +--R +--R +--R (242) +--R acoth(x) 4 acoth(x) 2 +--R -------- -------- +--R 2 2 acoth(x) 2 +--R ((%e ) - 2(%e ) + 1)(%e ) +--R + +--R acoth(x) 4 acoth(x) 2 acoth(x) 4 +--R -------- -------- -------- +--R 2 2 acoth(x) 2 +--R (2(%e ) - 4(%e ) + 2)%e + (%e ) +--R + +--R acoth(x) 2 +--R -------- +--R 2 +--R - 2(%e ) + 1 +--R * +--R x + 1 +--R log(-----) +--R x - 1 +--R ---------- +--R 4 +--R log(%e + 1) +--R + +--R acoth(x) 4 acoth(x) 2 +--R -------- -------- +--R 2 2 acoth(x) 2 +--R (- (%e ) + 2(%e ) - 1)(%e ) +--R + +--R acoth(x) 4 acoth(x) 2 acoth(x) 4 +--R -------- -------- -------- +--R 2 2 acoth(x) 2 +--R (- 2(%e ) + 4(%e ) - 2)%e - (%e ) +--R + +--R acoth(x) 2 +--R -------- +--R 2 +--R 2(%e ) - 1 +--R * +--R x + 1 +--R log(-----) +--R x - 1 +--R ---------- +--R 4 +--R log(%e - 1) +--R + +--R acoth(x) 4 acoth(x) 2 +--R -------- -------- +--R 2 2 acoth(x) 2 +--R (- (%e ) + 2(%e ) - 1)(%e ) +--R + +--R acoth(x) 4 acoth(x) 2 acoth(x) 4 +--R -------- -------- -------- +--R 2 2 acoth(x) 2 +--R (- 2(%e ) + 4(%e ) - 2)%e - (%e ) +--R + +--R acoth(x) 2 +--R -------- +--R 2 +--R 2(%e ) - 1 +--R * +--R acoth(x) +--R -------- +--R 2 +--R log(%e + 1) +--R + +--R acoth(x) 4 acoth(x) 2 +--R -------- -------- +--R 2 2 acoth(x) 2 +--R ((%e ) - 2(%e ) + 1)(%e ) +--R + +--R acoth(x) 4 acoth(x) 2 acoth(x) 4 +--R -------- -------- -------- +--R 2 2 acoth(x) 2 +--R (2(%e ) - 4(%e ) + 2)%e + (%e ) +--R + +--R acoth(x) 2 +--R -------- +--R 2 +--R - 2(%e ) + 1 +--R * +--R acoth(x) +--R -------- +--R 2 +--R log(%e - 1) +--R + +--R acoth(x) 4 acoth(x) 2 +--R -------- -------- +--R 2 2 acoth(x) 2 +--R (2(%e ) - 4(%e ) + 2)(%e ) +--R + +--R acoth(x) 4 acoth(x) 2 acoth(x) 4 +--R -------- -------- -------- +--R 2 2 acoth(x) 2 +--R (4(%e ) - 8(%e ) + 4)%e + 2(%e ) +--R + +--R acoth(x) 2 +--R -------- +--R 2 +--R - 4(%e ) + 2 +--R * +--R x + 1 +--R log(-----) +--R x - 1 +--R ---------- +--R 4 +--R atan(%e ) +--R + +--R acoth(x) 4 acoth(x) 2 +--R -------- -------- +--R 2 2 acoth(x) 2 +--R (- 2(%e ) + 4(%e ) - 2)(%e ) +--R + +--R acoth(x) 4 acoth(x) 2 acoth(x) 4 +--R -------- -------- -------- +--R 2 2 acoth(x) 2 +--R (- 4(%e ) + 8(%e ) - 4)%e - 2(%e ) +--R + +--R acoth(x) 2 +--R -------- +--R 2 +--R 4(%e ) - 2 +--R * +--R acoth(x) +--R -------- +--R 2 +--R atan(%e ) +--R + +--R acoth(x) 4 acoth(x) 2 +--R -------- -------- +--R 2 2 2 2 +--R (4x + 2x - 6)(%e ) + (- 8x - 4x + 12)(%e ) +--R + +--R 2 +--R 4x + 2x - 6 +--R * +--R acoth(x) 2 +--R (%e ) +--R + +--R acoth(x) 4 acoth(x) 2 +--R -------- -------- +--R 2 2 2 2 +--R (8x + 4x - 12)(%e ) + (- 16x - 8x + 24)(%e ) +--R + +--R 2 +--R 8x + 4x - 12 +--R * +--R acoth(x) +--R %e +--R + +--R acoth(x) 4 acoth(x) 2 +--R -------- -------- +--R 2 2 2 2 2 +--R (4x + 2x - 6)(%e ) + (- 8x - 4x + 12)(%e ) + 4x +--R + +--R 2x - 6 +--R * +--R x + 1 +--R log(-----) +--R x - 1 +--R ---------- +--R 4 +--R %e +--R + +--R acoth(x) 3 acoth(x) +--R -------- -------- +--R 2 2 acoth(x) 2 +--R (- 6(%e ) + 2%e )(%e ) +--R + +--R acoth(x) 5 acoth(x) 3 acoth(x) +--R -------- -------- -------- +--R 2 2 2 acoth(x) +--R (6(%e ) - 24(%e ) + 10%e )%e +--R + +--R acoth(x) 5 acoth(x) 3 acoth(x) +--R -------- -------- -------- +--R 2 2 2 +--R 2(%e ) - 10(%e ) + 4%e +--R / +--R acoth(x) 4 acoth(x) 2 +--R -------- -------- +--R 2 2 acoth(x) 2 +--R (8(%e ) - 16(%e ) + 8)(%e ) +--R + +--R acoth(x) 4 acoth(x) 2 acoth(x) 4 +--R -------- -------- -------- +--R 2 2 acoth(x) 2 +--R (16(%e ) - 32(%e ) + 16)%e + 8(%e ) +--R + +--R acoth(x) 2 +--R -------- +--R 2 +--R - 16(%e ) + 8 +--R Type: Expression Integer +--E 318 + +--S 319 of 489 +d0262:= D(m0262,x) +--R +--R +--R (243) +--R acoth(x) 8 acoth(x) 6 +--R -------- -------- +--R 3 2 3 2 +--R (8x - 9x + 1)(%e ) + (- 16x + 18x - 2)(%e ) +--R + +--R acoth(x) 2 +--R -------- +--R 3 2 3 +--R (16x - 18x + 2)(%e ) - 8x + 9x - 1 +--R * +--R acoth(x) 3 +--R (%e ) +--R + +--R acoth(x) 8 acoth(x) 6 +--R -------- -------- +--R 3 2 3 2 +--R (24x - 27x + 3)(%e ) + (- 48x + 54x - 6)(%e ) +--R + +--R acoth(x) 2 +--R -------- +--R 3 2 3 +--R (48x - 54x + 6)(%e ) - 24x + 27x - 3 +--R * +--R acoth(x) 2 +--R (%e ) +--R + +--R acoth(x) 8 acoth(x) 6 +--R -------- -------- +--R 3 2 3 2 +--R (24x - 27x + 3)(%e ) + (- 48x + 54x - 6)(%e ) +--R + +--R acoth(x) 2 +--R -------- +--R 3 2 3 +--R (48x - 54x + 6)(%e ) - 24x + 27x - 3 +--R * +--R acoth(x) +--R %e +--R + +--R acoth(x) 8 acoth(x) 6 +--R -------- -------- +--R 3 2 3 2 +--R (8x - 9x + 1)(%e ) + (- 16x + 18x - 2)(%e ) +--R + +--R acoth(x) 2 +--R -------- +--R 3 2 3 +--R (16x - 18x + 2)(%e ) - 8x + 9x - 1 +--R * +--R x + 1 5 +--R log(-----) +--R x - 1 +--R ---------- +--R 4 +--R (%e ) +--R + +--R acoth(x) 7 acoth(x) 5 acoth(x) 3 acoth(x) +--R -------- -------- -------- -------- +--R 2 2 2 2 +--R (- 3(%e ) - 11(%e ) - (%e ) - %e ) +--R * +--R acoth(x) 3 +--R (%e ) +--R + +--R acoth(x) 9 acoth(x) 7 acoth(x) 5 +--R -------- -------- -------- +--R 2 2 2 +--R 3(%e ) - 15(%e ) - 33(%e ) +--R + +--R acoth(x) 3 acoth(x) +--R -------- -------- +--R 2 2 +--R 3(%e ) - 6%e +--R * +--R acoth(x) 2 +--R (%e ) +--R + +--R acoth(x) 9 acoth(x) 7 acoth(x) 5 +--R -------- -------- -------- +--R 2 2 2 +--R - 6(%e ) + 3(%e ) - 33(%e ) +--R + +--R acoth(x) 3 acoth(x) +--R -------- -------- +--R 2 2 +--R - 15(%e ) + 3%e +--R * +--R acoth(x) +--R %e +--R + +--R acoth(x) 9 acoth(x) 7 acoth(x) 5 acoth(x) 3 +--R -------- -------- -------- -------- +--R 2 2 2 2 +--R - (%e ) - (%e ) - 11(%e ) - 3(%e ) +--R * +--R x + 1 4 +--R log(-----) +--R x - 1 +--R ---------- +--R 4 +--R (%e ) +--R + +--R acoth(x) 8 acoth(x) 6 +--R -------- -------- +--R 3 2 3 2 +--R (- 8x + 9x + 1)(%e ) + (16x - 18x - 2)(%e ) +--R + +--R acoth(x) 2 +--R -------- +--R 3 2 3 +--R (- 16x + 18x + 2)(%e ) + 8x - 9x - 1 +--R * +--R acoth(x) 3 +--R (%e ) +--R + +--R acoth(x) 8 acoth(x) 6 +--R -------- -------- +--R 3 2 3 2 +--R (- 24x + 27x + 3)(%e ) + (48x - 54x - 6)(%e ) +--R + +--R acoth(x) 2 +--R -------- +--R 3 2 3 +--R (- 48x + 54x + 6)(%e ) + 24x - 27x - 3 +--R * +--R acoth(x) 2 +--R (%e ) +--R + +--R acoth(x) 8 acoth(x) 6 +--R -------- -------- +--R 3 2 3 2 +--R (- 24x + 27x + 3)(%e ) + (48x - 54x - 6)(%e ) +--R + +--R acoth(x) 2 +--R -------- +--R 3 2 3 +--R (- 48x + 54x + 6)(%e ) + 24x - 27x - 3 +--R * +--R acoth(x) +--R %e +--R + +--R acoth(x) 8 acoth(x) 6 +--R -------- -------- +--R 3 2 3 2 +--R (- 8x + 9x + 1)(%e ) + (16x - 18x - 2)(%e ) +--R + +--R acoth(x) 2 +--R -------- +--R 3 2 3 +--R (- 16x + 18x + 2)(%e ) + 8x - 9x - 1 +--R * +--R x + 1 +--R log(-----) +--R x - 1 +--R ---------- +--R 4 +--R %e +--R + +--R acoth(x) 7 acoth(x) 5 acoth(x) 3 acoth(x) +--R -------- -------- -------- -------- +--R 2 2 2 2 +--R (3(%e ) + 11(%e ) + (%e ) + %e ) +--R * +--R acoth(x) 3 +--R (%e ) +--R + +--R acoth(x) 9 acoth(x) 7 acoth(x) 5 acoth(x) 3 +--R -------- -------- -------- -------- +--R 2 2 2 2 +--R - 3(%e ) + 15(%e ) + 33(%e ) - 3(%e ) +--R + +--R acoth(x) +--R -------- +--R 2 +--R 6%e +--R * +--R acoth(x) 2 +--R (%e ) +--R + +--R acoth(x) 9 acoth(x) 7 acoth(x) 5 acoth(x) 3 +--R -------- -------- -------- -------- +--R 2 2 2 2 +--R 6(%e ) - 3(%e ) + 33(%e ) + 15(%e ) +--R + +--R acoth(x) +--R -------- +--R 2 +--R - 3%e +--R * +--R acoth(x) +--R %e +--R + +--R acoth(x) 9 acoth(x) 7 acoth(x) 5 acoth(x) 3 +--R -------- -------- -------- -------- +--R 2 2 2 2 +--R (%e ) + (%e ) + 11(%e ) + 3(%e ) +--R / +--R acoth(x) 8 acoth(x) 6 +--R -------- -------- +--R 2 2 2 2 +--R (8x - 8)(%e ) + (- 16x + 16)(%e ) +--R + +--R acoth(x) 2 +--R -------- +--R 2 2 2 +--R (16x - 16)(%e ) - 8x + 8 +--R * +--R acoth(x) 3 +--R (%e ) +--R + +--R acoth(x) 8 acoth(x) 6 +--R -------- -------- +--R 2 2 2 2 +--R (24x - 24)(%e ) + (- 48x + 48)(%e ) +--R + +--R acoth(x) 2 +--R -------- +--R 2 2 2 +--R (48x - 48)(%e ) - 24x + 24 +--R * +--R acoth(x) 2 +--R (%e ) +--R + +--R acoth(x) 8 acoth(x) 6 +--R -------- -------- +--R 2 2 2 2 +--R (24x - 24)(%e ) + (- 48x + 48)(%e ) +--R + +--R acoth(x) 2 +--R -------- +--R 2 2 2 +--R (48x - 48)(%e ) - 24x + 24 +--R * +--R acoth(x) +--R %e +--R + +--R acoth(x) 8 acoth(x) 6 +--R -------- -------- +--R 2 2 2 2 +--R (8x - 8)(%e ) + (- 16x + 16)(%e ) +--R + +--R acoth(x) 2 +--R -------- +--R 2 2 2 +--R (16x - 16)(%e ) - 8x + 8 +--R * +--R x + 1 4 +--R log(-----) +--R x - 1 +--R ---------- +--R 4 +--R (%e ) +--R + +--R acoth(x) 8 acoth(x) 6 +--R -------- -------- +--R 2 2 2 2 +--R (- 8x + 8)(%e ) + (16x - 16)(%e ) +--R + +--R acoth(x) 2 +--R -------- +--R 2 2 2 +--R (- 16x + 16)(%e ) + 8x - 8 +--R * +--R acoth(x) 3 +--R (%e ) +--R + +--R acoth(x) 8 acoth(x) 6 +--R -------- -------- +--R 2 2 2 2 +--R (- 24x + 24)(%e ) + (48x - 48)(%e ) +--R + +--R acoth(x) 2 +--R -------- +--R 2 2 2 +--R (- 48x + 48)(%e ) + 24x - 24 +--R * +--R acoth(x) 2 +--R (%e ) +--R + +--R acoth(x) 8 acoth(x) 6 +--R -------- -------- +--R 2 2 2 2 +--R (- 24x + 24)(%e ) + (48x - 48)(%e ) +--R + +--R acoth(x) 2 +--R -------- +--R 2 2 2 +--R (- 48x + 48)(%e ) + 24x - 24 +--R * +--R acoth(x) +--R %e +--R + +--R acoth(x) 8 acoth(x) 6 +--R -------- -------- +--R 2 2 2 2 +--R (- 8x + 8)(%e ) + (16x - 16)(%e ) +--R + +--R acoth(x) 2 +--R -------- +--R 2 2 2 +--R (- 16x + 16)(%e ) + 8x - 8 +--R Type: Expression Integer +--E 319 + +--S 320 of 489 +t0263:= exp(1)^(1/2*acoth(x)) +--R +--R +--R acoth(x) +--R -------- +--R 2 +--R (244) %e +--R Type: Expression Integer +--E 320 + +--S 321 of 489 +r0263:= -(1-x)^(3/4)*(1+x)^(1/4)+1/4*2^(1/2)*(2*%pi-_ + 2*acot(-1+2^(1/2)*(1-x)^(1/4)/(1+x)^(1/4))-_ + 2*acot(1+2^(1/2)*(1-x)^(1/4)/(1+x)^(1/4))-_ + log(1+(1-x)^(1/2)/(1+x)^(1/2)-2^(1/2)*_ + (1-x)^(1/4)/(1+x)^(1/4))+log(1+(1-x)^(1/2)/(1+x)^(1/2)+_ + 2^(1/2)*(1-x)^(1/4)/(1+x)^(1/4))) +--R +--R +--R (245) +--R +-----+ +-------+ 4+-----+ +-+4+-------+ +-----+ +--R +-+ (\|x + 1 + \|- x + 1 )\|x + 1 + \|2 \|- x + 1 \|x + 1 +--R \|2 log(--------------------------------------------------------) +--R +-----+4+-----+ +--R \|x + 1 \|x + 1 +--R + +--R +-----+ +-------+ 4+-----+ +-+4+-------+ +-----+ +--R +-+ (\|x + 1 + \|- x + 1 )\|x + 1 - \|2 \|- x + 1 \|x + 1 +--R - \|2 log(--------------------------------------------------------) +--R +-----+4+-----+ +--R \|x + 1 \|x + 1 +--R + +--R 4+-----+ +-+4+-------+ +--R +-+ \|x + 1 + \|2 \|- x + 1 +--R - 2\|2 acot(-------------------------) +--R 4+-----+ +--R \|x + 1 +--R + +--R 4+-----+ +-+4+-------+ +--R +-+ - \|x + 1 + \|2 \|- x + 1 4+-------+3 4+-----+ +-+ +--R - 2\|2 acot(---------------------------) - 4\|- x + 1 \|x + 1 + 2%pi\|2 +--R 4+-----+ +--R \|x + 1 +--R / +--R 4 +--R Type: Expression Integer +--E 321 + +--S 322 of 489 +a0263:= integrate(t0263,x) +--R +--R +--R (246) +--R x + 1 x + 1 x + 1 +--R log(-----) log(-----) log(-----) +--R x - 1 x - 1 x - 1 +--R ---------- ---------- ---------- +--R 4 4 4 +--R log(%e + 1) - log(%e - 1) + 2atan(%e ) +--R + +--R x + 1 +--R log(-----) +--R x - 1 +--R ---------- +--R 4 +--R (2x - 2)%e +--R / +--R 2 +--R Type: Union(Expression Integer,...) +--E 322 + +--S 323 of 489 +m0263:= a0263-r0263 +--R +--R +--R (247) +--R x + 1 x + 1 x + 1 +--R log(-----) log(-----) log(-----) +--R x - 1 x - 1 x - 1 +--R ---------- ---------- ---------- +--R 4 4 4 +--R 2log(%e + 1) - 2log(%e - 1) + 4atan(%e ) +--R + +--R +-----+ +-------+ 4+-----+ +-+4+-------+ +-----+ +--R +-+ (\|x + 1 + \|- x + 1 )\|x + 1 + \|2 \|- x + 1 \|x + 1 +--R - \|2 log(--------------------------------------------------------) +--R +-----+4+-----+ +--R \|x + 1 \|x + 1 +--R + +--R +-----+ +-------+ 4+-----+ +-+4+-------+ +-----+ +--R +-+ (\|x + 1 + \|- x + 1 )\|x + 1 - \|2 \|- x + 1 \|x + 1 +--R \|2 log(--------------------------------------------------------) +--R +-----+4+-----+ +--R \|x + 1 \|x + 1 +--R + +--R x + 1 +--R log(-----) +--R x - 1 +--R ---------- 4+-----+ +-+4+-------+ +--R 4 +-+ \|x + 1 + \|2 \|- x + 1 +--R (4x - 4)%e + 2\|2 acot(-------------------------) +--R 4+-----+ +--R \|x + 1 +--R + +--R 4+-----+ +-+4+-------+ +--R +-+ - \|x + 1 + \|2 \|- x + 1 4+-------+3 4+-----+ +-+ +--R 2\|2 acot(---------------------------) + 4\|- x + 1 \|x + 1 - 2%pi\|2 +--R 4+-----+ +--R \|x + 1 +--R / +--R 4 +--R Type: Expression Integer +--E 323 + +--S 324 of 489 +d0263:= D(m0263,x) +--R +--R +--R (248) +--R 2 4+-------+3 4+-----+3 +--R (4x - 2x - 2)\|- x + 1 \|x + 1 +--R + +--R 2 +-------+4+-------+ +-----+ +--R (- 4x + 2x + 2)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 2 4+-------+ +--R (- 4x + 2x + 2)\|- x + 1 +--R * +--R 4+-----+ +--R \|x + 1 +--R * +--R x + 1 5 +--R log(-----) +--R x - 1 +--R ---------- +--R 4 +--R (%e ) +--R + +--R 2 +-------+ +-----+ 2 4+-----+2 +--R ((4x - 3x - 1)\|- x + 1 \|x + 1 + 5x - 3x - 2)\|x + 1 +--R + +--R +-------+4+-------+2 +-----+ 3 2 4+-------+2 +--R x\|- x + 1 \|- x + 1 \|x + 1 + (- 4x - x + 6x + 3)\|- x + 1 +--R * +--R x + 1 4 +--R log(-----) +--R x - 1 +--R ---------- +--R 4 +--R (%e ) +--R + +--R 2 4+-------+3 4+-----+3 +--R (- 4x + 2x + 6)\|- x + 1 \|x + 1 +--R + +--R 2 +-------+4+-------+ +-----+ +--R (4x - 2x - 6)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 2 4+-------+ +--R (4x - 2x - 6)\|- x + 1 +--R * +--R 4+-----+ +--R \|x + 1 +--R * +--R x + 1 +--R log(-----) +--R x - 1 +--R ---------- +--R 4 +--R %e +--R + +--R 2 +-------+ +-----+ 2 4+-----+2 +--R ((- 4x + 3x + 1)\|- x + 1 \|x + 1 - 5x + 3x + 2)\|x + 1 +--R + +--R +-------+4+-------+2 +-----+ 3 2 4+-------+2 +--R - x\|- x + 1 \|- x + 1 \|x + 1 + (4x + x - 6x - 3)\|- x + 1 +--R / +--R 2 4+-------+3 4+-----+3 +--R (4x - 4)\|- x + 1 \|x + 1 +--R + +--R 2 +-------+4+-------+ +-----+ 2 4+-------+ +--R ((- 4x + 4)\|- x + 1 \|- x + 1 \|x + 1 + (- 4x + 4)\|- x + 1 ) +--R * +--R 4+-----+ +--R \|x + 1 +--R * +--R x + 1 4 +--R log(-----) +--R x - 1 +--R ---------- +--R 4 +--R (%e ) +--R + +--R 2 4+-------+3 4+-----+3 +--R (- 4x + 4)\|- x + 1 \|x + 1 +--R + +--R 2 +-------+4+-------+ +-----+ 2 4+-------+ 4+-----+ +--R ((4x - 4)\|- x + 1 \|- x + 1 \|x + 1 + (4x - 4)\|- x + 1 )\|x + 1 +--R Type: Expression Integer +--E 324 + +--S 325 of 489 +t0264:= exp(1)^(1/2*acoth(x))/x +--R +--R +--R acoth(x) +--R -------- +--R 2 +--R %e +--R (249) ---------- +--R x +--R Type: Expression Integer +--E 325 + +--S 326 of 489 +r0264:= 2*atan(exp(1)^(1/2*acoth(x)))-2^(1/2)*_ + atan(-1+2^(1/2)*exp(1)^(1/2*acoth(x)))-2^(1/2)*_ + atan(1+2^(1/2)*exp(1)^(1/2*acoth(x)))-log(-1+exp(1)^(1/2*acoth(x)))+_ + log(1+exp(1)^(1/2*acoth(x)))+1/2*log(1-2^(1/2)*_ + exp(1)^(1/2*acoth(x))+exp(1)^acoth(x))*2^(1/2)-_ + 1/2*log(1+2^(1/2)*exp(1)^(1/2*acoth(x))+exp(1)^acoth(x))*2^(1/2) +--R +--R +--R (250) +--R acoth(x) +--R -------- +--R +-+ acoth(x) +-+ 2 +--R - \|2 log(%e + \|2 %e + 1) +--R + +--R acoth(x) acoth(x) +--R -------- -------- +--R +-+ acoth(x) +-+ 2 2 +--R \|2 log(%e - \|2 %e + 1) + 2log(%e + 1) +--R + +--R acoth(x) acoth(x) +--R -------- -------- +--R 2 +-+ +-+ 2 +--R - 2log(%e - 1) - 2\|2 atan(\|2 %e + 1) +--R + +--R acoth(x) acoth(x) +--R -------- -------- +--R +-+ +-+ 2 2 +--R - 2\|2 atan(\|2 %e - 1) + 4atan(%e ) +--R / +--R 2 +--R Type: Expression Integer +--E 326 + +--S 327 of 489 +a0264:= integrate(t0264,x) +--R +--R +--R (251) +--R x + 1 2 x + 1 +--R log(-----) log(-----) +--R x - 1 x - 1 +--R ---------- ---------- +--R 4 +-+ 4 +--R - log((%e ) + \|2 %e + 1) +--R + +--R x + 1 2 x + 1 x + 1 +--R log(-----) log(-----) log(-----) +--R x - 1 x - 1 x - 1 +--R ---------- ---------- ---------- +--R 4 +-+ 4 +-+ 4 +--R log((%e ) - \|2 %e + 1) + \|2 log(%e + 1) +--R + +--R x + 1 +--R x + 1 log(-----) +--R log(-----) x - 1 +--R x - 1 ---------- +--R ---------- 4 +--R +-+ 4 +-+ 2%e +--R - \|2 log(%e - 1) - \|2 atan(-------------------) +--R x + 1 2 +--R log(-----) +--R x - 1 +--R ---------- +--R 4 +--R (%e ) - 1 +--R + +--R 1 1 +--R 2atan(--------------------) + 2atan(--------------------) +--R x + 1 x + 1 +--R log(-----) log(-----) +--R x - 1 x - 1 +--R ---------- ---------- +--R +-+ 4 +-+ 4 +--R \|2 %e - 1 \|2 %e + 1 +--R / +--R +-+ +--R \|2 +--R Type: Union(Expression Integer,...) +--E 327 + +--S 328 of 489 +m0264:= a0264-r0264 +--R +--R +--R (252) +--R x + 1 2 x + 1 +--R log(-----) log(-----) +--R x - 1 x - 1 +--R ---------- ---------- +--R 4 +-+ 4 +--R - log((%e ) + \|2 %e + 1) +--R + +--R x + 1 2 x + 1 x + 1 +--R log(-----) log(-----) log(-----) +--R x - 1 x - 1 x - 1 +--R ---------- ---------- ---------- +--R 4 +-+ 4 +-+ 4 +--R log((%e ) - \|2 %e + 1) + \|2 log(%e + 1) +--R + +--R x + 1 +--R log(-----) +--R x - 1 acoth(x) +--R ---------- -------- +--R +-+ 4 acoth(x) +-+ 2 +--R - \|2 log(%e - 1) + log(%e + \|2 %e + 1) +--R + +--R acoth(x) acoth(x) +--R -------- -------- +--R acoth(x) +-+ 2 +-+ 2 +--R - log(%e - \|2 %e + 1) - \|2 log(%e + 1) +--R + +--R acoth(x) acoth(x) +--R -------- -------- +--R +-+ 2 +-+ 2 +--R \|2 log(%e - 1) + 2atan(\|2 %e + 1) +--R + +--R acoth(x) acoth(x) +--R -------- -------- +--R +-+ 2 +-+ 2 +--R 2atan(\|2 %e - 1) - 2\|2 atan(%e ) +--R + +--R x + 1 +--R log(-----) +--R x - 1 +--R ---------- +--R 4 +--R +-+ 2%e 1 +--R - \|2 atan(-------------------) + 2atan(--------------------) +--R x + 1 2 x + 1 +--R log(-----) log(-----) +--R x - 1 x - 1 +--R ---------- ---------- +--R 4 +-+ 4 +--R (%e ) - 1 \|2 %e - 1 +--R + +--R 1 +--R 2atan(--------------------) +--R x + 1 +--R log(-----) +--R x - 1 +--R ---------- +--R +-+ 4 +--R \|2 %e + 1 +--R / +--R +-+ +--R \|2 +--R Type: Expression Integer +--E 328 + +--S 329 of 489 +d0264:= D(m0264,x) +--R +--R +--R (253) +--R acoth(x) 7 acoth(x) 5 acoth(x) 3 acoth(x) +--R -------- -------- -------- -------- +--R 2 2 2 2 +--R (- (%e ) - 3(%e ) + (%e ) - %e ) +--R * +--R acoth(x) 2 +--R (%e ) +--R + +--R acoth(x) 9 acoth(x) 7 acoth(x) 5 acoth(x) 3 +--R -------- -------- -------- -------- +--R 2 2 2 2 +--R (%e ) - 2(%e ) - 6(%e ) + 2(%e ) +--R + +--R acoth(x) +--R -------- +--R 2 +--R - 3%e +--R * +--R acoth(x) +--R %e +--R + +--R acoth(x) 9 acoth(x) 7 acoth(x) 5 acoth(x) 3 +--R -------- -------- -------- -------- +--R 2 2 2 2 +--R (%e ) + 5(%e ) - 5(%e ) + 3(%e ) +--R * +--R x + 1 8 +--R log(-----) +--R x - 1 +--R ---------- +--R 4 +--R (%e ) +--R + +--R acoth(x) 8 acoth(x) 8 +--R -------- -------- +--R 2 acoth(x) 2 2 acoth(x) +--R (4(%e ) - 4)(%e ) + (8(%e ) - 8)%e +--R + +--R acoth(x) 10 acoth(x) 8 acoth(x) 2 +--R -------- -------- -------- +--R 2 2 2 +--R - 8(%e ) + 4(%e ) + 8(%e ) - 4 +--R * +--R x + 1 5 +--R log(-----) +--R x - 1 +--R ---------- +--R 4 +--R (%e ) +--R + +--R acoth(x) 7 acoth(x) 5 acoth(x) 3 acoth(x) +--R -------- -------- -------- -------- +--R 2 2 2 2 +--R ((%e ) + 3(%e ) - (%e ) + %e ) +--R * +--R acoth(x) 2 +--R (%e ) +--R + +--R acoth(x) 9 acoth(x) 7 acoth(x) 5 acoth(x) 3 +--R -------- -------- -------- -------- +--R 2 2 2 2 +--R - (%e ) + 2(%e ) + 6(%e ) - 2(%e ) +--R + +--R acoth(x) +--R -------- +--R 2 +--R 3%e +--R * +--R acoth(x) +--R %e +--R + +--R acoth(x) 9 acoth(x) 7 acoth(x) 5 acoth(x) 3 +--R -------- -------- -------- -------- +--R 2 2 2 2 +--R - (%e ) - 5(%e ) + 5(%e ) - 3(%e ) +--R / +--R acoth(x) 8 +--R -------- +--R 2 2 2 acoth(x) 2 +--R ((x - 1)(%e ) - x + 1)(%e ) +--R + +--R acoth(x) 8 +--R -------- +--R 2 2 2 acoth(x) +--R ((2x - 2)(%e ) - 2x + 2)%e +--R + +--R acoth(x) 10 acoth(x) 8 +--R -------- -------- +--R 2 2 2 2 +--R (- 2x + 2)(%e ) + (x - 1)(%e ) +--R + +--R acoth(x) 2 +--R -------- +--R 2 2 2 +--R (2x - 2)(%e ) - x + 1 +--R * +--R x + 1 8 +--R log(-----) +--R x - 1 +--R ---------- +--R 4 +--R (%e ) +--R + +--R acoth(x) 8 +--R -------- +--R 2 2 2 acoth(x) 2 +--R ((- x + 1)(%e ) + x - 1)(%e ) +--R + +--R acoth(x) 8 acoth(x) 10 +--R -------- -------- +--R 2 2 2 acoth(x) 2 2 +--R ((- 2x + 2)(%e ) + 2x - 2)%e + (2x - 2)(%e ) +--R + +--R acoth(x) 8 acoth(x) 2 +--R -------- -------- +--R 2 2 2 2 2 +--R (- x + 1)(%e ) + (- 2x + 2)(%e ) + x - 1 +--R Type: Expression Integer +--E 329 + +--S 330 of 489 +t0265:= exp(1)^(1/2*acoth(x))/x^2 +--R +--R +--R acoth(x) +--R -------- +--R 2 +--R %e +--R (254) ---------- +--R 2 +--R x +--R Type: Expression Integer +--E 330 + +--S 331 of 489 +r0265:= -exp(1)^(1/2*acoth(x))*(1-x)/x-1/2*2^(1/2)*atan(-1+2^(1/2)*_ + exp(1)^(1/2*acoth(x)))-1/2*2^(1/2)*atan(1+2^(1/2)*_ + exp(1)^(1/2*acoth(x)))+1/4*log(1-2^(1/2)*_ + exp(1)^(1/2*acoth(x))+exp(1)^acoth(x))*2^(1/2)-_ + 1/4*log(1+2^(1/2)*exp(1)^(1/2*acoth(x))+exp(1)^acoth(x))*2^(1/2) +--R +--R +--R (255) +--R acoth(x) +--R -------- +--R +-+ acoth(x) +-+ 2 +--R - x\|2 log(%e + \|2 %e + 1) +--R + +--R acoth(x) +--R -------- +--R +-+ acoth(x) +-+ 2 +--R x\|2 log(%e - \|2 %e + 1) +--R + +--R acoth(x) acoth(x) +--R -------- -------- +--R +-+ +-+ 2 +-+ +-+ 2 +--R - 2x\|2 atan(\|2 %e + 1) - 2x\|2 atan(\|2 %e - 1) +--R + +--R acoth(x) +--R -------- +--R 2 +--R (4x - 4)%e +--R / +--R 4x +--R Type: Expression Integer +--E 331 + +--S 332 of 489 +a0265:= integrate(t0265,x) +--R +--R +--R (256) +--R x + 1 2 x + 1 +--R log(-----) log(-----) +--R x - 1 x - 1 +--R ---------- ---------- +--R +-+ 4 +-+ 4 +--R - x\|2 log((%e ) + \|2 %e + 1) +--R + +--R x + 1 2 x + 1 +--R log(-----) log(-----) +--R x - 1 x - 1 +--R ---------- ---------- +--R +-+ 4 +-+ 4 +--R x\|2 log((%e ) - \|2 %e + 1) +--R + +--R +-+ 1 +-+ 1 +--R 2x\|2 atan(--------------------) + 2x\|2 atan(--------------------) +--R x + 1 x + 1 +--R log(-----) log(-----) +--R x - 1 x - 1 +--R ---------- ---------- +--R +-+ 4 +-+ 4 +--R \|2 %e - 1 \|2 %e + 1 +--R + +--R x + 1 +--R log(-----) +--R x - 1 +--R ---------- +--R 4 +--R (4x - 4)%e +--R / +--R 4x +--R Type: Union(Expression Integer,...) +--E 332 + +--S 333 of 489 +m0265:= a0265-r0265 +--R +--R +--R (257) +--R x + 1 2 x + 1 +--R log(-----) log(-----) +--R x - 1 x - 1 +--R ---------- ---------- +--R +-+ 4 +-+ 4 +--R - x\|2 log((%e ) + \|2 %e + 1) +--R + +--R x + 1 2 x + 1 +--R log(-----) log(-----) +--R x - 1 x - 1 +--R ---------- ---------- +--R +-+ 4 +-+ 4 +--R x\|2 log((%e ) - \|2 %e + 1) +--R + +--R acoth(x) +--R -------- +--R +-+ acoth(x) +-+ 2 +--R x\|2 log(%e + \|2 %e + 1) +--R + +--R acoth(x) +--R -------- +--R +-+ acoth(x) +-+ 2 +--R - x\|2 log(%e - \|2 %e + 1) +--R + +--R acoth(x) acoth(x) +--R -------- -------- +--R +-+ +-+ 2 +-+ +-+ 2 +--R 2x\|2 atan(\|2 %e + 1) + 2x\|2 atan(\|2 %e - 1) +--R + +--R +-+ 1 +-+ 1 +--R 2x\|2 atan(--------------------) + 2x\|2 atan(--------------------) +--R x + 1 x + 1 +--R log(-----) log(-----) +--R x - 1 x - 1 +--R ---------- ---------- +--R +-+ 4 +-+ 4 +--R \|2 %e - 1 \|2 %e + 1 +--R + +--R x + 1 +--R log(-----) +--R x - 1 acoth(x) +--R ---------- -------- +--R 4 2 +--R (4x - 4)%e + (- 4x + 4)%e +--R / +--R 4x +--R Type: Expression Integer +--E 333 + +--S 334 of 489 +d0265:= D(m0265,x) +--R +--R +--R (258) +--R acoth(x) 4 +--R -------- +--R 2 2 2 acoth(x) 2 +--R ((x + x - 2)(%e ) + x + x - 2)(%e ) +--R + +--R acoth(x) 4 +--R -------- +--R 2 2 2 acoth(x) +--R ((2x + 2x - 4)(%e ) + 2x + 2x - 4)%e +--R + +--R acoth(x) 6 acoth(x) 4 +--R -------- -------- +--R 2 2 2 2 +--R (- 2x - 2x + 4)(%e ) + (x + x - 2)(%e ) +--R + +--R acoth(x) 2 +--R -------- +--R 2 2 2 +--R (- 2x - 2x + 4)(%e ) + x + x - 2 +--R * +--R x + 1 5 +--R log(-----) +--R x - 1 +--R ---------- +--R 4 +--R (%e ) +--R + +--R acoth(x) 5 acoth(x) 3 +--R -------- -------- +--R 2 2 2 2 +--R (- x - x + 2)(%e ) - x (%e ) +--R + +--R acoth(x) +--R -------- +--R 2 2 +--R (- 2x - x + 2)%e +--R * +--R acoth(x) 2 +--R (%e ) +--R + +--R acoth(x) 5 acoth(x) 3 +--R -------- -------- +--R 2 2 2 2 +--R (- x - 2x + 4)(%e ) - 2x (%e ) +--R + +--R acoth(x) +--R -------- +--R 2 2 +--R (- 3x - 2x + 4)%e +--R * +--R acoth(x) +--R %e +--R + +--R acoth(x) 7 acoth(x) 5 +--R -------- -------- +--R 2 2 2 +--R (2x + 2x - 4)(%e ) + (- x + 2)(%e ) +--R + +--R acoth(x) 3 acoth(x) +--R -------- -------- +--R 2 2 2 2 +--R (3x + 2x - 4)(%e ) + (- 3x - x + 2)%e +--R * +--R x + 1 4 +--R log(-----) +--R x - 1 +--R ---------- +--R 4 +--R (%e ) +--R + +--R acoth(x) 4 +--R -------- +--R 2 2 2 acoth(x) 2 +--R ((3x + x - 2)(%e ) + 3x + x - 2)(%e ) +--R + +--R acoth(x) 4 +--R -------- +--R 2 2 2 acoth(x) +--R ((6x + 2x - 4)(%e ) + 6x + 2x - 4)%e +--R + +--R acoth(x) 6 acoth(x) 4 +--R -------- -------- +--R 2 2 2 2 +--R (- 6x - 2x + 4)(%e ) + (3x + x - 2)(%e ) +--R + +--R acoth(x) 2 +--R -------- +--R 2 2 2 +--R (- 6x - 2x + 4)(%e ) + 3x + x - 2 +--R * +--R x + 1 +--R log(-----) +--R x - 1 +--R ---------- +--R 4 +--R %e +--R + +--R acoth(x) 5 acoth(x) 3 +--R -------- -------- +--R 2 2 2 2 +--R (- x - x + 2)(%e ) - x (%e ) +--R + +--R acoth(x) +--R -------- +--R 2 2 +--R (- 2x - x + 2)%e +--R * +--R acoth(x) 2 +--R (%e ) +--R + +--R acoth(x) 5 acoth(x) 3 +--R -------- -------- +--R 2 2 2 2 +--R (- x - 2x + 4)(%e ) - 2x (%e ) +--R + +--R acoth(x) +--R -------- +--R 2 2 +--R (- 3x - 2x + 4)%e +--R * +--R acoth(x) +--R %e +--R + +--R acoth(x) 7 acoth(x) 5 +--R -------- -------- +--R 2 2 2 +--R (2x + 2x - 4)(%e ) + (- x + 2)(%e ) +--R + +--R acoth(x) 3 acoth(x) +--R -------- -------- +--R 2 2 2 2 +--R (3x + 2x - 4)(%e ) + (- 3x - x + 2)%e +--R / +--R acoth(x) 4 +--R -------- +--R 4 2 2 4 2 acoth(x) 2 +--R ((2x - 2x )(%e ) + 2x - 2x )(%e ) +--R + +--R acoth(x) 4 +--R -------- +--R 4 2 2 4 2 acoth(x) +--R ((4x - 4x )(%e ) + 4x - 4x )%e +--R + +--R acoth(x) 6 acoth(x) 4 +--R -------- -------- +--R 4 2 2 4 2 2 +--R (- 4x + 4x )(%e ) + (2x - 2x )(%e ) +--R + +--R acoth(x) 2 +--R -------- +--R 4 2 2 4 2 +--R (- 4x + 4x )(%e ) + 2x - 2x +--R * +--R x + 1 4 +--R log(-----) +--R x - 1 +--R ---------- +--R 4 +--R (%e ) +--R + +--R acoth(x) 4 +--R -------- +--R 4 2 2 4 2 acoth(x) 2 +--R ((2x - 2x )(%e ) + 2x - 2x )(%e ) +--R + +--R acoth(x) 4 +--R -------- +--R 4 2 2 4 2 acoth(x) +--R ((4x - 4x )(%e ) + 4x - 4x )%e +--R + +--R acoth(x) 6 acoth(x) 4 +--R -------- -------- +--R 4 2 2 4 2 2 +--R (- 4x + 4x )(%e ) + (2x - 2x )(%e ) +--R + +--R acoth(x) 2 +--R -------- +--R 4 2 2 4 2 +--R (- 4x + 4x )(%e ) + 2x - 2x +--R Type: Expression Integer +--E 334 + +--S 335 of 489 +t0266:= exp(1)^(1/2*acoth(x))/x^3 +--R +--R +--R acoth(x) +--R -------- +--R 2 +--R %e +--R (259) ---------- +--R 3 +--R x +--R Type: Expression Integer +--E 335 + +--S 336 of 489 +r0266:= -1/2*exp(1)^(1/2*acoth(x))*(1-x)^2/x^2-_ + 5/4*exp(1)^(1/2*acoth(x))*(1-x)/x-_ + 1/8*2^(1/2)*atan(-1+2^(1/2)*exp(1)^(1/2*acoth(x)))-_ + 1/8*2^(1/2)*atan(1+2^(1/2)*exp(1)^(1/2*acoth(x)))+_ + 1/16*log(1-2^(1/2)*exp(1)^(1/2*acoth(x))+exp(1)^acoth(x))*2^(1/2)-_ + 1/16*log(1+2^(1/2)*exp(1)^(1/2*acoth(x))+exp(1)^acoth(x))*2^(1/2) +--R +--R +--R (260) +--R acoth(x) +--R -------- +--R 2 +-+ acoth(x) +-+ 2 +--R - x \|2 log(%e + \|2 %e + 1) +--R + +--R acoth(x) +--R -------- +--R 2 +-+ acoth(x) +-+ 2 +--R x \|2 log(%e - \|2 %e + 1) +--R + +--R acoth(x) acoth(x) +--R -------- -------- +--R 2 +-+ +-+ 2 2 +-+ +-+ 2 +--R - 2x \|2 atan(\|2 %e + 1) - 2x \|2 atan(\|2 %e - 1) +--R + +--R acoth(x) +--R -------- +--R 2 2 +--R (12x - 4x - 8)%e +--R / +--R 2 +--R 16x +--R Type: Expression Integer +--E 336 + +--S 337 of 489 +a0266:= integrate(t0266,x) +--R +--R +--R (261) +--R x + 1 2 x + 1 +--R log(-----) log(-----) +--R x - 1 x - 1 +--R ---------- ---------- +--R 2 +-+ 4 +-+ 4 +--R - x \|2 log((%e ) + \|2 %e + 1) +--R + +--R x + 1 2 x + 1 +--R log(-----) log(-----) +--R x - 1 x - 1 +--R ---------- ---------- +--R 2 +-+ 4 +-+ 4 +--R x \|2 log((%e ) - \|2 %e + 1) +--R + +--R 2 +-+ 1 2 +-+ 1 +--R 2x \|2 atan(--------------------) + 2x \|2 atan(--------------------) +--R x + 1 x + 1 +--R log(-----) log(-----) +--R x - 1 x - 1 +--R ---------- ---------- +--R +-+ 4 +-+ 4 +--R \|2 %e - 1 \|2 %e + 1 +--R + +--R x + 1 +--R log(-----) +--R x - 1 +--R ---------- +--R 2 4 +--R (12x - 4x - 8)%e +--R / +--R 2 +--R 16x +--R Type: Union(Expression Integer,...) +--E 337 + +--S 338 of 489 +m0266:= a0266-r0266 +--R +--R +--R (262) +--R x + 1 2 x + 1 +--R log(-----) log(-----) +--R x - 1 x - 1 +--R ---------- ---------- +--R 2 +-+ 4 +-+ 4 +--R - x \|2 log((%e ) + \|2 %e + 1) +--R + +--R x + 1 2 x + 1 +--R log(-----) log(-----) +--R x - 1 x - 1 +--R ---------- ---------- +--R 2 +-+ 4 +-+ 4 +--R x \|2 log((%e ) - \|2 %e + 1) +--R + +--R acoth(x) +--R -------- +--R 2 +-+ acoth(x) +-+ 2 +--R x \|2 log(%e + \|2 %e + 1) +--R + +--R acoth(x) +--R -------- +--R 2 +-+ acoth(x) +-+ 2 +--R - x \|2 log(%e - \|2 %e + 1) +--R + +--R acoth(x) acoth(x) +--R -------- -------- +--R 2 +-+ +-+ 2 2 +-+ +-+ 2 +--R 2x \|2 atan(\|2 %e + 1) + 2x \|2 atan(\|2 %e - 1) +--R + +--R 2 +-+ 1 2 +-+ 1 +--R 2x \|2 atan(--------------------) + 2x \|2 atan(--------------------) +--R x + 1 x + 1 +--R log(-----) log(-----) +--R x - 1 x - 1 +--R ---------- ---------- +--R +-+ 4 +-+ 4 +--R \|2 %e - 1 \|2 %e + 1 +--R + +--R x + 1 +--R log(-----) +--R x - 1 acoth(x) +--R ---------- -------- +--R 2 4 2 2 +--R (12x - 4x - 8)%e + (- 12x + 4x + 8)%e +--R / +--R 2 +--R 16x +--R Type: Expression Integer +--E 338 + +--S 339 of 489 +d0266:= D(m0266,x) +--R +--R +--R (263) +--R acoth(x) 4 +--R -------- +--R 3 2 2 3 2 acoth(x) 2 +--R ((- x + 9x - 8)(%e ) - x + 9x - 8)(%e ) +--R + +--R acoth(x) 4 +--R -------- +--R 3 2 2 3 2 acoth(x) +--R ((- 2x + 18x - 16)(%e ) - 2x + 18x - 16)%e +--R + +--R acoth(x) 6 acoth(x) 4 +--R -------- -------- +--R 3 2 2 3 2 2 +--R (2x - 18x + 16)(%e ) + (- x + 9x - 8)(%e ) +--R + +--R acoth(x) 2 +--R -------- +--R 3 2 2 3 2 +--R (2x - 18x + 16)(%e ) - x + 9x - 8 +--R * +--R x + 1 5 +--R log(-----) +--R x - 1 +--R ---------- +--R 4 +--R (%e ) +--R + +--R acoth(x) 5 acoth(x) 3 +--R -------- -------- +--R 3 2 2 3 2 +--R (x - 9x + 8)(%e ) - x (%e ) +--R + +--R acoth(x) +--R -------- +--R 2 2 +--R (- 9x + 8)%e +--R * +--R acoth(x) 2 +--R (%e ) +--R + +--R acoth(x) 5 acoth(x) 3 +--R -------- -------- +--R 3 2 2 3 2 +--R (3x - 18x + 16)(%e ) - 2x (%e ) +--R + +--R acoth(x) +--R -------- +--R 3 2 2 +--R (x - 18x + 16)%e +--R * +--R acoth(x) +--R %e +--R + +--R acoth(x) 7 acoth(x) 5 +--R -------- -------- +--R 3 2 2 3 2 2 +--R (- 2x + 18x - 16)(%e ) + (2x - 9x + 8)(%e ) +--R + +--R acoth(x) 3 acoth(x) +--R -------- -------- +--R 3 2 2 3 2 2 +--R (- x + 18x - 16)(%e ) + (- x - 9x + 8)%e +--R * +--R x + 1 4 +--R log(-----) +--R x - 1 +--R ---------- +--R 4 +--R (%e ) +--R + +--R acoth(x) 4 +--R -------- +--R 3 2 2 3 2 acoth(x) 2 +--R ((x + 9x - 8)(%e ) + x + 9x - 8)(%e ) +--R + +--R acoth(x) 4 +--R -------- +--R 3 2 2 3 2 acoth(x) +--R ((2x + 18x - 16)(%e ) + 2x + 18x - 16)%e +--R + +--R acoth(x) 6 acoth(x) 4 +--R -------- -------- +--R 3 2 2 3 2 2 +--R (- 2x - 18x + 16)(%e ) + (x + 9x - 8)(%e ) +--R + +--R acoth(x) 2 +--R -------- +--R 3 2 2 3 2 +--R (- 2x - 18x + 16)(%e ) + x + 9x - 8 +--R * +--R x + 1 +--R log(-----) +--R x - 1 +--R ---------- +--R 4 +--R %e +--R + +--R acoth(x) 5 acoth(x) 3 acoth(x) +--R -------- -------- -------- +--R 3 2 2 3 2 2 2 +--R ((x - 9x + 8)(%e ) - x (%e ) + (- 9x + 8)%e ) +--R * +--R acoth(x) 2 +--R (%e ) +--R + +--R acoth(x) 5 acoth(x) 3 +--R -------- -------- +--R 3 2 2 3 2 +--R (3x - 18x + 16)(%e ) - 2x (%e ) +--R + +--R acoth(x) +--R -------- +--R 3 2 2 +--R (x - 18x + 16)%e +--R * +--R acoth(x) +--R %e +--R + +--R acoth(x) 7 acoth(x) 5 +--R -------- -------- +--R 3 2 2 3 2 2 +--R (- 2x + 18x - 16)(%e ) + (2x - 9x + 8)(%e ) +--R + +--R acoth(x) 3 acoth(x) +--R -------- -------- +--R 3 2 2 3 2 2 +--R (- x + 18x - 16)(%e ) + (- x - 9x + 8)%e +--R / +--R acoth(x) 4 +--R -------- +--R 5 3 2 5 3 acoth(x) 2 +--R ((8x - 8x )(%e ) + 8x - 8x )(%e ) +--R + +--R acoth(x) 4 +--R -------- +--R 5 3 2 5 3 acoth(x) +--R ((16x - 16x )(%e ) + 16x - 16x )%e +--R + +--R acoth(x) 6 acoth(x) 4 +--R -------- -------- +--R 5 3 2 5 3 2 +--R (- 16x + 16x )(%e ) + (8x - 8x )(%e ) +--R + +--R acoth(x) 2 +--R -------- +--R 5 3 2 5 3 +--R (- 16x + 16x )(%e ) + 8x - 8x +--R * +--R x + 1 4 +--R log(-----) +--R x - 1 +--R ---------- +--R 4 +--R (%e ) +--R + +--R acoth(x) 4 +--R -------- +--R 5 3 2 5 3 acoth(x) 2 +--R ((8x - 8x )(%e ) + 8x - 8x )(%e ) +--R + +--R acoth(x) 4 +--R -------- +--R 5 3 2 5 3 acoth(x) +--R ((16x - 16x )(%e ) + 16x - 16x )%e +--R + +--R acoth(x) 6 acoth(x) 4 +--R -------- -------- +--R 5 3 2 5 3 2 +--R (- 16x + 16x )(%e ) + (8x - 8x )(%e ) +--R + +--R acoth(x) 2 +--R -------- +--R 5 3 2 5 3 +--R (- 16x + 16x )(%e ) + 8x - 8x +--R Type: Expression Integer +--E 339 + +--S 340 of 489 +t0267:= exp(1)^acoth(x)*(1-x) +--R +--R +--R acoth(x) +--R (264) (- x + 1)%e +--R Type: Expression Integer +--E 340 + +--S 341 of 489 +r0267:= -1/2*(1-1/x^2)^(1/2)*x^2+1/2*atanh((1-1/x^2)^(1/2)) +--R +--R +--R +------+ +------+ +--R | 2 | 2 +--R |x - 1 2 |x - 1 +--R atanh( |------ ) - x |------ +--R | 2 | 2 +--R \| x \| x +--R (265) ------------------------------ +--R 2 +--R Type: Expression Integer +--E 341 + +--S 342 of 489 +a0267:= integrate(t0267,x) +--R +--R +--R (266) +--R x + 1 x + 1 x + 1 +--R log(-----) log(-----) log(-----) +--R x - 1 x - 1 x - 1 +--R ---------- ---------- ---------- +--R 2 2 2 2 +--R log(%e + 1) - log(%e - 1) + (- x + x)%e +--R ---------------------------------------------------------------------- +--R 2 +--R Type: Union(Expression Integer,...) +--E 342 + +--S 343 of 489 +m0267:= a0267-r0267 +--R +--R +--R (267) +--R x + 1 x + 1 x + 1 +--R log(-----) log(-----) log(-----) +--R x - 1 x - 1 x - 1 +--R ---------- ---------- ---------- +--R 2 2 2 2 +--R log(%e + 1) - log(%e - 1) + (- x + x)%e +--R + +--R +------+ +------+ +--R | 2 | 2 +--R |x - 1 2 |x - 1 +--R - atanh( |------ ) + x |------ +--R | 2 | 2 +--R \| x \| x +--R / +--R 2 +--R Type: Expression Integer +--E 343 + +--S 344 of 489 +d0267:= D(m0267,x) +--R +--R +--R (268) +--R x + 1 3 x + 1 2 +--R log(-----) log(-----) +--R x - 1 +------+ x - 1 +--R ---------- | 2 ---------- +--R 3 2 2 3 |x - 1 2 +--R (- 2x + 2x + x - 1)(%e ) + (2x - 2x) |------ (%e ) +--R | 2 +--R \| x +--R + +--R x + 1 +--R log(-----) +--R x - 1 +------+ +--R ---------- | 2 +--R 3 2 2 3 |x - 1 +--R (2x - 2x - x + 3)%e + (- 2x + 2x) |------ +--R | 2 +--R \| x +--R / +--R x + 1 2 +--R log(-----) +--R x - 1 +--R ---------- +--R 2 2 2 +--R (2x - 2)(%e ) - 2x + 2 +--R Type: Expression Integer +--E 344 + +--S 345 of 489 +t0268:= exp(1)^acoth(x)/(1-x) +--R +--R +--R acoth(x) +--R %e +--R (269) - ---------- +--R x - 1 +--R Type: Expression Integer +--E 345 + +--S 346 of 489 +r0268:= -2*x*(-(1-x^2)/x^2)^(1/2)/(1-x)-atanh((1-1/x^2)^(1/2)) +--R +--R +--R +------+ +------+ +--R | 2 | 2 +--R |x - 1 |x - 1 +--R (- x + 1)atanh( |------ ) + 2x |------ +--R | 2 | 2 +--R \| x \| x +--R (270) --------------------------------------- +--R x - 1 +--R Type: Expression Integer +--E 346 + +--S 347 of 489 +a0268:= integrate(t0268,x) +--R +--R +--R x + 1 x + 1 x + 1 +--R log(-----) log(-----) log(-----) +--R x - 1 x - 1 x - 1 +--R ---------- ---------- ---------- +--R 2 2 2 +--R (271) - log(%e + 1) + log(%e - 1) + 2%e +--R Type: Union(Expression Integer,...) +--E 347 + +--S 348 of 489 +m0268:= a0268-r0268 +--R +--R +--R (272) +--R x + 1 x + 1 +--R log(-----) log(-----) +--R x - 1 x - 1 +--R ---------- ---------- +--R 2 2 +--R (- x + 1)log(%e + 1) + (x - 1)log(%e - 1) +--R + +--R x + 1 +--R log(-----) +--R x - 1 +------+ +------+ +--R ---------- | 2 | 2 +--R 2 |x - 1 |x - 1 +--R (2x - 2)%e + (x - 1)atanh( |------ ) - 2x |------ +--R | 2 | 2 +--R \| x \| x +--R / +--R x - 1 +--R Type: Expression Integer +--E 348 + +--S 349 of 489 +d0268:= D(m0268,x) +--R +--R +--R (273) +--R x + 1 3 x + 1 2 +--R log(-----) log(-----) +--R +------+ x - 1 x - 1 +--R | 2 ---------- ---------- +--R |x - 1 2 2 2 2 +--R - 2x |------ (%e ) + (x + 2x + 1)(%e ) - x - 2x - 1 +--R | 2 +--R \| x +--R ------------------------------------------------------------------------- +--R x + 1 2 +--R log(-----) +--R +------+ x - 1 +------+ +--R | 2 ---------- | 2 +--R 3 |x - 1 2 3 |x - 1 +--R (x - x) |------ (%e ) + (- x + x) |------ +--R | 2 | 2 +--R \| x \| x +--R Type: Expression Integer +--E 349 + +--S 350 of 489 +t0269:= exp(1)^acoth(x)/(-1+x) +--R +--R +--R acoth(x) +--R %e +--R (274) ---------- +--R x - 1 +--R Type: Expression Integer +--E 350 + +--S 351 of 489 +r0269:= 2*x*(-(1-x^2)/x^2)^(1/2)/(1-x)+atanh((1-1/x^2)^(1/2)) +--R +--R +--R +------+ +------+ +--R | 2 | 2 +--R |x - 1 |x - 1 +--R (x - 1)atanh( |------ ) - 2x |------ +--R | 2 | 2 +--R \| x \| x +--R (275) ------------------------------------- +--R x - 1 +--R Type: Expression Integer +--E 351 + +--S 352 of 489 +a0269:= integrate(t0269,x) +--R +--R +--R x + 1 x + 1 x + 1 +--R log(-----) log(-----) log(-----) +--R x - 1 x - 1 x - 1 +--R ---------- ---------- ---------- +--R 2 2 2 +--R (276) log(%e + 1) - log(%e - 1) - 2%e +--R Type: Union(Expression Integer,...) +--E 352 + +--S 353 of 489 +m0269:= a0269-r0269 +--R +--R +--R (277) +--R x + 1 x + 1 +--R log(-----) log(-----) +--R x - 1 x - 1 +--R ---------- ---------- +--R 2 2 +--R (x - 1)log(%e + 1) + (- x + 1)log(%e - 1) +--R + +--R x + 1 +--R log(-----) +--R x - 1 +------+ +------+ +--R ---------- | 2 | 2 +--R 2 |x - 1 |x - 1 +--R (- 2x + 2)%e + (- x + 1)atanh( |------ ) + 2x |------ +--R | 2 | 2 +--R \| x \| x +--R / +--R x - 1 +--R Type: Expression Integer +--E 353 + +--S 354 of 489 +d0269:= D(m0269,x) +--R +--R +--R (278) +--R x + 1 3 x + 1 2 +--R log(-----) log(-----) +--R +------+ x - 1 x - 1 +--R | 2 ---------- ---------- +--R |x - 1 2 2 2 2 +--R 2x |------ (%e ) + (- x - 2x - 1)(%e ) + x + 2x + 1 +--R | 2 +--R \| x +--R ------------------------------------------------------------------------- +--R x + 1 2 +--R log(-----) +--R +------+ x - 1 +------+ +--R | 2 ---------- | 2 +--R 3 |x - 1 2 3 |x - 1 +--R (x - x) |------ (%e ) + (- x + x) |------ +--R | 2 | 2 +--R \| x \| x +--R Type: Expression Integer +--E 354 + +--S 355 of 489 +t0270:= exp(1)^acoth(x)*(1-x^2) +--R +--R +--R 2 acoth(x) +--R (279) (- x + 1)%e +--R Type: Expression Integer +--E 355 + +--S 356 of 489 +r0270:= -1/2*(1-1/x^2)^(1/2)*x^2-1/3*(1-1/x^2)^(3/2)*x^3+_ + 1/2*atanh((1-1/x^2)^(1/2)) +--R +--R +--R +------+ +------+ +--R | 2 | 2 +--R |x - 1 3 2 |x - 1 +--R 3atanh( |------ ) + (- 2x - 3x + 2x) |------ +--R | 2 | 2 +--R \| x \| x +--R (280) ----------------------------------------------- +--R 6 +--R Type: Expression Integer +--E 356 + +--S 357 of 489 +a0270:= integrate(t0270,x) +--R +--R +--R (281) +--R x + 1 x + 1 +--R log(-----) log(-----) +--R x - 1 x - 1 +--R ---------- ---------- +--R 2 2 +--R 3log(%e + 1) - 3log(%e - 1) +--R + +--R x + 1 +--R log(-----) +--R x - 1 +--R ---------- +--R 3 2 2 +--R (- 2x - x + 5x - 2)%e +--R / +--R 6 +--R Type: Union(Expression Integer,...) +--E 357 + +--S 358 of 489 +m0270:= a0270-r0270 +--R +--R +--R (282) +--R x + 1 x + 1 +--R log(-----) log(-----) +--R x - 1 x - 1 +--R ---------- ---------- +--R 2 2 +--R 3log(%e + 1) - 3log(%e - 1) +--R + +--R x + 1 +--R log(-----) +--R x - 1 +------+ +--R ---------- | 2 +--R 3 2 2 |x - 1 +--R (- 2x - x + 5x - 2)%e - 3atanh( |------ ) +--R | 2 +--R \| x +--R + +--R +------+ +--R | 2 +--R 3 2 |x - 1 +--R (2x + 3x - 2x) |------ +--R | 2 +--R \| x +--R / +--R 6 +--R Type: Expression Integer +--E 358 + +--S 359 of 489 +d0270:= D(m0270,x) +--R +--R +--R (283) +--R x + 1 3 +--R log(-----) +--R +------+ x - 1 +--R | 2 ---------- +--R 5 3 2 |x - 1 2 +--R (- 2x + 4x - x - x) |------ (%e ) +--R | 2 +--R \| x +--R + +--R x + 1 2 +--R log(-----) +--R x - 1 +--R ---------- +--R 5 4 3 2 2 +--R (2x + 2x - 4x - 4x + 2x + 2)(%e ) +--R + +--R x + 1 +--R log(-----) +--R +------+ x - 1 +--R | 2 ---------- +--R 5 3 2 |x - 1 2 5 4 3 2 +--R (2x - 4x + x + 3x) |------ %e - 2x - 2x + 4x + 4x - 2x - 2 +--R | 2 +--R \| x +--R / +--R x + 1 2 +--R log(-----) +--R +------+ x - 1 +------+ +--R | 2 ---------- | 2 +--R 3 |x - 1 2 3 |x - 1 +--R (2x - 2x) |------ (%e ) + (- 2x + 2x) |------ +--R | 2 | 2 +--R \| x \| x +--R Type: Expression Integer +--E 359 + +--S 360 of 489 +t0271:= exp(1)^acoth(x)/(1-x^2)^(3/2) +--R +--R +--R acoth(x) +--R %e +--R (284) - ------------------- +--R +--------+ +--R 2 | 2 +--R (x - 1)\|- x + 1 +--R Type: Expression Integer +--E 360 + +--S 361 of 489 +r0271:= -1/2*(1-1/x^2)^(1/2)*x*(1/(1-x)+atanh(x))/(1-x^2)^(1/2) +--R +--R +--R +------+ +--R | 2 +--R 2 |x - 1 +--R ((- x + x)atanh(x) + x) |------ +--R | 2 +--R \| x +--R (285) --------------------------------- +--R +--------+ +--R | 2 +--R (2x - 2)\|- x + 1 +--R Type: Expression Integer +--E 361 + +--S 362 of 489 +--a0271:= integrate(t0271,x) +--E 362 + +--S 363 of 489 +--m0271:= a0271-r0271 +--E 363 + +--S 364 of 489 +--d0271:= D(m0271,x) +--E 364 + +--S 365 of 489 +t0272:= exp(1)^acoth(x)/(1-x^2)^(5/2) +--R +--R +--R acoth(x) +--R %e +--R (286) ------------------------- +--R +--------+ +--R 4 2 | 2 +--R (x - 2x + 1)\|- x + 1 +--R Type: Expression Integer +--E 365 + +--S 366 of 489 +r0272:= -1/8*(1-1/x^2)^(1/2)*x*(1/(1-x)^2+_ + 2/(1-x)-1/(1+x)+3*atanh(x))/(1-x^2)^(1/2) +--R +--R +--R +------+ +--R | 2 +--R 4 3 2 3 2 |x - 1 +--R ((- 3x + 3x + 3x - 3x)atanh(x) + 3x - 3x - 2x) |------ +--R | 2 +--R \| x +--R (287) ------------------------------------------------------------ +--R +--------+ +--R 3 2 | 2 +--R (8x - 8x - 8x + 8)\|- x + 1 +--R Type: Expression Integer +--E 366 + +--S 367 of 489 +--a0272:= integrate(t0272,x) +--E 367 + +--S 368 of 489 +--m0272:= a0272-r0272 +--E 368 + +--S 369 of 489 +--d0272:= D(m0272,x) +--E 369 + +--S 370 of 489 +t0273:= exp(1)^acoth(x)/(a-a*x^2)^(3/2) +--R +--R +--R acoth(x) +--R %e +--R (288) - ----------------------- +--R +----------+ +--R 2 | 2 +--R (a x - a)\|- a x + a +--R Type: Expression Integer +--E 370 + +--S 371 of 489 +r0273:= 1/2*(1-1/x^2)^(3/2)*x^3*(1/(1-x)+atanh(x))/(a-a*x^2)^(3/2) +--R +--R +--R +------+ +--R | 2 +--R 2 |x - 1 +--R ((- x + x)atanh(x) + x) |------ +--R | 2 +--R \| x +--R (289) --------------------------------- +--R +----------+ +--R | 2 +--R (2a x - 2a)\|- a x + a +--R Type: Expression Integer +--E 371 + +--S 372 of 489 +--a0273:= integrate(t0273,x) +--E 372 + +--S 373 of 489 +--m0273:= a0273-r0273 +--E 373 + +--S 374 of 489 +--d0273:= D(m0273,x) +--E 374 + +--S 375 of 489 +t0274:= exp(1)^acoth(x)/(a-a*x^2)^(5/2) +--R +--R +--R acoth(x) +--R %e +--R (290) -------------------------------- +--R +----------+ +--R 2 4 2 2 2 | 2 +--R (a x - 2a x + a )\|- a x + a +--R Type: Expression Integer +--E 375 + +--S 376 of 489 +r0274:= -1/8*(1-1/x^2)^(5/2)*x^5*(1/(1-x)^2+2/(1-x)-1/(1+x)+_ + 3*atanh(x))/(a-a*x^2)^(5/2) +--R +--R +--R +------+ +--R | 2 +--R 4 3 2 3 2 |x - 1 +--R ((- 3x + 3x + 3x - 3x)atanh(x) + 3x - 3x - 2x) |------ +--R | 2 +--R \| x +--R (291) ------------------------------------------------------------ +--R +----------+ +--R 2 3 2 2 2 2 | 2 +--R (8a x - 8a x - 8a x + 8a )\|- a x + a +--R Type: Expression Integer +--E 376 + +--S 377 of 489 +--a0274:= integrate(t0274,x) +--E 377 + +--S 378 of 489 +--m0274:= a0274-r0274 +--E 378 + +--S 379 of 489 +--d0274:= D(m0274,x) +--E 379 + +--S 380 of 489 +t0275:= exp(1)^acoth(x)*(1-1/x^2) +--R +--R +--R 2 acoth(x) +--R (x - 1)%e +--R (292) ------------------ +--R 2 +--R x +--R Type: Expression Integer +--E 380 + +--S 381 of 489 +r0275:= -(1-1/x^2)^(1/2)+(1-1/x^2)^(1/2)*x+acsc(x)+atanh((1-1/x^2)^(1/2)) +--R +--R +--R +------+ +------+ +--R | 2 | 2 +--R |x - 1 |x - 1 +--R (293) atanh( |------ ) + (x - 1) |------ + acsc(x) +--R | 2 | 2 +--R \| x \| x +--R Type: Expression Integer +--E 381 + +--S 382 of 489 +a0275:= integrate(t0275,x) +--R +--R +--R (294) +--R x + 1 x + 1 x + 1 +--R log(-----) log(-----) log(-----) +--R x - 1 x - 1 x - 1 +--R ---------- ---------- ---------- +--R 2 2 2 +--R x log(%e + 1) - x log(%e - 1) + 2x atan(%e ) +--R + +--R x + 1 +--R log(-----) +--R x - 1 +--R ---------- +--R 2 2 +--R (x - 2x + 1)%e +--R / +--R x +--R Type: Union(Expression Integer,...) +--E 382 + +--S 383 of 489 +m0275:= a0275-r0275 +--R +--R +--R (295) +--R x + 1 x + 1 x + 1 +--R log(-----) log(-----) log(-----) +--R x - 1 x - 1 x - 1 +--R ---------- ---------- ---------- +--R 2 2 2 +--R x log(%e + 1) - x log(%e - 1) + 2x atan(%e ) +--R + +--R x + 1 +--R log(-----) +--R x - 1 +------+ +------+ +--R ---------- | 2 | 2 +--R 2 2 |x - 1 2 |x - 1 +--R (x - 2x + 1)%e - x atanh( |------ ) + (- x + x) |------ +--R | 2 | 2 +--R \| x \| x +--R + +--R - x acsc(x) +--R / +--R x +--R Type: Expression Integer +--E 383 + +--S 384 of 489 +d0275:= D(m0275,x) +--R +--R +--R (296) +--R x + 1 5 +--R log(-----) +--R +------+ x - 1 +--R | 2 +------+ ---------- +--R 5 4 2 |x - 1 | 2 2 +--R (x - x - x + x) |------ \|x - 1 (%e ) +--R | 2 +--R \| x +--R + +--R x + 1 4 +--R log(-----) +--R +------+ x - 1 +--R +------+ | 2 ---------- +--R 5 4 3 2 | 2 4 2 |x - 1 2 +--R ((- x - x + x + 2x - 1)\|x - 1 + (x - x ) |------ )(%e ) +--R | 2 +--R \| x +--R + +--R x + 1 +--R log(-----) +--R +------+ x - 1 +--R | 2 +------+ ---------- +--R 5 4 3 2 |x - 1 | 2 2 +--R (- x + x + 4x + x - x) |------ \|x - 1 %e +--R | 2 +--R \| x +--R + +--R +------+ +--R +------+ | 2 +--R 5 4 3 2 | 2 4 2 |x - 1 +--R (x + x - x - 2x + 1)\|x - 1 + (- x + x ) |------ +--R | 2 +--R \| x +--R / +--R x + 1 4 +--R log(-----) +--R +------+ x - 1 +------+ +--R | 2 +------+ ---------- | 2 +------+ +--R 5 3 |x - 1 | 2 2 5 3 |x - 1 | 2 +--R (x - x ) |------ \|x - 1 (%e ) + (- x + x ) |------ \|x - 1 +--R | 2 | 2 +--R \| x \| x +--R Type: Expression Integer +--E 384 + +--S 385 of 489 +t0276:= exp(1)^acoth(x)*(1-1/x^2)^2 +--R +--R +--R 4 2 acoth(x) +--R (x - 2x + 1)%e +--R (297) ------------------------ +--R 4 +--R x +--R Type: Expression Integer +--E 385 + +--S 386 of 489 +r0276:= -(1-1/x^2)^(1/2)-1/3*(1-1/x^2)^(3/2)+_ + 1/2*(1-1/x^2)^(1/2)/x+(1-1/x^2)^(1/2)*x+3/2*acsc(x)+_ + atanh((1-1/x^2)^(1/2)) +--R +--R +--R +------+ +------+ +--R | 2 | 2 +--R 2 |x - 1 3 2 |x - 1 2 +--R 6x atanh( |------ ) + (6x - 8x + 3x + 2) |------ + 9x acsc(x) +--R | 2 | 2 +--R \| x \| x +--R (298) ---------------------------------------------------------------- +--R 2 +--R 6x +--R Type: Expression Integer +--E 386 + +--S 387 of 489 +a0276:= integrate(t0276,x) +--R +--R +--R (299) +--R x + 1 x + 1 +--R log(-----) log(-----) +--R x - 1 x - 1 +--R ---------- ---------- +--R 3 2 3 2 +--R 6x log(%e + 1) - 6x log(%e - 1) +--R + +--R x + 1 x + 1 +--R log(-----) log(-----) +--R x - 1 x - 1 +--R ---------- ---------- +--R 3 2 4 3 2 2 +--R 18x atan(%e ) + (6x - 14x + 11x - x - 2)%e +--R / +--R 3 +--R 6x +--R Type: Union(Expression Integer,...) +--E 387 + +--S 388 of 489 +m0276:= a0276-r0276 +--R +--R +--R (300) +--R x + 1 x + 1 +--R log(-----) log(-----) +--R x - 1 x - 1 +--R ---------- ---------- +--R 3 2 3 2 +--R 6x log(%e + 1) - 6x log(%e - 1) +--R + +--R x + 1 x + 1 +--R log(-----) log(-----) +--R x - 1 x - 1 +--R ---------- ---------- +--R 3 2 4 3 2 2 +--R 18x atan(%e ) + (6x - 14x + 11x - x - 2)%e +--R + +--R +------+ +------+ +--R | 2 | 2 +--R 3 |x - 1 4 3 2 |x - 1 3 +--R - 6x atanh( |------ ) + (- 6x + 8x - 3x - 2x) |------ - 9x acsc(x) +--R | 2 | 2 +--R \| x \| x +--R / +--R 3 +--R 6x +--R Type: Expression Integer +--E 388 + +--S 389 of 489 +d0276:= D(m0276,x) +--R +--R +--R (301) +--R x + 1 5 +--R log(-----) +--R +------+ x - 1 +--R | 2 +------+ ---------- +--R 7 6 5 4 3 |x - 1 | 2 2 +--R (2x - 2x - x - 3x + 6x - 2x) |------ \|x - 1 (%e ) +--R | 2 +--R \| x +--R + +--R +------+ +--R 7 6 5 4 3 2 | 2 +--R (- 2x - 2x + 3x + 6x - 3x - 6x + 2x + 2)\|x - 1 +--R + +--R +------+ +--R | 2 +--R 6 4 |x - 1 +--R (3x - 3x ) |------ +--R | 2 +--R \| x +--R * +--R x + 1 4 +--R log(-----) +--R x - 1 +--R ---------- +--R 2 +--R (%e ) +--R + +--R x + 1 3 +--R log(-----) +--R +------+ x - 1 +--R | 2 +------+ ---------- +--R 5 |x - 1 | 2 2 +--R - 2x |------ \|x - 1 (%e ) +--R | 2 +--R \| x +--R + +--R x + 1 +--R log(-----) +--R +------+ x - 1 +--R | 2 +------+ ---------- +--R 7 6 5 4 3 |x - 1 | 2 2 +--R (- 2x + 2x + 11x + 3x - 6x + 2x) |------ \|x - 1 %e +--R | 2 +--R \| x +--R + +--R +------+ +--R 7 6 5 4 3 2 | 2 +--R (2x + 2x - 3x - 6x + 3x + 6x - 2x - 2)\|x - 1 +--R + +--R +------+ +--R | 2 +--R 6 4 |x - 1 +--R (- 3x + 3x ) |------ +--R | 2 +--R \| x +--R / +--R x + 1 4 +--R log(-----) +--R +------+ x - 1 +--R | 2 +------+ ---------- +--R 7 5 |x - 1 | 2 2 +--R (2x - 2x ) |------ \|x - 1 (%e ) +--R | 2 +--R \| x +--R + +--R +------+ +--R | 2 +------+ +--R 7 5 |x - 1 | 2 +--R (- 2x + 2x ) |------ \|x - 1 +--R | 2 +--R \| x +--R Type: Expression Integer +--E 389 + +--S 390 of 489 +t0277:= exp(1)^acoth(x)/(1-1/x^2) +--R +--R +--R 2 acoth(x) +--R x %e +--R (302) ------------ +--R 2 +--R x - 1 +--R Type: Expression Integer +--E 390 + +--S 391 of 489 +r0277:= -1/(1-1/x^2)^(1/2)-x/(1-1/x^2)^(1/2)+_ + 2*(1-1/x^2)^(1/2)*x+atanh((1-1/x^2)^(1/2)) +--R +--R +--R +------+ +------+ +--R | 2 | 2 +--R |x - 1 |x - 1 2 +--R x |------ atanh( |------ ) + x - x - 2 +--R | 2 | 2 +--R \| x \| x +--R (303) --------------------------------------- +--R +------+ +--R | 2 +--R |x - 1 +--R x |------ +--R | 2 +--R \| x +--R Type: Expression Integer +--E 391 + +--S 392 of 489 +a0277:= integrate(t0277,x) +--R +--R +--R x + 1 x + 1 x + 1 +--R log(-----) log(-----) log(-----) +--R x - 1 x - 1 x - 1 +--R ---------- ---------- ---------- +--R 2 2 2 +--R (304) log(%e + 1) - log(%e - 1) + (x - 2)%e +--R Type: Union(Expression Integer,...) +--E 392 + +--S 393 of 489 +m0277:= a0277-r0277 +--R +--R +--R (305) +--R x + 1 x + 1 +--R log(-----) log(-----) +--R +------+ x - 1 +------+ x - 1 +--R | 2 ---------- | 2 ---------- +--R |x - 1 2 |x - 1 2 +--R x |------ log(%e + 1) - x |------ log(%e - 1) +--R | 2 | 2 +--R \| x \| x +--R + +--R x + 1 +--R log(-----) +--R +------+ x - 1 +------+ +------+ +--R | 2 ---------- | 2 | 2 +--R 2 |x - 1 2 |x - 1 |x - 1 2 +--R (x - 2x) |------ %e - x |------ atanh( |------ ) - x + x + 2 +--R | 2 | 2 | 2 +--R \| x \| x \| x +--R / +--R +------+ +--R | 2 +--R |x - 1 +--R x |------ +--R | 2 +--R \| x +--R Type: Expression Integer +--E 393 + +--S 394 of 489 +d0277:= D(m0277,x) +--R +--R +--R (306) +--R x + 1 3 x + 1 2 +--R log(-----) log(-----) +--R +------+ x - 1 x - 1 +--R | 2 ---------- ---------- +--R 2 |x - 1 2 2 2 +--R (x - x + 1) |------ (%e ) + (- x - x)(%e ) +--R | 2 +--R \| x +--R + +--R x + 1 +--R log(-----) +--R +------+ x - 1 +--R | 2 ---------- +--R 2 |x - 1 2 2 +--R (- x + x + 1) |------ %e + x + x +--R | 2 +--R \| x +--R / +--R x + 1 2 +--R log(-----) +--R +------+ x - 1 +------+ +--R | 2 ---------- | 2 +--R 2 |x - 1 2 2 |x - 1 +--R (x - 1) |------ (%e ) + (- x + 1) |------ +--R | 2 | 2 +--R \| x \| x +--R Type: Expression Integer +--E 394 + +--S 395 of 489 +t0278:= exp(1)^acoth(x)/(1-1/x^2)^2 +--R +--R +--R 4 acoth(x) +--R x %e +--R (307) ------------ +--R 4 2 +--R x - 2x + 1 +--R Type: Expression Integer +--E 395 + +--S 396 of 489 +r0278:= -1/3/(1-1/x^2)^(3/2)-1/(1-1/x^2)^(1/2)-_ + 1/3*x/(1-1/x^2)^(3/2)-4/3*x/(1-1/x^2)^(1/2)+_ + 8/3*(1-1/x^2)^(1/2)*x+atanh((1-1/x^2)^(1/2)) +--R +--R +--R +------+ +------+ +--R | 2 | 2 +--R 2 |x - 1 |x - 1 3 2 +--R (3x - 3x) |------ atanh( |------ ) + 3x - 7x - 5x + 8 +--R | 2 | 2 +--R \| x \| x +--R (308) -------------------------------------------------------- +--R +------+ +--R | 2 +--R 2 |x - 1 +--R (3x - 3x) |------ +--R | 2 +--R \| x +--R Type: Expression Integer +--E 396 + +--S 397 of 489 +a0278:= integrate(t0278,x) +--R +--R +--R (309) +--R x + 1 x + 1 +--R log(-----) log(-----) +--R x - 1 x - 1 +--R ---------- ---------- +--R 2 2 2 2 +--R (3x - 3)log(%e + 1) + (- 3x + 3)log(%e - 1) +--R + +--R x + 1 +--R log(-----) +--R x - 1 +--R ---------- +--R 3 2 2 +--R (3x - 7x - 5x + 8)%e +--R / +--R 2 +--R 3x - 3 +--R Type: Union(Expression Integer,...) +--E 397 + +--S 398 of 489 +m0278:= a0278-r0278 +--R +--R +--R (310) +--R x + 1 +--R log(-----) +--R +------+ x - 1 +--R | 2 ---------- +--R 3 |x - 1 2 +--R (3x - 3x) |------ log(%e + 1) +--R | 2 +--R \| x +--R + +--R x + 1 +--R log(-----) +--R +------+ x - 1 +--R | 2 ---------- +--R 3 |x - 1 2 +--R (- 3x + 3x) |------ log(%e - 1) +--R | 2 +--R \| x +--R + +--R x + 1 +--R log(-----) +--R +------+ x - 1 +--R | 2 ---------- +--R 4 3 2 |x - 1 2 +--R (3x - 7x - 5x + 8x) |------ %e +--R | 2 +--R \| x +--R + +--R +------+ +------+ +--R | 2 | 2 +--R 3 |x - 1 |x - 1 4 3 2 +--R (- 3x + 3x) |------ atanh( |------ ) - 3x + 4x + 12x - 3x - 8 +--R | 2 | 2 +--R \| x \| x +--R / +--R +------+ +--R | 2 +--R 3 |x - 1 +--R (3x - 3x) |------ +--R | 2 +--R \| x +--R Type: Expression Integer +--E 398 + +--S 399 of 489 +d0278:= D(m0278,x) +--R +--R +--R (311) +--R x + 1 3 +--R log(-----) +--R +------+ x - 1 +--R | 2 ---------- +--R 4 3 2 |x - 1 2 +--R (x - x + x + x - 1) |------ (%e ) +--R | 2 +--R \| x +--R + +--R x + 1 2 +--R log(-----) +--R x - 1 +--R ---------- +--R 4 3 2 +--R (- x - x )(%e ) +--R + +--R x + 1 +--R log(-----) +--R +------+ x - 1 +--R | 2 ---------- +--R 4 3 2 |x - 1 2 4 3 +--R (- x + x + x - x - 1) |------ %e + x + x +--R | 2 +--R \| x +--R / +--R x + 1 2 +--R log(-----) +--R +------+ x - 1 +------+ +--R | 2 ---------- | 2 +--R 4 2 |x - 1 2 4 2 |x - 1 +--R (x - 2x + 1) |------ (%e ) + (- x + 2x - 1) |------ +--R | 2 | 2 +--R \| x \| x +--R Type: Expression Integer +--E 399 + +--S 400 of 489 +t0279:= exp(1)^acoth(x)/(1-1/x^2)^3 +--R +--R +--R 6 acoth(x) +--R x %e +--R (312) ------------------ +--R 6 4 2 +--R x - 3x + 3x - 1 +--R Type: Expression Integer +--E 400 + +--S 401 of 489 +r0279:= -1/5/(1-1/x^2)^(5/2)-1/3/(1-1/x^2)^(3/2)-1/(1-1/x^2)^(1/2)-_ + 1/5*x/(1-1/x^2)^(5/2)-2/5*x/(1-1/x^2)^(3/2)-_ + 8/5*x/(1-1/x^2)^(1/2)+16/5*(1-1/x^2)^(1/2)*x+atanh((1-1/x^2)^(1/2)) +--R +--R +--R (313) +--R +------+ +------+ +--R | 2 | 2 +--R 4 3 2 |x - 1 |x - 1 5 4 3 +--R (15x - 15x - 15x + 15x) |------ atanh( |------ ) + 15x - 38x - 52x +--R | 2 | 2 +--R \| x \| x +--R + +--R 2 +--R 87x + 33x - 48 +--R / +--R +------+ +--R | 2 +--R 4 3 2 |x - 1 +--R (15x - 15x - 15x + 15x) |------ +--R | 2 +--R \| x +--R Type: Expression Integer +--E 401 + +--S 402 of 489 +a0279:= integrate(t0279,x) +--R +--R +--R (314) +--R x + 1 +--R log(-----) +--R x - 1 +--R ---------- +--R 4 2 2 +--R (15x - 30x + 15)log(%e + 1) +--R + +--R x + 1 +--R log(-----) +--R x - 1 +--R ---------- +--R 4 2 2 +--R (- 15x + 30x - 15)log(%e - 1) +--R + +--R x + 1 +--R log(-----) +--R x - 1 +--R ---------- +--R 5 4 3 2 2 +--R (15x - 38x - 52x + 87x + 33x - 48)%e +--R / +--R 4 2 +--R 15x - 30x + 15 +--R Type: Union(Expression Integer,...) +--E 402 + +--S 403 of 489 +m0279:= a0279-r0279 +--R +--R +--R (315) +--R x + 1 +--R log(-----) +--R +------+ x - 1 +--R | 2 ---------- +--R 5 3 |x - 1 2 +--R (15x - 30x + 15x) |------ log(%e + 1) +--R | 2 +--R \| x +--R + +--R x + 1 +--R log(-----) +--R +------+ x - 1 +--R | 2 ---------- +--R 5 3 |x - 1 2 +--R (- 15x + 30x - 15x) |------ log(%e - 1) +--R | 2 +--R \| x +--R + +--R x + 1 +--R log(-----) +--R +------+ x - 1 +--R | 2 ---------- +--R 6 5 4 3 2 |x - 1 2 +--R (15x - 38x - 52x + 87x + 33x - 48x) |------ %e +--R | 2 +--R \| x +--R + +--R +------+ +------+ +--R | 2 | 2 +--R 5 3 |x - 1 |x - 1 6 5 4 +--R (- 15x + 30x - 15x) |------ atanh( |------ ) - 15x + 23x + 90x +--R | 2 | 2 +--R \| x \| x +--R + +--R 3 2 +--R - 35x - 120x + 15x + 48 +--R / +--R +------+ +--R | 2 +--R 5 3 |x - 1 +--R (15x - 30x + 15x) |------ +--R | 2 +--R \| x +--R Type: Expression Integer +--E 403 + +--S 404 of 489 +d0279:= D(m0279,x) +--R +--R +--R (316) +--R x + 1 3 +--R log(-----) +--R +------+ x - 1 +--R | 2 ---------- +--R 6 5 4 3 2 |x - 1 2 +--R (x - x + x + 2x - 2x - x + 1) |------ (%e ) +--R | 2 +--R \| x +--R + +--R x + 1 2 +--R log(-----) +--R x - 1 +--R ---------- +--R 6 5 2 +--R (- x - x )(%e ) +--R + +--R x + 1 +--R log(-----) +--R +------+ x - 1 +--R | 2 ---------- +--R 6 5 4 3 2 |x - 1 2 6 5 +--R (- x + x + x - 2x - 2x + x + 1) |------ %e + x + x +--R | 2 +--R \| x +--R / +--R x + 1 2 +--R log(-----) +--R +------+ x - 1 +--R | 2 ---------- +--R 6 4 2 |x - 1 2 +--R (x - 3x + 3x - 1) |------ (%e ) +--R | 2 +--R \| x +--R + +--R +------+ +--R | 2 +--R 6 4 2 |x - 1 +--R (- x + 3x - 3x + 1) |------ +--R | 2 +--R \| x +--R Type: Expression Integer +--E 404 + +--S 405 of 489 +t0280:= exp(1)^(3*acoth(x))*(1-1/x^2) +--R +--R +--R 2 3acoth(x) +--R (x - 1)%e +--R (317) ------------------- +--R 2 +--R x +--R Type: Expression Integer +--E 405 + +--S 406 of 489 +r0280:= (1-1/x^2)^(1/2)+(1-1/x^2)^(1/2)*x-3*acsc(x)+3*atanh((1-1/x^2)^(1/2)) +--R +--R +--R +------+ +------+ +--R | 2 | 2 +--R |x - 1 |x - 1 +--R (318) 3atanh( |------ ) + (x + 1) |------ - 3acsc(x) +--R | 2 | 2 +--R \| x \| x +--R Type: Expression Integer +--E 406 + +--S 407 of 489 +a0280:= integrate(t0280,x) +--R +--R +--R (319) +--R +-----+ +-----+ +-----+ +--R |x + 1 |x + 1 |x + 1 +--R 3x log( |----- + 1) - 3x log( |----- - 1) - 6x atan( |----- ) +--R \|x - 1 \|x - 1 \|x - 1 +--R + +--R +-----+ +--R 2 |x + 1 +--R (x - 1) |----- +--R \|x - 1 +--R / +--R x +--R Type: Union(Expression Integer,...) +--E 407 + +--S 408 of 489 +m0280:= a0280-r0280 +--R +--R +--R (320) +--R +------+ +--R +-----+ +-----+ | 2 +--R |x + 1 |x + 1 |x - 1 +--R 3x log( |----- + 1) - 3x log( |----- - 1) - 3x atanh( |------ ) +--R \|x - 1 \|x - 1 | 2 +--R \| x +--R + +--R +------+ +--R +-----+ +-----+ | 2 +--R |x + 1 2 |x + 1 2 |x - 1 +--R - 6x atan( |----- ) + (x - 1) |----- + (- x - x) |------ + 3x acsc(x) +--R \|x - 1 \|x - 1 | 2 +--R \| x +--R / +--R x +--R Type: Expression Integer +--E 408 + +--S 409 of 489 +d0280:= D(m0280,x) +--R +--R +--R (321) +--R +------+ +--R +-----+ | 2 +--R 4 3 2 |x + 1 4 3 2 |x - 1 +--R ((- x - 2x + 3x - x + 1) |----- + (x + 3x + 3x + x) |------ ) +--R \|x - 1 | 2 +--R \| x +--R * +--R +------+ +--R | 2 +--R \|x - 1 +--R + +--R +------+ +--R | 2 +-----+ +--R 3 2 |x - 1 |x + 1 +--R (- 3x + 3x ) |------ |----- +--R | 2 \|x - 1 +--R \| x +--R / +--R +------+ +--R | 2 +-----+ +------+ +--R 4 3 |x - 1 |x + 1 | 2 +--R (x - x ) |------ |----- \|x - 1 +--R | 2 \|x - 1 +--R \| x +--R Type: Expression Integer +--E 409 + +--S 410 of 489 +t0281:= exp(1)^(3*acoth(x))*(1-1/x^2)^2 +--R +--R +--R 4 2 3acoth(x) +--R (x - 2x + 1)%e +--R (322) ------------------------- +--R 4 +--R x +--R Type: Expression Integer +--E 410 + +--S 411 of 489 +r0281:= -3*(1-1/x^2)^(1/2)+1/3*(1-1/x^2)^(3/2)-_ + 3/2*(1-1/x^2)^(1/2)/x+(1-1/x^2)^(1/2)*x-1/2*acsc(x)+_ + 3*atanh((1-1/x^2)^(1/2)) +--R +--R +--R +------+ +------+ +--R | 2 | 2 +--R 2 |x - 1 3 2 |x - 1 2 +--R 18x atanh( |------ ) + (6x - 16x - 9x - 2) |------ - 3x acsc(x) +--R | 2 | 2 +--R \| x \| x +--R (323) ------------------------------------------------------------------ +--R 2 +--R 6x +--R Type: Expression Integer +--E 411 + +--S 412 of 489 +a0281:= integrate(t0281,x) +--R +--R +--R (324) +--R +-----+ +-----+ +-----+ +--R 3 |x + 1 3 |x + 1 3 |x + 1 +--R 18x log( |----- + 1) - 18x log( |----- - 1) - 6x atan( |----- ) +--R \|x - 1 \|x - 1 \|x - 1 +--R + +--R +-----+ +--R 4 3 2 |x + 1 +--R (6x - 22x + 7x + 7x + 2) |----- +--R \|x - 1 +--R / +--R 3 +--R 6x +--R Type: Union(Expression Integer,...) +--E 412 + +--S 413 of 489 +m0281:= a0281-r0281 +--R +--R +--R (325) +--R +------+ +--R +-----+ +-----+ | 2 +--R 3 |x + 1 3 |x + 1 3 |x - 1 +--R 18x log( |----- + 1) - 18x log( |----- - 1) - 18x atanh( |------ ) +--R \|x - 1 \|x - 1 | 2 +--R \| x +--R + +--R +-----+ +-----+ +--R 3 |x + 1 4 3 2 |x + 1 +--R - 6x atan( |----- ) + (6x - 22x + 7x + 7x + 2) |----- +--R \|x - 1 \|x - 1 +--R + +--R +------+ +--R | 2 +--R 4 3 2 |x - 1 3 +--R (- 6x + 16x + 9x + 2x) |------ + 3x acsc(x) +--R | 2 +--R \| x +--R / +--R 3 +--R 6x +--R Type: Expression Integer +--E 413 + +--S 414 of 489 +d0281:= D(m0281,x) +--R +--R +--R (326) +--R +-----+ +--R 5 4 3 2 |x + 1 +--R (- 2x - 6x - 3x + 4x + 6x + 2) |----- +--R \|x - 1 +--R + +--R +------+ +--R | 2 +--R 5 4 3 2 |x - 1 +--R (2x + 8x + 12x + 8x + 2x) |------ +--R | 2 +--R \| x +--R * +--R +------+ +--R | 2 +--R \|x - 1 +--R + +--R +------+ +--R | 2 +-----+ +--R 4 |x - 1 |x + 1 +--R - x |------ |----- +--R | 2 \|x - 1 +--R \| x +--R / +--R +------+ +--R | 2 +-----+ +------+ +--R 5 |x - 1 |x + 1 | 2 +--R 2x |------ |----- \|x - 1 +--R | 2 \|x - 1 +--R \| x +--R Type: Expression Integer +--E 414 + +--S 415 of 489 +t0282:= exp(1)^acoth(x)*(1-1/x^2)^(1/2) +--R +--R +--R +------+ +--R | 2 +--R |x - 1 acoth(x) +--R (327) |------ %e +--R | 2 +--R \| x +--R Type: Expression Integer +--E 415 + +--S 416 of 489 +r0282:= x+log(x) +--R +--R +--R (328) log(x) + x +--R Type: Expression Integer +--E 416 + +--S 417 of 489 +a0282:= integrate(t0282,x) +--R +--R +--R (329) +--R x + 1 +--R log(-----) +--R x - 1 +--R +------+ ---------- +--R 2 | 2 2 3 2 +--R (- x + 4)\|x - 1 %e + x + x + 4x + 4 +--R (- x - 1)log(--------------------------------------------------) +--R 2 +--R x + x +--R + +--R x + 1 +--R log(-----) +--R x - 1 +--R +------+ ---------- +--R | 2 2 +--R (x - 2)\|x - 1 %e +--R / +--R x + 1 +--R Type: Union(Expression Integer,...) +--E 417 + +--S 418 of 489 +m0282:= a0282-r0282 +--R +--R +--R (330) +--R x + 1 +--R log(-----) +--R x - 1 +--R +------+ ---------- +--R 2 | 2 2 3 2 +--R (- x + 4)\|x - 1 %e + x + x + 4x + 4 +--R (- x - 1)log(--------------------------------------------------) +--R 2 +--R x + x +--R + +--R x + 1 +--R log(-----) +--R x - 1 +--R +------+ ---------- +--R | 2 2 2 +--R (x - 2)\|x - 1 %e + (- x - 1)log(x) - x - x +--R / +--R x + 1 +--R Type: Expression Integer +--E 418 + +--S 419 of 489 +d0282:= D(m0282,x) +--R +--R +--R (331) +--R x + 1 2 x + 1 +--R log(-----) log(-----) +--R x - 1 x - 1 +--R ---------- +------+ ---------- +--R 3 2 2 2 | 2 2 +--R (x - x - 4x + 4)(%e ) + (- 2x - 2x)\|x - 1 %e +--R + +--R 3 2 +--R x + 3x + 6x + 4 +--R / +--R x + 1 +--R log(-----) +--R x - 1 +--R +------+ ---------- +--R 2 | 2 2 3 2 +--R (x - 4)\|x - 1 %e - x - x - 4x - 4 +--R Type: Expression Integer +--E 419 + +--S 420 of 489 +t0283:= exp(1)^acoth(x)*(1-1/x^2)^(3/2) +--R +--R +--R +------+ +--R | 2 +--R 2 |x - 1 acoth(x) +--R (x - 1) |------ %e +--R | 2 +--R \| x +--R (332) --------------------------- +--R 2 +--R x +--R Type: Expression Integer +--E 420 + +--S 421 of 489 +r0283:= 1/2/x^2+1/x+x+log(x) +--R +--R +--R 2 3 +--R 2x log(x) + 2x + 2x + 1 +--R (333) ------------------------ +--R 2 +--R 2x +--R Type: Expression Integer +--E 421 + +--S 422 of 489 +a0283:= integrate(t0283,x) +--R +--R +--R (334) +--R x + 1 +--R log(-----) +--R x - 1 +--R +------+ ---------- +--R 2 | 2 2 3 2 +--R 3 2 (- x + 4)\|x - 1 %e + x + x + 4x + 4 +--R (- 8x - 8x )log(--------------------------------------------------) +--R 2 +--R x + x +--R + +--R x + 1 +--R log(-----) +--R x - 1 +--R +------+ ---------- +--R 3 2 | 2 2 +--R (8x - 21x + 8x + 4)\|x - 1 %e +--R / +--R 3 2 +--R 8x + 8x +--R Type: Union(Expression Integer,...) +--E 422 + +--S 423 of 489 +m0283:= a0283-r0283 +--R +--R +--R (335) +--R x + 1 +--R log(-----) +--R x - 1 +--R +------+ ---------- +--R 2 | 2 2 3 2 +--R 3 2 (- x + 4)\|x - 1 %e + x + x + 4x + 4 +--R (- 8x - 8x )log(--------------------------------------------------) +--R 2 +--R x + x +--R + +--R x + 1 +--R log(-----) +--R x - 1 +--R +------+ ---------- +--R 3 2 | 2 2 3 2 4 +--R (8x - 21x + 8x + 4)\|x - 1 %e + (- 8x - 8x )log(x) - 8x +--R + +--R 3 2 +--R - 8x - 8x - 12x - 4 +--R / +--R 3 2 +--R 8x + 8x +--R Type: Expression Integer +--E 423 + +--S 424 of 489 +d0283:= D(m0283,x) +--R +--R +--R (336) +--R x + 1 2 +--R log(-----) +--R x - 1 +--R ---------- +--R 6 5 4 3 2 2 +--R (x - x - 5x + 4x + 5x - 4)(%e ) +--R + +--R x + 1 +--R log(-----) +--R x - 1 +--R +------+ ---------- +--R 5 4 3 2 | 2 2 6 5 4 3 +--R (- 2x - 2x + 2x + 2x )\|x - 1 %e + x + 3x + 5x + 2x +--R + +--R 2 +--R - 5x - 8x - 4 +--R / +--R x + 1 +--R log(-----) +--R x - 1 +--R +------+ ---------- +--R 5 3 | 2 2 6 5 4 3 +--R (x - 4x )\|x - 1 %e - x - x - 4x - 4x +--R Type: Expression Integer +--E 424 + +--S 425 of 489 +t0284:= exp(1)^acoth(x)*(1-1/x^2)^(5/2) +--R +--R +--R +------+ +--R | 2 +--R 4 2 |x - 1 acoth(x) +--R (x - 2x + 1) |------ %e +--R | 2 +--R \| x +--R (337) --------------------------------- +--R 4 +--R x +--R Type: Expression Integer +--E 425 + +--S 426 of 489 +r0284:= -1/4/x^4-1/3/x^3+1/x^2+2/x+x+log(x) +--R +--R +--R 4 5 3 2 +--R 12x log(x) + 12x + 24x + 12x - 4x - 3 +--R (338) ---------------------------------------- +--R 4 +--R 12x +--R Type: Expression Integer +--E 426 + +--S 427 of 489 +a0284:= integrate(t0284,x) +--R +--R +--R (339) +--R x + 1 +--R log(-----) +--R x - 1 +--R +------+ ---------- +--R 2 | 2 2 3 2 +--R 5 4 (x - 4)\|x - 1 %e - x - x - 4x - 4 +--R (- 192x - 192x )log(------------------------------------------------) +--R 2 +--R x + x +--R + +--R x + 1 +--R log(-----) +--R x - 1 +--R +------+ ---------- +--R 5 4 3 2 | 2 2 +--R (192x + 523x + 384x + 192x - 64x - 48)\|x - 1 %e +--R / +--R 5 4 +--R 192x + 192x +--R Type: Union(Expression Integer,...) +--E 427 + +--S 428 of 489 +m0284:= a0284-r0284 +--R +--R +--R (340) +--R x + 1 +--R log(-----) +--R x - 1 +--R +------+ ---------- +--R 2 | 2 2 3 2 +--R 5 4 (x - 4)\|x - 1 %e - x - x - 4x - 4 +--R (- 192x - 192x )log(------------------------------------------------) +--R 2 +--R x + x +--R + +--R x + 1 +--R log(-----) +--R x - 1 +--R +------+ ---------- +--R 5 4 3 2 | 2 2 +--R (192x + 523x + 384x + 192x - 64x - 48)\|x - 1 %e +--R + +--R 5 4 6 5 4 3 2 +--R (- 192x - 192x )log(x) - 192x - 192x - 384x - 576x - 128x + 112x + 48 +--R / +--R 5 4 +--R 192x + 192x +--R Type: Expression Integer +--E 428 + +--S 429 of 489 +d0284:= D(m0284,x) +--R +--R +--R (341) +--R x + 1 2 +--R log(-----) +--R x - 1 +--R ---------- +--R 8 7 6 5 4 2 2 +--R (x - x - 6x + 4x + 11x - 13x + 4)(%e ) +--R + +--R x + 1 +--R log(-----) +--R x - 1 +--R +------+ ---------- +--R 7 6 5 4 3 2 | 2 2 8 7 +--R (- 2x - 2x + 4x + 4x - 2x - 2x )\|x - 1 %e + x + 3x +--R + +--R 6 4 3 2 +--R 4x - 9x - 14x - 3x + 8x + 4 +--R / +--R x + 1 +--R log(-----) +--R x - 1 +--R +------+ ---------- +--R 7 5 | 2 2 8 7 6 5 +--R (x - 4x )\|x - 1 %e - x - x - 4x - 4x +--R Type: Expression Integer +--E 429 + +--S 430 of 489 +t0285:= exp(1)^acoth(x)/(1-1/x^2)^(1/2) +--R +--R +--R acoth(x) +--R %e +--R (342) ---------- +--R +------+ +--R | 2 +--R |x - 1 +--R |------ +--R | 2 +--R \| x +--R Type: Expression Integer +--E 430 + +--S 431 of 489 +r0285:= x+log(1-x) +--R +--R +--R (343) log(- x + 1) + x +--R Type: Expression Integer +--E 431 + +--S 432 of 489 +a0285:= integrate(t0285,x) +--R +--R +--R (344) +--R x + 1 +--R log(-----) +--R x - 1 +--R +------+ ---------- +--R 2 | 2 2 3 2 +--R (- x + 2x)\|x - 1 %e + x - x + 2 +--R (- x - 1)log(----------------------------------------------) +--R 2 +--R x - 1 +--R + +--R x + 1 +--R log(-----) +--R x - 1 +--R +------+ ---------- +--R | 2 2 +--R x\|x - 1 %e +--R / +--R x + 1 +--R Type: Union(Expression Integer,...) +--E 432 + +--S 433 of 489 +m0285:= a0285-r0285 +--R +--R +--R (345) +--R x + 1 +--R log(-----) +--R x - 1 +--R +------+ ---------- +--R 2 | 2 2 3 2 +--R (- x + 2x)\|x - 1 %e + x - x + 2 +--R (- x - 1)log(----------------------------------------------) +--R 2 +--R x - 1 +--R + +--R x + 1 +--R log(-----) +--R x - 1 +--R +------+ ---------- +--R | 2 2 2 +--R x\|x - 1 %e + (- x - 1)log(- x + 1) - x - x +--R / +--R x + 1 +--R Type: Expression Integer +--E 433 + +--S 434 of 489 +d0285:= D(m0285,x) +--R +--R +--R (346) +--R x + 1 2 x + 1 +--R log(-----) log(-----) +--R x - 1 x - 1 +--R ---------- +------+ ---------- +--R 3 2 2 2 | 2 2 3 2 +--R (x - 3x + 2x)(%e ) + (- 2x + 2x)\|x - 1 %e + x + x +--R ---------------------------------------------------------------------------- +--R x + 1 +--R log(-----) +--R x - 1 +--R +------+ ---------- +--R 2 | 2 2 3 2 +--R (x - 2x)\|x - 1 %e - x + x - 2 +--R Type: Expression Integer +--E 434 + +--S 435 of 489 +t0286:= exp(1)^acoth(x)/(1-1/x^2)^(3/2) +--R +--R +--R 2 acoth(x) +--R x %e +--R (347) ----------------- +--R +------+ +--R | 2 +--R 2 |x - 1 +--R (x - 1) |------ +--R | 2 +--R \| x +--R Type: Expression Integer +--E 435 + +--S 436 of 489 +r0286:= 1/(2-2*x)+x+5/4*log(1-x)-1/4*log(1+x) +--R +--R +--R 2 +--R (- x + 1)log(x + 1) + (5x - 5)log(- x + 1) + 4x - 4x - 2 +--R (348) --------------------------------------------------------- +--R 4x - 4 +--R Type: Expression Integer +--E 436 + +--S 437 of 489 +--a0286:= integrate(t0286,x) +--E 437 + +--S 438 of 489 +--m0286:= a0286-r0286 +--E 438 + +--S 439 of 489 +--d0286:= D(m0286,x) +--E 439 + +--S 440 of 489 +t0287:= exp(1)^acoth(x)/(1-1/x^2)^(5/2) +--R +--R +--R 4 acoth(x) +--R x %e +--R (349) ----------------------- +--R +------+ +--R | 2 +--R 4 2 |x - 1 +--R (x - 2x + 1) |------ +--R | 2 +--R \| x +--R Type: Expression Integer +--E 440 + +--S 441 of 489 +r0287:= -1/8/(1-x)^2+1/(1-x)+x-1/(8+8*x)+23/16*log(1-x)-7/16*log(1+x) +--R +--R +--R (350) +--R 3 2 3 2 +--R (- 7x + 7x + 7x - 7)log(x + 1) + (23x - 23x - 23x + 23)log(- x + 1) +--R + +--R 4 3 2 +--R 16x - 16x - 34x + 18x + 12 +--R / +--R 3 2 +--R 16x - 16x - 16x + 16 +--R Type: Expression Integer +--E 441 + +--S 442 of 489 +--a0287:= integrate(t0287,x) +--E 442 + +--S 443 of 489 +--m0287:= a0287-r0287 +--E 443 + +--S 444 of 489 +--d0287:= D(m0287,x) +--E 444 + +--S 445 of 489 +t0288:= x^2*exp(1)^asech(x) +--R +--R +--R 2 asech(x) +--R (351) x %e +--R Type: Expression Integer +--E 445 + +--S 446 of 489 +r0288:= 1/2*x^2-1/3*(-(-1+x)/(1+x))^(1/2)-_ + 1/3*x*(-(-1+x)/(1+x))^(1/2)+_ + 1/3*x^2*(-(-1+x)/(1+x))^(1/2)+1/3*x^3*(-(-1+x)/(1+x))^(1/2) +--R +--R +--R +-------+ +--R 3 2 |- x + 1 2 +--R (2x + 2x - 2x - 2) |------- + 3x +--R \| x + 1 +--R (352) ------------------------------------ +--R 6 +--R Type: Expression Integer +--E 446 + +--S 447 of 489 +a0288:= integrate(t0288,x) +--R +--R +--R +--------+ +--R 4 | 2 6 4 +--R - 3x \|- x + 1 - 2x + 3x +--R (353) --------------------------------- +--R +--------+ +--R 2 | 2 2 +--R (6x - 24)\|- x + 1 - 18x + 24 +--R Type: Union(Expression Integer,...) +--E 447 + +--S 448 of 489 +m0288:= a0288-r0288 +--R +--R +--R (354) +--R +--------+ +--R 5 4 3 2 | 2 5 4 3 2 +--R (- x - x + 5x + 5x - 4x - 4)\|- x + 1 + 3x + 3x - 7x - 7x +--R + +--R 4x + 4 +--R * +--R +-------+ +--R |- x + 1 +--R |------- +--R \| x + 1 +--R + +--R +--------+ +--R 4 2 | 2 6 4 2 +--R (- 3x + 6x )\|- x + 1 - x + 6x - 6x +--R / +--R +--------+ +--R 2 | 2 2 +--R (3x - 12)\|- x + 1 - 9x + 12 +--R Type: Expression Integer +--E 448 + +--S 449 of 489 +d0288:= D(m0288,x) +--R +--R +--R (355) +--R +--------+ +--R 7 5 3 | 2 9 7 5 3 +--R (- 6x + 38x - 64x + 32x)\|- x + 1 - x + 19x - 66x + 80x +--R + +--R - 32x +--R * +--R +-------+ +--R |- x + 1 +--R |------- +--R \| x + 1 +--R + +--R +--------+ +--R 8 7 6 5 4 3 2 | 2 8 7 +--R (x - x - 18x + 18x + 48x - 48x - 32x + 32x)\|- x + 1 - 6x + 6x +--R + +--R 6 5 4 3 2 +--R 38x - 38x - 64x + 64x + 32x - 32x +--R / +--R +--------+ +-------+ +--R 6 4 2 | 2 6 4 2 |- x + 1 +--R ((x - 18x + 48x - 32)\|- x + 1 - 6x + 38x - 64x + 32) |------- +--R \| x + 1 +--R Type: Expression Integer +--E 449 + +--S 450 of 489 +t0289:= exp(1)^asech(x) +--R +--R +--R asech(x) +--R (356) %e +--R Type: Expression Integer +--E 450 + +--S 451 of 489 +r0289:= ((1-x)/(1+x))^(1/2)*(1+x)-2*atanh(((1-x)/(1+x))^(1/2))+log(x) +--R +--R +--R +-------+ +-------+ +--R |- x + 1 |- x + 1 +--R (357) - 2atanh( |------- ) + (x + 1) |------- + log(x) +--R \| x + 1 \| x + 1 +--R Type: Expression Integer +--E 451 + +--S 452 of 489 +a0289:= integrate(t0289,x) +--R +--R +--R (358) +--R +--------+ +--R +--------+ | 2 +--------+ +--R | 2 \|- x + 1 - 1 | 2 2 +--R (\|- x + 1 - 1)log(---------------) + log(x)\|- x + 1 - log(x) - x +--R x +--R ----------------------------------------------------------------------- +--R +--------+ +--R | 2 +--R \|- x + 1 - 1 +--R Type: Union(Expression Integer,...) +--E 452 + +--S 453 of 489 +m0289:= a0289-r0289 +--R +--R +--R (359) +--R +--------+ +--R +--------+ | 2 +--R | 2 \|- x + 1 - 1 +--R (\|- x + 1 - 1)log(---------------) +--R x +--R + +--R +--------+ +-------+ +--R | 2 |- x + 1 +--R (2\|- x + 1 - 2)atanh( |------- ) +--R \| x + 1 +--R + +--R +--------+ +-------+ +--R | 2 |- x + 1 2 +--R ((- x - 1)\|- x + 1 + x + 1) |------- - x +--R \| x + 1 +--R / +--R +--------+ +--R | 2 +--R \|- x + 1 - 1 +--R Type: Expression Integer +--E 453 + +--S 454 of 489 +d0289:= D(m0289,x) +--R +--R +--R (360) +--R +--------+ +-------+ +--R 2 | 2 4 2 |- x + 1 +--R ((- 2x + 2)\|- x + 1 - x + 3x - 2) |------- +--R \| x + 1 +--R + +--R +--------+ +--R 3 2 | 2 3 2 +--R (x - x - 2x + 2)\|- x + 1 - 2x + 2x + 2x - 2 +--R / +--R +--------+ +-------+ +--R 3 | 2 3 |- x + 1 +--R ((x - 2x)\|- x + 1 - 2x + 2x) |------- +--R \| x + 1 +--R Type: Expression Integer +--E 454 + +--S 455 of 489 +t0290:= exp(1)^asech(x)/x^2 +--R +--R +--R asech(x) +--R %e +--R (361) ---------- +--R 2 +--R x +--R Type: Expression Integer +--E 455 + +--S 456 of 489 +r0290:= -1/2*(1+x*(-(-1+x)/(1+x))^(1/2)+(-(-1+x)/(1+x))^(1/2)-_ + 2*atanh((-(-1+x)/(1+x))^(1/2))*x^2)/x^2 +--R +--R +--R +-------+ +-------+ +--R 2 |- x + 1 |- x + 1 +--R 2x atanh( |------- ) + (- x - 1) |------- - 1 +--R \| x + 1 \| x + 1 +--R (362) ---------------------------------------------- +--R 2 +--R 2x +--R Type: Expression Integer +--E 456 + +--S 457 of 489 +a0290:= integrate(t0290,x) +--R +--R +--R +--------+ +--R +--------+ | 2 +--------+ +--R | 2 2 \|- x + 1 - 1 | 2 +--R (- 2\|- x + 1 - x + 2)log(---------------) - \|- x + 1 + 1 +--R x +--R (363) --------------------------------------------------------------- +--R +--------+ +--R | 2 2 +--R 4\|- x + 1 + 2x - 4 +--R Type: Union(Expression Integer,...) +--E 457 + +--S 458 of 489 +m0290:= a0290-r0290 +--R +--R +--R (364) +--R +--------+ +--R +--------+ | 2 +--R 2 | 2 4 2 \|- x + 1 - 1 +--R (- 2x \|- x + 1 - x + 2x )log(---------------) +--R x +--R + +--R +--------+ +-------+ +--R 2 | 2 4 2 |- x + 1 +--R (- 4x \|- x + 1 - 2x + 4x )atanh( |------- ) +--R \| x + 1 +--R + +--R +--------+ +-------+ +--R | 2 3 2 |- x + 1 +--R ((2x + 2)\|- x + 1 + x + x - 2x - 2) |------- +--R \| x + 1 +--R + +--R +--------+ +--R 2 | 2 2 +--R (- x + 2)\|- x + 1 + 2x - 2 +--R / +--R +--------+ +--R 2 | 2 4 2 +--R 4x \|- x + 1 + 2x - 4x +--R Type: Expression Integer +--E 458 + +--S 459 of 489 +d0290:= D(m0290,x) +--R +--R +--R (365) +--R +--------+ +-------+ +--R 4 2 | 2 6 4 2 |- x + 1 +--R ((- 4x + 12x - 8)\|- x + 1 - x + 9x - 16x + 8) |------- +--R \| x + 1 +--R + +--R +--------+ +--R 5 4 3 2 | 2 5 4 3 2 +--R (x - x - 8x + 8x + 8x - 8)\|- x + 1 - 4x + 4x + 12x - 12x - 8x +--R + +--R 8 +--R / +--R +--------+ +-------+ +--R 7 5 3 | 2 7 5 3 |- x + 1 +--R ((x - 8x + 8x )\|- x + 1 - 4x + 12x - 8x ) |------- +--R \| x + 1 +--R Type: Expression Integer +--E 459 + +--S 460 of 489 +t0291:= x*exp(1)^acsch(x) +--R +--R +--R acsch(x) +--R (366) x %e +--R Type: Expression Integer +--E 460 + +--S 461 of 489 +r0291:= x+1/2*(1+1/x^2)^(1/2)*x^2+1/2*atanh((1+1/x^2)^(1/2)) +--R +--R +--R +------+ +------+ +--R | 2 | 2 +--R |x + 1 2 |x + 1 +--R atanh( |------ ) + x |------ + 2x +--R | 2 | 2 +--R \| x \| x +--R (367) ----------------------------------- +--R 2 +--R Type: Expression Integer +--E 461 + +--S 462 of 489 +a0291:= integrate(t0291,x) +--R +--R +--R (368) +--R +------+ +------+ +------+ +--R | 2 2 | 2 3 2 | 2 +--R (- 2x\|x + 1 + 2x + 1)log(\|x + 1 - x) + (- 2x + 4x - x)\|x + 1 +--R + +--R 4 3 2 +--R 2x - 4x + 2x - 2x +--R / +--R +------+ +--R | 2 2 +--R 4x\|x + 1 - 4x - 2 +--R Type: Union(Expression Integer,...) +--E 462 + +--S 463 of 489 +m0291:= a0291-r0291 +--R +--R +--R (369) +--R +------+ +------+ +--R | 2 2 | 2 +--R (- 2x\|x + 1 + 2x + 1)log(\|x + 1 - x) +--R + +--R +------+ +--R +------+ | 2 +--R | 2 2 |x + 1 +--R (- 2x\|x + 1 + 2x + 1)atanh( |------ ) +--R | 2 +--R \| x +--R + +--R +------+ +------+ +--R | 2 +------+ | 2 +--R 3 |x + 1 3 | 2 4 2 |x + 1 4 2 +--R (- 2x |------ - 2x - x)\|x + 1 + (2x + x ) |------ + 2x + 2x +--R | 2 | 2 +--R \| x \| x +--R / +--R +------+ +--R | 2 2 +--R 4x\|x + 1 - 4x - 2 +--R Type: Expression Integer +--E 463 + +--S 464 of 489 +d0291:= D(m0291,x) +--R +--R +--R (370) +--R +------+ +--R | 2 +------+ +--R 6 4 2 |x + 1 6 4 2 | 2 +--R ((- 8x - 12x - 4x ) |------ - 8x - 16x - 9x - 1)\|x + 1 +--R | 2 +--R \| x +--R + +--R +------+ +--R | 2 +--R 7 5 3 |x + 1 7 5 3 +--R (8x + 16x + 9x + x) |------ + 8x + 20x + 16x + 4x +--R | 2 +--R \| x +--R / +--R +------+ +------+ +--R | 2 +------+ | 2 +--R 5 3 |x + 1 | 2 6 4 2 |x + 1 +--R (8x + 8x + x) |------ \|x + 1 + (- 8x - 12x - 4x ) |------ +--R | 2 | 2 +--R \| x \| x +--R Type: Expression Integer +--E 464 + +--S 465 of 489 +t0292:= exp(1)^acsch(x) +--R +--R +--R acsch(x) +--R (371) %e +--R Type: Expression Integer +--E 465 + +--S 466 of 489 +r0292:= (1+1/x^2)^(1/2)*x-acsch(x)+log(x) +--R +--R +--R +------+ +--R | 2 +--R |x + 1 +--R (372) x |------ + log(x) - acsch(x) +--R | 2 +--R \| x +--R Type: Expression Integer +--E 466 + +--S 467 of 489 +a0292:= integrate(t0292,x) +--R +--R +--R (373) +--R +------+ +------+ +--R | 2 | 2 +--R (- \|x + 1 + x)log(\|x + 1 - x + 1) +--R + +--R +------+ +------+ +------+ +--R | 2 | 2 | 2 +--R (\|x + 1 - x)log(\|x + 1 - x - 1) + (log(x) - x)\|x + 1 - x log(x) +--R + +--R 2 +--R x + 1 +--R / +--R +------+ +--R | 2 +--R \|x + 1 - x +--R Type: Union(Expression Integer,...) +--E 467 + +--S 468 of 489 +m0292:= a0292-r0292 +--R +--R +--R (374) +--R +------+ +------+ +--R | 2 | 2 +--R (- \|x + 1 + x)log(\|x + 1 - x + 1) +--R + +--R +------+ +------+ +--R | 2 | 2 +--R (\|x + 1 - x)log(\|x + 1 - x - 1) +--R + +--R +------+ +------+ +--R | 2 +------+ | 2 +--R |x + 1 | 2 2 |x + 1 2 +--R (- x |------ + acsch(x) - x)\|x + 1 + x |------ - x acsch(x) + x + 1 +--R | 2 | 2 +--R \| x \| x +--R / +--R +------+ +--R | 2 +--R \|x + 1 - x +--R Type: Expression Integer +--E 468 + +--S 469 of 489 +d0292:= D(m0292,x) +--R +--R +--R +------+ +------+ +--R | 2 +------+ | 2 +--R 2 |x + 1 2 | 2 3 |x + 1 3 +--R (- 2x |------ - 2x - 1)\|x + 1 + (2x + x) |------ + 2x + 2x +--R | 2 | 2 +--R \| x \| x +--R (375) ------------------------------------------------------------------- +--R +------+ +------+ +--R | 2 +------+ | 2 +--R 2 |x + 1 | 2 3 |x + 1 +--R (2x + 1) |------ \|x + 1 + (- 2x - 2x) |------ +--R | 2 | 2 +--R \| x \| x +--R Type: Expression Integer +--E 469 + +--S 470 of 489 +t0293:= exp(1)^acsch(x)/x +--R +--R +--R acsch(x) +--R %e +--R (376) ---------- +--R x +--R Type: Expression Integer +--E 470 + +--S 471 of 489 +r0293:= -(1+1/x^2)^(1/2)-1/x+atanh((1+1/x^2)^(1/2)) +--R +--R +--R +------+ +------+ +--R | 2 | 2 +--R |x + 1 |x + 1 +--R x atanh( |------ ) - x |------ - 1 +--R | 2 | 2 +--R \| x \| x +--R (377) ----------------------------------- +--R x +--R Type: Expression Integer +--E 471 + +--S 472 of 489 +a0293:= integrate(t0293,x) +--R +--R +--R +------+ +------+ +------+ +--R | 2 2 | 2 | 2 +--R (- x\|x + 1 + x )log(\|x + 1 - x) - \|x + 1 + x - 1 +--R (378) --------------------------------------------------------- +--R +------+ +--R | 2 2 +--R x\|x + 1 - x +--R Type: Union(Expression Integer,...) +--E 472 + +--S 473 of 489 +m0293:= a0293-r0293 +--R +--R +--R (379) +--R +------+ +------+ +--R | 2 2 | 2 +--R (- x\|x + 1 + x )log(\|x + 1 - x) +--R + +--R +------+ +------+ +------+ +--R +------+ | 2 | 2 +------+ | 2 +--R | 2 2 |x + 1 |x + 1 | 2 2 |x + 1 +--R (- x\|x + 1 + x )atanh( |------ ) + x |------ \|x + 1 - x |------ - 1 +--R | 2 | 2 | 2 +--R \| x \| x \| x +--R / +--R +------+ +--R | 2 2 +--R x\|x + 1 - x +--R Type: Expression Integer +--E 473 + +--S 474 of 489 +d0293:= D(m0293,x) +--R +--R +--R (380) +--R +------+ +--R | 2 +------+ +--R 4 2 |x + 1 4 2 | 2 +--R ((- 2x - 2x ) |------ - 2x - 3x - 1)\|x + 1 +--R | 2 +--R \| x +--R + +--R +------+ +--R | 2 +--R 5 3 |x + 1 5 3 +--R (2x + 3x + x) |------ + 2x + 4x + 2x +--R | 2 +--R \| x +--R / +--R +------+ +------+ +--R | 2 +------+ | 2 +--R 5 3 |x + 1 | 2 6 4 |x + 1 +--R (2x + x ) |------ \|x + 1 + (- 2x - 2x ) |------ +--R | 2 | 2 +--R \| x \| x +--R Type: Expression Integer +--E 474 + +--S 475 of 489 +t0294:= exp(1)^acsch(x)/x^2 +--R +--R +--R acsch(x) +--R %e +--R (381) ---------- +--R 2 +--R x +--R Type: Expression Integer +--E 475 + +--S 476 of 489 +r0294:= -1/2/x^2-1/2*(1+1/x^2)^(1/2)/x-1/2*acsch(x) +--R +--R +--R +------+ +--R | 2 +--R |x + 1 2 +--R - x |------ - x acsch(x) - 1 +--R | 2 +--R \| x +--R (382) ----------------------------- +--R 2 +--R 2x +--R Type: Expression Integer +--E 476 + +--S 477 of 489 +a0294:= integrate(t0294,x) +--R +--R +--R (383) +--R +------+ +------+ +--R 3 | 2 4 2 | 2 +--R (- 2x \|x + 1 + 2x + x )log(\|x + 1 - x + 1) +--R + +--R +------+ +------+ +------+ +--R 3 | 2 4 2 | 2 2 | 2 +--R (2x \|x + 1 - 2x - x )log(\|x + 1 - x - 1) + (2x - 2x + 1)\|x + 1 +--R + +--R 3 2 +--R - 2x + 2x - 2x + 1 +--R / +--R +------+ +--R 3 | 2 4 2 +--R 4x \|x + 1 - 4x - 2x +--R Type: Union(Expression Integer,...) +--E 477 + +--S 478 of 489 +m0294:= a0294-r0294 +--R +--R +--R (384) +--R +------+ +------+ +--R 3 | 2 4 2 | 2 +--R (- 2x \|x + 1 + 2x + x )log(\|x + 1 - x + 1) +--R + +--R +------+ +------+ +--R 3 | 2 4 2 | 2 +--R (2x \|x + 1 - 2x - x )log(\|x + 1 - x - 1) +--R + +--R +------+ +------+ +--R | 2 +------+ | 2 +--R 2 |x + 1 3 2 | 2 3 |x + 1 +--R (2x |------ + 2x acsch(x) + 2x + 1)\|x + 1 + (- 2x - x) |------ +--R | 2 | 2 +--R \| x \| x +--R + +--R 4 2 3 +--R (- 2x - x )acsch(x) - 2x - 2x +--R / +--R +------+ +--R 3 | 2 4 2 +--R 4x \|x + 1 - 4x - 2x +--R Type: Expression Integer +--E 478 + +--S 479 of 489 +d0294:= D(m0294,x) +--R +--R +--R (385) +--R +------+ +--R | 2 +--R 7 5 3 |x + 1 7 5 3 +--R ((- 16x - 44x - 25x - 2x) |------ - 16x - 52x - 45x - 10x) +--R | 2 +--R \| x +--R * +--R +------+ +--R | 2 +--R \|x + 1 +--R + +--R +------+ +--R | 2 +--R 8 6 4 2 |x + 1 8 6 4 2 +--R (16x + 52x + 45x + 10x ) |------ + 16x + 60x + 69x + 27x + 2 +--R | 2 +--R \| x +--R / +--R +------+ +--R | 2 +------+ +--R 9 7 5 |x + 1 | 2 +--R (32x + 40x + 10x ) |------ \|x + 1 +--R | 2 +--R \| x +--R + +--R +------+ +--R | 2 +--R 10 8 6 4 |x + 1 +--R (- 32x - 56x - 26x - 2x ) |------ +--R | 2 +--R \| x +--R Type: Expression Integer +--E 479 + +--S 480 of 489 +t0295:= exp(1)^acsch(x)/x^4 +--R +--R +--R acsch(x) +--R %e +--R (386) ---------- +--R 4 +--R x +--R Type: Expression Integer +--E 480 + +--S 481 of 489 +r0295:= -1/4/x^4-1/4*(1+1/x^2)^(1/2)/x^3-1/8*(1+1/x^2)^(1/2)/x+1/8*acsch(x) +--R +--R +--R +------+ +--R | 2 +--R 3 |x + 1 4 +--R (- x - 2x) |------ + x acsch(x) - 2 +--R | 2 +--R \| x +--R (387) ------------------------------------- +--R 4 +--R 8x +--R Type: Expression Integer +--E 481 + +--S 482 of 489 +a0295:= integrate(t0295,x) +--R +--R +--R (388) +--R +------+ +------+ +--R 7 5 | 2 8 6 4 | 2 +--R ((8x + 4x )\|x + 1 - 8x - 8x - x )log(\|x + 1 - x + 1) +--R + +--R +------+ +------+ +--R 7 5 | 2 8 6 4 | 2 +--R ((- 8x - 4x )\|x + 1 + 8x + 8x + x )log(\|x + 1 - x - 1) +--R + +--R +------+ +--R 6 4 3 2 | 2 7 5 4 3 +--R (8x + 24x - 16x + 17x - 8x + 2)\|x + 1 - 8x - 28x + 16x - 28x +--R + +--R 2 +--R 16x - 8x + 2 +--R / +--R +------+ +--R 7 5 | 2 8 6 4 +--R (64x + 32x )\|x + 1 - 64x - 64x - 8x +--R Type: Union(Expression Integer,...) +--E 482 + +--S 483 of 489 +m0295:= a0295-r0295 +--R +--R +--R (389) +--R +------+ +------+ +--R 7 5 | 2 8 6 4 | 2 +--R ((8x + 4x )\|x + 1 - 8x - 8x - x )log(\|x + 1 - x + 1) +--R + +--R +------+ +------+ +--R 7 5 | 2 8 6 4 | 2 +--R ((- 8x - 4x )\|x + 1 + 8x + 8x + x )log(\|x + 1 - x - 1) +--R + +--R +------+ +--R | 2 +--R 6 4 2 |x + 1 7 5 6 4 +--R (8x + 20x + 8x ) |------ + (- 8x - 4x )acsch(x) + 8x + 24x +--R | 2 +--R \| x +--R + +--R 2 +--R 17x + 2 +--R * +--R +------+ +--R | 2 +--R \|x + 1 +--R + +--R +------+ +--R | 2 +--R 7 5 3 |x + 1 8 6 4 7 +--R (- 8x - 24x - 17x - 2x) |------ + (8x + 8x + x )acsch(x) - 8x +--R | 2 +--R \| x +--R + +--R 5 3 +--R - 28x - 28x - 8x +--R / +--R +------+ +--R 7 5 | 2 8 6 4 +--R (64x + 32x )\|x + 1 - 64x - 64x - 8x +--R Type: Expression Integer +--E 483 + +--S 484 of 489 +d0295:= D(m0295,x) +--R +--R +--R (390) +--R +------+ +--R | 2 +--R 13 11 9 7 5 3 |x + 1 +--R (- 256x - 2496x - 5872x - 5544x - 2241x - 328x - 8x) |------ +--R | 2 +--R \| x +--R + +--R 13 11 9 7 5 3 +--R - 256x - 2624x - 7088x - 8184x - 4425x - 1032x - 72x +--R * +--R +------+ +--R | 2 +--R \|x + 1 +--R + +--R +------+ +--R | 2 +--R 14 12 10 8 6 4 2 |x + 1 +--R (256x + 2624x + 7088x + 8184x + 4425x + 1032x + 72x ) |------ +--R | 2 +--R \| x +--R + +--R 14 12 10 8 6 4 2 +--R 256x + 2752x + 8368x + 11416x + 7785x + 2569x + 336x + 8 +--R / +--R +------+ +--R | 2 +------+ +--R 15 13 11 9 7 |x + 1 | 2 +--R (2048x + 4608x + 3456x + 960x + 72x ) |------ \|x + 1 +--R | 2 +--R \| x +--R + +--R +------+ +--R | 2 +--R 16 14 12 10 8 6 |x + 1 +--R (- 2048x - 5632x - 5504x - 2240x - 328x - 8x ) |------ +--R | 2 +--R \| x +--R Type: Expression Integer +--E 484 + +--S 485 of 489 +t0296:= acosh(c/(a+b*x)) +--R +--R +--R c +--R (391) acosh(-------) +--R b x + a +--R Type: Expression Integer +--E 485 + +--S 486 of 489 +r0296:= -(-asech((a+b*x)/c)*a-_ + asech((a+b*x)/c)*b*x+2*c*atan((-(-c+a+b*x)/(c+a+b*x))^(1/2)))/b +--R +--R +--R +-------------+ +--R |- b x + c - a b x + a +--R - 2c atan( |------------- ) + (b x + a)asech(-------) +--R \| b x + c + a c +--R (392) ----------------------------------------------------- +--R b +--R Type: Expression Integer +--E 486 + +--S 487 of 489 +a0296:= integrate(t0296,x) +--R +--R +--R (393) +--R +-------------------------+ +--R | 2 2 2 2 +--R \|- b x - 2a b x + c - a + c +--R b x log(--------------------------------) +--R b x + a +--R + +--R +-------+ +-------------------------+ +--R | 2 2 | 2 2 2 2 +--R (- b x - a)\|c - a + a\|- b x - 2a b x + c - a + b c x +--R - a log(-------------------------------------------------------------) +--R x +--R + +--R +-------+ +-------------------------+ +--R | 2 2 | 2 2 2 2 +--R (- b x - a)\|c - a + a\|- b x - 2a b x + c - a - b c x +--R a log(-------------------------------------------------------------) +--R x +--R + +--R +-------+ +-------------------------+ +--R | 2 2 | 2 2 2 2 +--R \|c - a - \|- b x - 2a b x + c - a +--R 2c atan(-----------------------------------------) +--R b x +--R / +--R b +--R Type: Union(Expression Integer,...) +--E 487 + +--S 488 of 489 +m0296:= a0296-r0296 +--R +--R +--R (394) +--R +-------------------------+ +--R | 2 2 2 2 +--R \|- b x - 2a b x + c - a + c +--R b x log(--------------------------------) +--R b x + a +--R + +--R +-------+ +-------------------------+ +--R | 2 2 | 2 2 2 2 +--R (- b x - a)\|c - a + a\|- b x - 2a b x + c - a + b c x +--R - a log(-------------------------------------------------------------) +--R x +--R + +--R +-------+ +-------------------------+ +--R | 2 2 | 2 2 2 2 +--R (- b x - a)\|c - a + a\|- b x - 2a b x + c - a - b c x +--R a log(-------------------------------------------------------------) +--R x +--R + +--R +-------+ +-------------------------+ +--R | 2 2 | 2 2 2 2 +--R \|c - a - \|- b x - 2a b x + c - a +--R 2c atan(-----------------------------------------) +--R b x +--R + +--R +-------------+ +--R |- b x + c - a b x + a +--R 2c atan( |------------- ) + (- b x - a)asech(-------) +--R \| b x + c + a c +--R / +--R b +--R Type: Expression Integer +--E 488 + +--S 489 of 489 +d0296:= D(m0296,x) +--R +--R +--R (395) +--R +-------------------------+ +--R | 2 2 2 2 +-------------+ +--R |- b x - 2a b x + c - a |- b x + c - a +--R (b x + c + a) |------------------------- |------------- +--R | 2 \| b x + c + a +--R \| c +--R * +--R +-------------------------+ +--R | 2 2 2 2 +--R \|- b x - 2a b x + c - a + c +--R log(--------------------------------) +--R b x + a +--R + +--R +-------------------------+ +--R | 2 2 2 2 +--R b x + a |- b x - 2a b x + c - a +--R (- b x - c - a)asech(-------) |------------------------- + b x + c +--R c | 2 +--R \| c +--R + +--R a +--R * +--R +-------------+ +--R |- b x + c - a +--R |------------- +--R \| b x + c + a +--R + +--R +-------------------------+ +--R | 2 2 2 2 +--R |- b x - 2a b x + c - a +--R - c |------------------------- +--R | 2 +--R \| c +--R / +--R +-------------------------+ +--R | 2 2 2 2 +-------------+ +--R |- b x - 2a b x + c - a |- b x + c - a +--R (b x + c + a) |------------------------- |------------- +--R | 2 \| b x + c + a +--R \| c +--R Type: Expression Integer +--E 489 + +)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}