diff --git a/changelog b/changelog index 74613d0..c812b3b 100644 --- a/changelog +++ b/changelog @@ -1,3 +1,6 @@ +20100607 tpd src/axiom-website/patches.html 20100607.01.tpd.patch +20100607 tpd src/input/Makefile rule-based algebraic integration +20100607 tpd src/input/richalgebraic400-461.input rule-based algebraic int. 20100606 tpd src/axiom-website/patches.html 20100606.01.tpd.patch 20100606 tpd src/input/Makefile rule-based algebraic integration 20100606 tpd src/input/richalgebraic300-399.input rule-based algebraic int. diff --git a/src/axiom-website/patches.html b/src/axiom-website/patches.html index 43cd8c2..c00fc81 100644 --- a/src/axiom-website/patches.html +++ b/src/axiom-website/patches.html @@ -2856,6 +2856,8 @@ books/bookvol8 add 3D graphic file format table
src/input/richalgebraic200-299.input rule-based algebraic integration.
20100606.01.tpd.patch src/input/richalgebraic300-399.input rule-based algebraic integration.
+20100607.01.tpd.patch +src/input/richalgebraic400-461.input rule-based algebraic integration.
diff --git a/src/input/Makefile.pamphlet b/src/input/Makefile.pamphlet index 332efce..2b8634c 100644 --- a/src/input/Makefile.pamphlet +++ b/src/input/Makefile.pamphlet @@ -373,6 +373,7 @@ REGRES= ackermann.regress \ richalgebraic100-199.regress \ richalgebraic200-299.regress \ richalgebraic300-399.regress \ + richalgebraic400-461.regress \ richrational.regress robidoux.regress \ roman.regress roots.regress ruleset.regress rules.regress \ rubey.regress sae.regress spline.regress \ @@ -689,6 +690,7 @@ FILES= ${OUT}/ackermann.input \ ${OUT}/richalgebraic100-199.input \ ${OUT}/richalgebraic200-299.input \ ${OUT}/richalgebraic300-399.input \ + ${OUT}/richalgebraic400-461.input \ ${OUT}/richrational.input \ ${OUT}/robidoux.input ${OUT}/roman.input ${OUT}/roots.input \ ${OUT}/ruleset.input ${OUT}/rules.input ${OUT}/rubey.input \ @@ -1035,6 +1037,7 @@ DOCFILES= \ ${DOC}/richalgebraic100-199.input.dvi \ ${DOC}/richalgebraic200-299.input.dvi \ ${DOC}/richalgebraic300-399.input.dvi \ + ${DOC}/richalgebraic400-461.input.dvi \ ${DOC}/richrational.input.dvi \ ${DOC}/rk4draw.input.dvi \ ${DOC}/robidoux.input.dvi ${DOC}/roman.input.dvi \ diff --git a/src/input/richalgebraic400-461.input.pamphlet b/src/input/richalgebraic400-461.input.pamphlet new file mode 100644 index 0000000..f290355 --- /dev/null +++ b/src/input/richalgebraic400-461.input.pamphlet @@ -0,0 +1,8102 @@ +\documentclass{article} +\usepackage{axiom} +\begin{document} +\title{\$SPAD/src/input richalgebraic400-461.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f richalgebraic400-461.output +)spool richalgebraic400-461.output +)set message test on +)set message auto off +)clear all + +--S 1 of 324 +t0400:= 1/(x^3)^(1/3) +--R +--R +--R 1 +--R (1) ----- +--R +--+ +--R 3| 3 +--R \|x +--R Type: Expression Integer +--E 1 + +--S 2 of 324 +r0400:= x*log(x)/(x^3)^(1/3) +--R +--R +--R x log(x) +--R (2) -------- +--R +--+ +--R 3| 3 +--R \|x +--R Type: Expression Integer +--E 2 + +--S 3 of 324 +a0400:= integrate(t0400,x) +--R +--R +--R (3) log(x) +--R Type: Union(Expression Integer,...) +--E 3 + +--S 4 of 324 +m0400:= a0400-r0400 +--R +--R +--R +--+ +--R 3| 3 +--R log(x)\|x - x log(x) +--R (4) ---------------------- +--R +--+ +--R 3| 3 +--R \|x +--R Type: Expression Integer +--E 4 + +--S 5 of 324 +d0400:= D(m0400,x) +--R +--R +--R +--+ +--R 3| 3 +--R \|x - x +--R (5) --------- +--R +--+ +--R 3| 3 +--R x\|x +--R Type: Expression Integer +--E 5 + +--S 6 of 324 +t0401:= (x^m)^(-1/m) +--R +--R +--R 1 +--R (6) - +--R x +--R Type: Expression Integer +--E 6 + +--S 7 of 324 +r0401:= x*log(x)/((x^m)^(1/m)) +--R +--R +--R (7) log(x) +--R Type: Expression Integer +--E 7 + +--S 8 of 324 +a0401:= integrate(t0401,x) +--R +--R +--R (8) log(x) +--R Type: Union(Expression Integer,...) +--E 8 + +--S 9 of 324 +m0401:= a0401-r0401 +--R +--R +--R (9) 0 +--R Type: Expression Integer +--E 9 + +--S 10 of 324 +d0401:= D(m0401,x) +--R +--R +--R (10) 0 +--R Type: Expression Integer +--E 10 + +--S 11 of 324 +t0402:= (a*(b*x^m)^n)^(-1/m/n) +--R +--R +--R 1 +--R - --- +--R m n m n +--R (11) (a (b x ) ) +--R Type: Expression Integer +--E 11 + +--S 12 of 324 +r0402:= x*log(x)*(a*(b*x^m)^n)^(-1/m/n) +--R +--R +--R 1 +--R - --- +--R m n m n +--R (12) x log(x)(a (b x ) ) +--R Type: Expression Integer +--E 12 + +--S 13 of 324 +a0402:= integrate(t0402,x) +--R +--R +--R - n log(b) - log(a) +--R ------------------- +--R m n +--R (13) log(x)%e +--R Type: Union(Expression Integer,...) +--E 13 + +--S 14 of 324 +m0402:= a0402-r0402 +--R +--R +--R 1 - n log(b) - log(a) +--R - --- ------------------- +--R m n m n m n +--R (14) - x log(x)(a (b x ) ) + log(x)%e +--R Type: Expression Integer +--E 14 + +--S 15 of 324 +d0402:= D(m0402,x) +--R +--R +--R (15) +--R 1 +--R - --- +--R m n m n +--R (- x log(x) - x)(a (b x ) ) +--R + +--R - m n - 1 - n log(b) - log(a) +--R --------- ------------------- +--R 2 m - 1 m n - 1 m n m n m n +--R a b x log(x)x (b x ) (a (b x ) ) + %e +--R / +--R x +--R Type: Expression Integer +--E 15 + +--S 16 of 324 +t0403:= x^(1/2)/(1+x)^(1/2) +--R +--R +--R +-+ +--R \|x +--R (16) -------- +--R +-----+ +--R \|x + 1 +--R Type: Expression Integer +--E 16 + +--S 17 of 324 +r0403:= x^(1/2)*(1+x)^(1/2)-asinh(x^(1/2)) +--R +--R +--R +-+ +-+ +-----+ +--R (17) - asinh(\|x ) + \|x \|x + 1 +--R Type: Expression Integer +--E 17 + +--S 18 of 324 +a0403:= integrate(t0403,x) +--R +--R +--R +-+ +-----+ +-+ +-----+ +--R - log(2\|x \|x + 1 + 2x + 1) + 2\|x \|x + 1 +--R (18) --------------------------------------------- +--R 2 +--R Type: Union(Expression Integer,...) +--E 18 + +--S 19 of 324 +m0403:= a0403-r0403 +--R +--R +--R +-+ +-----+ +-+ +--R - log(2\|x \|x + 1 + 2x + 1) + 2asinh(\|x ) +--R (19) -------------------------------------------- +--R 2 +--R Type: Expression Integer +--E 19 + +--S 20 of 324 +d0403:= D(m0403,x) +--R +--R +--R (20) 0 +--R Type: Expression Integer +--E 20 + +--S 21 of 324 +t0404:= (-1+x)^(1/2)/x^(1/2) +--R +--R +--R +-----+ +--R \|x - 1 +--R (21) -------- +--R +-+ +--R \|x +--R Type: Expression Integer +--E 21 + +--S 22 of 324 +r0404:= (-1+x)^(1/2)*x^(1/2)-asinh((-1+x)^(1/2)) +--R +--R +--R +-----+ +-----+ +-+ +--R (22) - asinh(\|x - 1 ) + \|x - 1 \|x +--R Type: Expression Integer +--E 22 + +--S 23 of 324 +a0404:= integrate(t0404,x) +--R +--R +--R +-----+ +-+ +-----+ +-+ +--R - log(- 2\|x - 1 \|x - 2x + 1) + 2\|x - 1 \|x +--R (23) ----------------------------------------------- +--R 2 +--R Type: Union(Expression Integer,...) +--E 23 + +--S 24 of 324 +m0404:= a0404-r0404 +--R +--R +--R +-----+ +-+ +-----+ +--R - log(- 2\|x - 1 \|x - 2x + 1) + 2asinh(\|x - 1 ) +--R (24) -------------------------------------------------- +--R 2 +--R Type: Expression Integer +--E 24 + +--S 25 of 324 +d0404:= D(m0404,x) +--R +--R +--R (25) 0 +--R Type: Expression Integer +--E 25 + +--S 26 of 324 +t0405:= (1+x^(1/2))^2/x^(1/2) +--R +--R +--R +-+ +--R 2\|x + x + 1 +--R (26) ------------- +--R +-+ +--R \|x +--R Type: Expression Integer +--E 26 + +--S 27 of 324 +r0405:= 2/3*(1+x^(1/2))^3 +--R +--R +--R +-+ +--R (2x + 6)\|x + 6x + 2 +--R (27) --------------------- +--R 3 +--R Type: Expression Integer +--E 27 + +--S 28 of 324 +a0405:= integrate(t0405,x) +--R +--R +--R +-+ +--R (2x + 6)\|x + 6x +--R (28) ----------------- +--R 3 +--R Type: Union(Expression Integer,...) +--E 28 + +--S 29 of 324 +m0405:= a0405-r0405 +--R +--R +--R 2 +--R (29) - - +--R 3 +--R Type: Expression Integer +--E 29 + +--S 30 of 324 +d0405:= D(m0405,x) +--R +--R +--R (30) 0 +--R Type: Expression Integer +--E 30 + +--S 31 of 324 +t0406:= (1+x^(1/2))^3/x^(1/2) +--R +--R +--R +-+ +--R (x + 3)\|x + 3x + 1 +--R (31) -------------------- +--R +-+ +--R \|x +--R Type: Expression Integer +--E 31 + +--S 32 of 324 +r0406:= 1/2*(1+x^(1/2))^4 +--R +--R +--R +-+ 2 +--R (4x + 4)\|x + x + 6x + 1 +--R (32) -------------------------- +--R 2 +--R Type: Expression Integer +--E 32 + +--S 33 of 324 +a0406:= integrate(t0406,x) +--R +--R +--R +-+ 2 +--R (4x + 4)\|x + x + 6x +--R (33) ---------------------- +--R 2 +--R Type: Union(Expression Integer,...) +--E 33 + +--S 34 of 324 +m0406:= a0406-r0406 +--R +--R +--R 1 +--R (34) - - +--R 2 +--R Type: Expression Integer +--E 34 + +--S 35 of 324 +d0406:= D(m0406,x) +--R +--R +--R (35) 0 +--R Type: Expression Integer +--E 35 + +--S 36 of 324 +t0407:= (x/(1+x))^(1/2) +--R +--R +--R +-----+ +--R | x +--R (36) |----- +--R \|x + 1 +--R Type: Expression Integer +--E 36 + +--S 37 of 324 +r0407:= x^(1/2)*(1+x)^(1/2)-asinh(x^(1/2)) +--R +--R +--R +-+ +-+ +-----+ +--R (37) - asinh(\|x ) + \|x \|x + 1 +--R Type: Expression Integer +--E 37 + +--S 38 of 324 +a0407:= integrate(t0407,x) +--R +--R +--R +-----+ +-----+ +-----+ +--R | x | x | x +--R - log( |----- + 1) + log( |----- - 1) + (2x + 2) |----- +--R \|x + 1 \|x + 1 \|x + 1 +--R (38) ---------------------------------------------------------- +--R 2 +--R Type: Union(Expression Integer,...) +--E 38 + +--S 39 of 324 +m0407:= a0407-r0407 +--R +--R +--R (39) +--R +-----+ +-----+ +--R | x | x +-+ +-+ +-----+ +--R - log( |----- + 1) + log( |----- - 1) + 2asinh(\|x ) - 2\|x \|x + 1 +--R \|x + 1 \|x + 1 +--R + +--R +-----+ +--R | x +--R (2x + 2) |----- +--R \|x + 1 +--R / +--R 2 +--R Type: Expression Integer +--E 39 + +--S 40 of 324 +d0407:= D(m0407,x) +--R +--R +--R +-----+ +--R | x +-+ +-----+ +--R |----- \|x \|x + 1 - x +--R \|x + 1 +--R (40) ------------------------ +--R +-+ +-----+ +--R \|x \|x + 1 +--R Type: Expression Integer +--E 40 + +--S 41 of 324 +t0408:= (-x/(1+x))^(1/2) +--R +--R +--R +-------+ +--R | x +--R (41) |- ----- +--R \| x + 1 +--R Type: Expression Integer +--E 41 + +--S 42 of 324 +r0408:= (-x/(1+x))^(1/2)*(1+x)-atan((-x/(1+x))^(1/2)) +--R +--R +--R +-------+ +-------+ +--R | x | x +--R (42) - atan( |- ----- ) + (x + 1) |- ----- +--R \| x + 1 \| x + 1 +--R Type: Expression Integer +--E 42 + +--S 43 of 324 +a0408:= integrate(t0408,x) +--R +--R +--R +-------+ +-------+ +--R | x | x +--R (43) - atan( |- ----- ) + (x + 1) |- ----- +--R \| x + 1 \| x + 1 +--R Type: Union(Expression Integer,...) +--E 43 + +--S 44 of 324 +m0408:= a0408-r0408 +--R +--R +--R (44) 0 +--R Type: Expression Integer +--E 44 + +--S 45 of 324 +d0408:= D(m0408,x) +--R +--R +--R (45) 0 +--R Type: Expression Integer +--E 45 + +--S 46 of 324 +t0409:= ((1+x)/x)^(1/2) +--R +--R +--R +-----+ +--R |x + 1 +--R (46) |----- +--R \| x +--R Type: Expression Integer +--E 46 + +--S 47 of 324 +r0409:= x*((1+x)/x)^(1/2)+atanh(((1+x)/x)^(1/2)) +--R +--R +--R +-----+ +-----+ +--R |x + 1 |x + 1 +--R (47) atanh( |----- ) + x |----- +--R \| x \| x +--R Type: Expression Integer +--E 47 + +--S 48 of 324 +a0409:= integrate(t0409,x) +--R +--R +--R +-----+ +-----+ +-----+ +--R |x + 1 |x + 1 |x + 1 +--R log( |----- + 1) - log( |----- - 1) + 2x |----- +--R \| x \| x \| x +--R (48) -------------------------------------------------- +--R 2 +--R Type: Union(Expression Integer,...) +--E 48 + +--S 49 of 324 +m0409:= a0409-r0409 +--R +--R +--R +-----+ +-----+ +-----+ +--R |x + 1 |x + 1 |x + 1 +--R log( |----- + 1) - log( |----- - 1) - 2atanh( |----- ) +--R \| x \| x \| x +--R (49) -------------------------------------------------------- +--R 2 +--R Type: Expression Integer +--E 49 + +--S 50 of 324 +d0409:= D(m0409,x) +--R +--R +--R (50) 0 +--R Type: Expression Integer +--E 50 + +--S 51 of 324 +t0410:= ((1-x)/x)^(1/2) +--R +--R +--R +-------+ +--R |- x + 1 +--R (51) |------- +--R \| x +--R Type: Expression Integer +--E 51 + +--S 52 of 324 +r0410:= (-(-1+x)/x)^(1/2)*x-atan((-(-1+x)/x)^(1/2)) +--R +--R +--R +-------+ +-------+ +--R |- x + 1 |- x + 1 +--R (52) - atan( |------- ) + x |------- +--R \| x \| x +--R Type: Expression Integer +--E 52 + +--S 53 of 324 +a0410:= integrate(t0410,x) +--R +--R +--R +-------+ +-------+ +--R |- x + 1 |- x + 1 +--R (53) - atan( |------- ) + x |------- +--R \| x \| x +--R Type: Union(Expression Integer,...) +--E 53 + +--S 54 of 324 +m0410:= a0410-r0410 +--R +--R +--R (54) 0 +--R Type: Expression Integer +--E 54 + +--S 55 of 324 +d0410:= D(m0410,x) +--R +--R +--R (55) 0 +--R Type: Expression Integer +--E 55 + +--S 56 of 324 +t0411:= ((-1+x)/x)^(1/2) +--R +--R +--R +-----+ +--R |x - 1 +--R (56) |----- +--R \| x +--R Type: Expression Integer +--E 56 + +--S 57 of 324 +r0411:= (-1+x)^(1/2)*x^(1/2)-asinh((-1+x)^(1/2)) +--R +--R +--R +-----+ +-----+ +-+ +--R (57) - asinh(\|x - 1 ) + \|x - 1 \|x +--R Type: Expression Integer +--E 57 + +--S 58 of 324 +a0411:= integrate(t0411,x) +--R +--R +--R +-----+ +-----+ +-----+ +--R |x - 1 |x - 1 |x - 1 +--R - log( |----- + 1) + log( |----- - 1) + 2x |----- +--R \| x \| x \| x +--R (58) ---------------------------------------------------- +--R 2 +--R Type: Union(Expression Integer,...) +--E 58 + +--S 59 of 324 +m0411:= a0411-r0411 +--R +--R +--R (59) +--R +-----+ +-----+ +--R |x - 1 |x - 1 +-----+ +--R - log( |----- + 1) + log( |----- - 1) + 2asinh(\|x - 1 ) +--R \| x \| x +--R + +--R +-----+ +--R +-----+ +-+ |x - 1 +--R - 2\|x - 1 \|x + 2x |----- +--R \| x +--R / +--R 2 +--R Type: Expression Integer +--E 59 + +--S 60 of 324 +d0411:= D(m0411,x) +--R +--R +--R +-----+ +--R |x - 1 +-----+ +-+ +--R |----- \|x - 1 \|x - x + 1 +--R \| x +--R (60) ---------------------------- +--R +-----+ +-+ +--R \|x - 1 \|x +--R Type: Expression Integer +--E 60 + +--S 61 of 324 +t0412:= (-x/(1+x))^(1/2)/x +--R +--R +--R +-------+ +--R | x +--R |- ----- +--R \| x + 1 +--R (61) ---------- +--R x +--R Type: Expression Integer +--E 61 + +--S 62 of 324 +r0412:= 2*atan((-x/(1+x))^(1/2)) +--R +--R +--R +-------+ +--R | x +--R (62) 2atan( |- ----- ) +--R \| x + 1 +--R Type: Expression Integer +--E 62 + +--S 63 of 324 +a0412:= integrate(t0412,x) +--R +--R +--R +-------+ +--R | x +--R (63) 2atan( |- ----- ) +--R \| x + 1 +--R Type: Union(Expression Integer,...) +--E 63 + +--S 64 of 324 +m0412:= a0412-r0412 +--R +--R +--R (64) 0 +--R Type: Expression Integer +--E 64 + +--S 65 of 324 +d0412:= D(m0412,x) +--R +--R +--R (65) 0 +--R Type: Expression Integer +--E 65 + +--S 66 of 324 +t0413:= ((1+x)/x)^(1/2)/x +--R +--R +--R +-----+ +--R |x + 1 +--R |----- +--R \| x +--R (66) -------- +--R x +--R Type: Expression Integer +--E 66 + +--S 67 of 324 +r0413:= -2*((1+x)/x)^(1/2)+2*atanh(((1+x)/x)^(1/2)) +--R +--R +--R +-----+ +-----+ +--R |x + 1 |x + 1 +--R (67) 2atanh( |----- ) - 2 |----- +--R \| x \| x +--R Type: Expression Integer +--E 67 + +--S 68 of 324 +a0413:= integrate(t0413,x) +--R +--R +--R +-----+ +-----+ +-----+ +--R |x + 1 |x + 1 |x + 1 +--R (68) log( |----- + 1) - log( |----- - 1) - 2 |----- +--R \| x \| x \| x +--R Type: Union(Expression Integer,...) +--E 68 + +--S 69 of 324 +m0413:= a0413-r0413 +--R +--R +--R +-----+ +-----+ +-----+ +--R |x + 1 |x + 1 |x + 1 +--R (69) log( |----- + 1) - log( |----- - 1) - 2atanh( |----- ) +--R \| x \| x \| x +--R Type: Expression Integer +--E 69 + +--S 70 of 324 +d0413:= D(m0413,x) +--R +--R +--R (70) 0 +--R Type: Expression Integer +--E 70 + +--S 71 of 324 +t0414:= ((1-x)/(1+x))^(1/2)/(-1+x) +--R +--R +--R +-------+ +--R |- x + 1 +--R |------- +--R \| x + 1 +--R (71) ---------- +--R x - 1 +--R Type: Expression Integer +--E 71 + +--S 72 of 324 +r0414:= 2*atan((-(-1+x)/(1+x))^(1/2)) +--R +--R +--R +-------+ +--R |- x + 1 +--R (72) 2atan( |------- ) +--R \| x + 1 +--R Type: Expression Integer +--E 72 + +--S 73 of 324 +a0414:= integrate(t0414,x) +--R +--R +--R +-------+ +--R |- x + 1 +--R (73) 2atan( |------- ) +--R \| x + 1 +--R Type: Union(Expression Integer,...) +--E 73 + +--S 74 of 324 +m0414:= a0414-r0414 +--R +--R +--R (74) 0 +--R Type: Expression Integer +--E 74 + +--S 75 of 324 +d0414:= D(m0414,x) +--R +--R +--R (75) 0 +--R Type: Expression Integer +--E 75 + +--S 76 of 324 +t0415:= (2+(4+x^(1/2))^(1/2))^(1/2) +--R +--R +--R +---------------+ +--R | +--------+ +--R | | +-+ +--R (76) \|\|\|x + 4 + 2 +--R Type: Expression Integer +--E 76 + +--S 77 of 324 +r0415:= 64/5*(2+(4+x^(1/2))^(1/2))^(5/2)-48/7*(2+(4+x^(1/2))^(1/2))^(7/2)+_ + 8/9*(2+(4+x^(1/2))^(1/2))^(9/2) +--R +--R +--R +---------------+ +--R +--------+ | +--------+ +--R +-+ | +-+ +-+ | | +-+ +--R ((80\|x - 512)\|\|x + 4 + 32\|x + 280x - 1024)\|\|\|x + 4 + 2 +--R (77) -------------------------------------------------------------------- +--R 315 +--R Type: Expression Integer +--E 77 + +--S 78 of 324 +a0415:= integrate(t0415,x) +--R +--R +--R +---------------+ +--R +--------+ | +--------+ +--R +-+ | +-+ +-+ | | +-+ +--R ((80\|x - 512)\|\|x + 4 + 32\|x + 280x - 1024)\|\|\|x + 4 + 2 +--R (78) -------------------------------------------------------------------- +--R 315 +--R Type: Union(Expression Integer,...) +--E 78 + +--S 79 of 324 +m0415:= a0415-r0415 +--R +--R +--R (79) 0 +--R Type: Expression Integer +--E 79 + +--S 80 of 324 +d0415:= D(m0415,x) +--R +--R +--R (80) 0 +--R Type: Expression Integer +--E 80 + +--S 81 of 324 +t0416:= (2-(4+(-9+5*x)^(1/2))^(1/2))^(1/2) +--R +--R +--R +----------------------+ +--R | +-------------+ +--R | | +------+ +--R (81) \|- \|\|5x - 9 + 4 + 2 +--R Type: Expression Integer +--E 81 + +--S 82 of 324 +r0416:= 64/25*(2-(4+(-9+5*x)^(1/2))^(1/2))^(5/2)-48/_ + 35*(2-(4+(-9+5*x)^(1/2))^(1/2))^(7/2)+8/45*_ + (2-(4+(-9+5*x)^(1/2))^(1/2))^(9/2) +--R +--R +--R (82) +--R +-------------+ +--R +------+ | +------+ +------+ +--R ((- 80\|5x - 9 + 512)\|\|5x - 9 + 4 + 32\|5x - 9 + 1400x - 3544) +--R * +--R +----------------------+ +--R | +-------------+ +--R | | +------+ +--R \|- \|\|5x - 9 + 4 + 2 +--R / +--R 1575 +--R Type: Expression Integer +--E 82 + +--S 83 of 324 +a0416:= integrate(t0416,x) +--R +--R +--R (83) +--R +-------------+ +--R +------+ | +------+ +------+ +--R ((- 80\|5x - 9 + 512)\|\|5x - 9 + 4 + 32\|5x - 9 + 1400x - 3544) +--R * +--R +----------------------+ +--R | +-------------+ +--R | | +------+ +--R \|- \|\|5x - 9 + 4 + 2 +--R / +--R 1575 +--R Type: Union(Expression Integer,...) +--E 83 + +--S 84 of 324 +m0416:= a0416-r0416 +--R +--R +--R (84) 0 +--R Type: Expression Integer +--E 84 + +--S 85 of 324 +d0416:= D(m0416,x) +--R +--R +--R (85) 0 +--R Type: Expression Integer +--E 85 + +--S 86 of 324 +t0417:= (1+(1+(1+x^(1/2))^(1/2))^(1/2))^(1/2) +--R +--R +--R +----------------------+ +--R | +---------------+ +--R | | +--------+ +--R | | | +-+ +--R (86) \|\|\|\|x + 1 + 1 + 1 +--R Type: Expression Integer +--E 86 + +--S 87 of 324 +r0417:= -32/5*(1+(1+(1+x^(1/2))^(1/2))^(1/2))^(5/2)+48/7*_ + (1+(1+(1+x^(1/2))^(1/2))^(1/2))^(7/2)+112/9*_ + (1+(1+(1+x^(1/2))^(1/2))^(1/2))^(9/2)-320/11*_ + (1+(1+(1+x^(1/2))^(1/2))^(1/2))^(11/2)+288/13*_ + (1+(1+(1+x^(1/2))^(1/2))^(1/2))^(13/2)-112/15*_ + (1+(1+(1+x^(1/2))^(1/2))^(1/2))^(15/2)+16/17*_ + (1+(1+(1+x^(1/2))^(1/2))^(1/2))^(17/2) +--R +--R +--R (87) +--R +---------------+ +--R +--------+ | +--------+ +--R +-+ | +-+ +-+ | | +-+ +--R ((48048\|x - 74752)\|\|x + 1 - 56448\|x + 140032)\|\|\|x + 1 + 1 +--R + +--R +--------+ +--R +-+ | +-+ +-+ +--R (3696\|x - 20864)\|\|x + 1 + 73808\|x + 720720x - 450432 +--R * +--R +----------------------+ +--R | +---------------+ +--R | | +--------+ +--R | | | +-+ +--R \|\|\|\|x + 1 + 1 + 1 +--R / +--R 765765 +--R Type: Expression Integer +--E 87 + +--S 88 of 324 +a0417:= integrate(t0417,x) +--R +--R +--R (88) +--R +---------------+ +--R +--------+ | +--------+ +--R +-+ | +-+ +-+ | | +-+ +--R ((48048\|x - 74752)\|\|x + 1 - 56448\|x + 140032)\|\|\|x + 1 + 1 +--R + +--R +--------+ +--R +-+ | +-+ +-+ +--R (3696\|x - 20864)\|\|x + 1 + 73808\|x + 720720x - 450432 +--R * +--R +----------------------+ +--R | +---------------+ +--R | | +--------+ +--R | | | +-+ +--R \|\|\|\|x + 1 + 1 + 1 +--R / +--R 765765 +--R Type: Union(Expression Integer,...) +--E 88 + +--S 89 of 324 +m0417:= a0417-r0417 +--R +--R +--R (89) 0 +--R Type: Expression Integer +--E 89 + +--S 90 of 324 +d0417:= D(m0417,x) +--R +--R +--R (90) 0 +--R Type: Expression Integer +--E 90 + +--S 91 of 324 +t0418:= (2+(3+(-1+2*x^(1/2))^(1/2))^(1/2))^(1/2) +--R +--R +--R +-----------------------+ +--R | +----------------+ +--R | | +---------+ +--R | | | +-+ +--R (91) \|\|\|2\|x - 1 + 3 + 2 +--R Type: Expression Integer +--E 91 + +--S 92 of 324 +r0418:= -16/3*(2+(3+(-1+2*x^(1/2))^(1/2))^(1/2))^(3/2)+136/5*_ + (2+(3+(-1+2*x^(1/2))^(1/2))^(1/2))^(5/2)-480/7*_ + (2+(3+(-1+2*x^(1/2))^(1/2))^(1/2))^(7/2)+304/3*_ + (2+(3+(-1+2*x^(1/2))^(1/2))^(1/2))^(9/2)-760/11*_ + (2+(3+(-1+2*x^(1/2))^(1/2))^(1/2))^(11/2)+300/13*_ + (2+(3+(-1+2*x^(1/2))^(1/2))^(1/2))^(13/2)-56/15*_ + (2+(3+(-1+2*x^(1/2))^(1/2))^(1/2))^(15/2)+4/17*_ + (2+(3+(-1+2*x^(1/2))^(1/2))^(1/2))^(17/2) +--R +--R +--R (92) +--R +---------+ +--R +-+ | +-+ +-+ +--R ((16016\|x + 108800)\|2\|x - 1 - 37632\|x - 475392) +--R * +--R +----------------+ +--R | +---------+ +--R | | +-+ +--R \|\|2\|x - 1 + 3 +--R + +--R +---------+ +--R +-+ | +-+ +-+ +--R (- 6776\|x + 13504)\|2\|x - 1 - 30744\|x + 240240x - 992640 +--R * +--R +-----------------------+ +--R | +----------------+ +--R | | +---------+ +--R | | | +-+ +--R \|\|\|2\|x - 1 + 3 + 2 +--R / +--R 255255 +--R Type: Expression Integer +--E 92 + +--S 93 of 324 +a0418:= integrate(t0418,x) +--R +--R +--R (93) +--R +---------+ +--R +-+ | +-+ +-+ +--R ((16016\|x + 108800)\|2\|x - 1 - 37632\|x - 475392) +--R * +--R +----------------+ +--R | +---------+ +--R | | +-+ +--R \|\|2\|x - 1 + 3 +--R + +--R +---------+ +--R +-+ | +-+ +-+ +--R (- 6776\|x + 13504)\|2\|x - 1 - 30744\|x + 240240x - 992640 +--R * +--R +-----------------------+ +--R | +----------------+ +--R | | +---------+ +--R | | | +-+ +--R \|\|\|2\|x - 1 + 3 + 2 +--R / +--R 255255 +--R Type: Union(Expression Integer,...) +--E 93 + +--S 94 of 324 +m0418:= a0418-r0418 +--R +--R +--R (94) 0 +--R Type: Expression Integer +--E 94 + +--S 95 of 324 +d0418:= D(m0418,x) +--R +--R +--R (95) 0 +--R Type: Expression Integer +--E 95 + +--S 96 of 324 +t0419:= x^3/(3*x^2-4*x^4)^(1/2) +--R +--R +--R 3 +--R x +--R (96) -------------- +--R +-----------+ +--R | 4 2 +--R \|- 4x + 3x +--R Type: Expression Integer +--E 96 + +--S 97 of 324 +r0419:= -1/8*(3*x^2-4*x^4)^(1/2)+3/32*asin(-1+8/3*x^2) +--R +--R +--R +-----------+ 2 +--R | 4 2 8x - 3 +--R - 4\|- 4x + 3x + 3asin(-------) +--R 3 +--R (97) ---------------------------------- +--R 32 +--R Type: Expression Integer +--E 97 + +--S 98 of 324 +a0419:= integrate(t0419,x) +--R +--R +--R (98) +--R +---------+ +--R +---------+ | 2 +-+ +--R +-+ | 2 2 \|- 4x + 3 - \|3 +--R (- 3\|3 \|- 4x + 3 - 6x + 9)atan(-------------------) +--R 2x +--R + +--R +---------+ +--R 3 | 2 3 +-+ +--R (- 2x + 3x)\|- 4x + 3 + (4x - 3x)\|3 +--R / +--R +---------+ +--R +-+ | 2 2 +--R 8\|3 \|- 4x + 3 + 16x - 24 +--R Type: Union(Expression Integer,...) +--E 98 + +--S 99 of 324 +m0419:= a0419-r0419 +--R +--R +--R (99) +--R +---------+ +--R +---------+ | 2 +-+ +--R +-+ | 2 2 \|- 4x + 3 - \|3 +--R (- 12\|3 \|- 4x + 3 - 24x + 36)atan(-------------------) +--R 2x +--R + +--R +-----------+ 2 +---------+ +--R +-+ | 4 2 +-+ 8x - 3 3 | 2 +--R (4\|3 \|- 4x + 3x - 3\|3 asin(-------) - 8x + 12x)\|- 4x + 3 +--R 3 +--R + +--R +-----------+ 2 +--R 2 | 4 2 2 8x - 3 3 +-+ +--R (8x - 12)\|- 4x + 3x + (- 6x + 9)asin(-------) + (16x - 12x)\|3 +--R 3 +--R / +--R +---------+ +--R +-+ | 2 2 +--R 32\|3 \|- 4x + 3 + 64x - 96 +--R Type: Expression Integer +--E 99 + +--S 100 of 324 +d0419:= D(m0419,x) +--R +--R +--R (100) +--R +-------------+ +--R 4 2 +-+ | 4 2 5 3 +--R ((16x - 24x )\|3 \|- 64x + 48x - 24x + 144x - 108x) +--R * +--R +-----------+ +--R | 4 2 +--R \|- 4x + 3x +--R + +--R +-------------+ +--R 7 5 3 | 4 2 +--R (- 16x + 102x - 108x + 27x)\|- 64x + 48x +--R * +--R +---------+ +--R | 2 +--R \|- 4x + 3 +--R + +--R +-------------+ +--R 6 4 2 | 4 2 5 3 +-+ +--R ((16x - 96x + 72x )\|- 64x + 48x + (96x - 216x + 108x)\|3 ) +--R * +--R +-----------+ +--R | 4 2 +--R \|- 4x + 3x +--R + +--R +-------------+ +--R 7 5 3 +-+ | 4 2 +--R (64x - 168x + 126x - 27x)\|3 \|- 64x + 48x +--R / +--R +-------------+ +-----------+ +---------+ +--R 4 2 | 4 2 | 4 2 | 2 +--R (16x - 96x + 72)\|- 64x + 48x \|- 4x + 3x \|- 4x + 3 +--R + +--R +-------------+ +-----------+ +--R 4 2 +-+ | 4 2 | 4 2 +--R (- 64x + 144x - 72)\|3 \|- 64x + 48x \|- 4x + 3x +--R Type: Expression Integer +--E 100 + +--S 101 of 324 +t0420:= x^3/(-3*x^2-4*x^4)^(1/2) +--R +--R +--R 3 +--R x +--R (101) -------------- +--R +-----------+ +--R | 4 2 +--R \|- 4x - 3x +--R Type: Expression Integer +--E 101 + +--S 102 of 324 +r0420:= -1/8*(-3*x^2-4*x^4)^(1/2)-3/32*asin(1+8/3*x^2) +--R +--R +--R +-----------+ 2 +--R | 4 2 8x + 3 +--R - 4\|- 4x - 3x - 3asin(-------) +--R 3 +--R (102) ---------------------------------- +--R 32 +--R Type: Expression Integer +--E 102 + +--S 103 of 324 +a0420:= integrate(t0420,x) +--R +--R +--R (103) +--R +---------+ +--R +---+ +---+ | 2 2 +---+ +--R (3\|- 3 \|- 1 \|- 4x - 3 + (6x + 9)\|- 1 ) +--R * +--R +---------+ +--R | 2 +---+ +---+ +--R \|- 4x - 3 + 2x\|- 1 - \|- 3 +--R log(--------------------------------) +--R x +--R + +--R +---------+ +--R +---+ +---+ | 2 2 +---+ +--R (- 3\|- 3 \|- 1 \|- 4x - 3 + (- 6x - 9)\|- 1 ) +--R * +--R +---------+ +--R | 2 +---+ +---+ +--R \|- 4x - 3 - 2x\|- 1 - \|- 3 +--R log(--------------------------------) +--R x +--R + +--R +---------+ +--R 3 | 2 3 +---+ +--R (- 4x - 6x)\|- 4x - 3 + (8x + 6x)\|- 3 +--R / +--R +---------+ +--R +---+ | 2 2 +--R 16\|- 3 \|- 4x - 3 + 32x + 48 +--R Type: Union(Expression Integer,...) +--E 103 + +--S 104 of 324 +m0420:= a0420-r0420 +--R +--R +--R (104) +--R +---------+ +--R +---+ +---+ | 2 2 +---+ +--R (6\|- 3 \|- 1 \|- 4x - 3 + (12x + 18)\|- 1 ) +--R * +--R +---------+ +--R | 2 +---+ +---+ +--R \|- 4x - 3 + 2x\|- 1 - \|- 3 +--R log(--------------------------------) +--R x +--R + +--R +---------+ +--R +---+ +---+ | 2 2 +---+ +--R (- 6\|- 3 \|- 1 \|- 4x - 3 + (- 12x - 18)\|- 1 ) +--R * +--R +---------+ +--R | 2 +---+ +---+ +--R \|- 4x - 3 - 2x\|- 1 - \|- 3 +--R log(--------------------------------) +--R x +--R + +--R +-----------+ 2 +---------+ +--R +---+ | 4 2 +---+ 8x + 3 3 | 2 +--R (4\|- 3 \|- 4x - 3x + 3\|- 3 asin(-------) - 8x - 12x)\|- 4x - 3 +--R 3 +--R + +--R +-----------+ 2 +--R 2 | 4 2 2 8x + 3 3 +---+ +--R (8x + 12)\|- 4x - 3x + (6x + 9)asin(-------) + (16x + 12x)\|- 3 +--R 3 +--R / +--R +---------+ +--R +---+ | 2 2 +--R 32\|- 3 \|- 4x - 3 + 64x + 96 +--R Type: Expression Integer +--E 104 + +--S 105 of 324 +d0420:= D(m0420,x) +--R +--R +--R (105) +--R +-------------+ +--R 6 4 2 | 4 2 +--R (- 120x - 360x - 216x )\|- 64x - 48x +--R + +--R 7 5 3 +---+ +--R (48x + 468x + 756x + 324x)\|- 3 +--R * +--R +-----------+ +--R | 4 2 +--R \|- 4x - 3x +--R + +--R +-------------+ +--R 9 7 5 3 +---+ | 4 2 +--R (- 32x - 324x - 621x - 405x - 81x)\|- 3 \|- 64x - 48x +--R * +--R +---------+ +--R | 2 +--R \|- 4x - 3 +--R + +--R +-------------+ +--R 8 6 4 2 +---+ | 4 2 7 5 +--R (32x + 312x + 504x + 216x )\|- 3 \|- 64x - 48x + 720x + 2700x +--R + +--R 3 +--R 2916x + 972x +--R * +--R +-----------+ +--R | 4 2 +--R \|- 4x - 3x +--R + +--R +-------------+ +--R 9 7 5 3 | 4 2 +--R (- 480x - 1980x - 2619x - 1377x - 243x)\|- 64x - 48x +--R / +--R +-------------+ +-----------+ +--R 6 4 2 +---+ | 4 2 | 4 2 +--R (32x + 312x + 504x + 216)\|- 3 \|- 64x - 48x \|- 4x - 3x +--R * +--R +---------+ +--R | 2 +--R \|- 4x - 3 +--R + +--R +-------------+ +-----------+ +--R 6 4 2 | 4 2 | 4 2 +--R (480x + 1800x + 1944x + 648)\|- 64x - 48x \|- 4x - 3x +--R Type: Expression Integer +--E 105 + +--S 106 of 324 +t0421:= 1/(-x^(3/5)+x) +--R +--R +--R 1 +--R (106) - --------- +--R 5+-+3 +--R \|x - x +--R Type: Expression Integer +--E 106 + +--S 107 of 324 +r0421:= 5/2*log(-1+x^(2/5)) +--R +--R +--R 5+-+2 +--R 5log(\|x - 1) +--R (107) --------------- +--R 2 +--R Type: Expression Integer +--E 107 + +--S 108 of 324 +a0421:= integrate(t0421,x) +--R +--R +--R 5+-+2 +--R 5log(\|x - 1) +--R (108) --------------- +--R 2 +--R Type: Union(Expression Integer,...) +--E 108 + +--S 109 of 324 +m0421:= a0421-r0421 +--R +--R +--R (109) 0 +--R Type: Expression Integer +--E 109 + +--S 110 of 324 +d0421:= D(m0421,x) +--R +--R +--R (110) 0 +--R Type: Expression Integer +--E 110 + +--S 111 of 324 +t0422:= 1/(x+x^(2^(1/2))) +--R +--R +--R 1 +--R (111) --------- +--R +-+ +--R \|2 +--R x + x +--R Type: Expression Integer +--E 111 + +--S 112 of 324 +r0422:= -log(1+x^(-2^(1/2)+1))/(2^(1/2)-1) +--R +--R +--R +-+ +--R - \|2 + 1 +--R log(x + 1) +--R (112) - -------------------- +--R +-+ +--R \|2 - 1 +--R Type: Expression Integer +--E 112 + +--S 113 of 324 +a0422:= integrate(t0422,x) +--R +--R +--R +-+ +--R +-+ \|2 log(x) +-+ +--R (113) (- \|2 - 1)log(%e + x) + (\|2 + 2)log(x) +--R Type: Union(Expression Integer,...) +--E 113 + +--S 114 of 324 +m0422:= a0422-r0422 +--R +--R +--R +-+ +-+ +--R \|2 log(x) - \|2 + 1 +-+ +--R - log(%e + x) + log(x + 1) + \|2 log(x) +--R (114) ----------------------------------------------------------- +--R +-+ +--R \|2 - 1 +--R Type: Expression Integer +--E 114 + +--S 115 of 324 +d0422:= D(m0422,x) +--R +--R +--R +-+ +-+ +-+ +-+ +--R - \|2 \|2 log(x) - \|2 + 1 - \|2 +--R - x %e + x - x x + 1 +--R (115) --------------------------------------------------- +--R +-+ +-+ +-+ +--R - \|2 + 1 \|2 log(x) - \|2 + 1 +--R (x + 1)%e + x x + x +--R Type: Expression Integer +--E 115 + +--S 116 of 324 +t0423:= 1/(-x^(1/4)+x^(1/2)) +--R +--R +--R 1 +--R (116) - ----------- +--R 4+-+ +-+ +--R \|x - \|x +--R Type: Expression Integer +--E 116 + +--S 117 of 324 +r0423:= 4*x^(1/4)+2*x^(1/2)+4*log(1-x^(1/4)) +--R +--R +--R 4+-+ 4+-+ +-+ +--R (117) 4log(- \|x + 1) + 4\|x + 2\|x +--R Type: Expression Integer +--E 117 + +--S 118 of 324 +a0423:= integrate(t0423,x) +--R +--R +--R 4+-+ 4+-+2 4+-+ +--R (118) 4log(\|x - 1) + 2\|x + 4\|x +--R Type: Union(Expression Integer,...) +--E 118 + +--S 119 of 324 +m0423:= a0423-r0423 +--R +--R +--R 4+-+ 4+-+ 4+-+2 +-+ +--R (119) 4log(\|x - 1) - 4log(- \|x + 1) + 2\|x - 2\|x +--R Type: Expression Integer +--E 119 + +--S 120 of 324 +d0423:= D(m0423,x) +--R +--R +--R 4+-+2 +-+ +--R - \|x + \|x +--R (120) -------------- +--R +-+4+-+2 +--R \|x \|x +--R Type: Expression Integer +--E 120 + +--S 121 of 324 +t0424:= 1/(x^(1/4)+x^(1/3)) +--R +--R +--R 1 +--R (121) ----------- +--R 4+-+ 3+-+ +--R \|x + \|x +--R Type: Expression Integer +--E 121 + +--S 122 of 324 +r0424:= -12*x^(1/12)+6*x^(1/6)-4*x^(1/4)+3*x^(1/3)-12/5*x^(5/12)+_ + 2*x^(1/2)-12/7*x^(7/12)+3/2*x^(2/3)+12*log(1+x^(1/12)) +--R +--R +--R (122) +--R 12+-+ 12+-+7 12+-+5 12+-+ 6+-+ 4+-+ +--R 840log( \|x + 1) - 120 \|x - 168 \|x - 840 \|x + 420\|x - 280\|x +--R + +--R 3+-+2 3+-+ +-+ +--R 105\|x + 210\|x + 140\|x +--R / +--R 70 +--R Type: Expression Integer +--E 122 + +--S 123 of 324 +a0424:= integrate(t0424,x) +--R +--R +--R (123) +--R 12+-+ 12+-+8 12+-+7 12+-+6 12+-+5 +--R 840log( \|x + 1) + 105 \|x - 120 \|x + 140 \|x - 168 \|x +--R + +--R 12+-+4 12+-+3 12+-+2 12+-+ +--R 210 \|x - 280 \|x + 420 \|x - 840 \|x +--R / +--R 70 +--R Type: Union(Expression Integer,...) +--E 123 + +--S 124 of 324 +m0424:= a0424-r0424 +--R +--R +--R (124) +--R 12+-+8 12+-+6 12+-+4 12+-+3 12+-+2 6+-+ 4+-+ +--R 3 \|x + 4 \|x + 6 \|x - 8 \|x + 12 \|x - 12\|x + 8\|x +--R + +--R 3+-+2 3+-+ +-+ +--R - 3\|x - 6\|x - 4\|x +--R / +--R 2 +--R Type: Expression Integer +--E 124 + +--S 125 of 324 +d0424:= D(m0424,x) +--R +--R +--R (125) +--R 3+-+2 +-+3+-+ +-+ 4+-+3 +-+3+-+2 6+-+5 +-+3+-+2 4+-+3 +--R (((- \|x - \|x \|x - \|x )\|x + \|x \|x )\|x - \|x \|x \|x ) +--R * +--R 12+-+10 +--R \|x +--R + +--R +-+3+-+2 4+-+3 6+-+5 12+-+6 +-+3+-+2 4+-+3 6+-+5 12+-+4 +--R \|x \|x \|x \|x \| + \|x \|x \|x \|x \|x +--R + +--R +-+3+-+2 4+-+3 6+-+5 12+-+2 +-+3+-+2 4+-+3 6+-+5 12+-+ +-+3+-+2 4+-+3 6+-+5 +--R \|x \|x \|x \|x \| - \|x \|x \|x \|x \ + \|x \|x \|x \|x +--R / +--R +-+3+-+2 4+-+3 6+-+5 12+-+10 +--R \|x \|x \|x \|x \|x +--R Type: Expression Integer +--E 125 + +--S 126 of 324 +t0425:= 1/(x^(1/3)+x^(1/2)) +--R +--R +--R 1 +--R (126) ----------- +--R 3+-+ +-+ +--R \|x + \|x +--R Type: Expression Integer +--E 126 + +--S 127 of 324 +r0425:= 6*x^(1/6)-3*x^(1/3)+2*x^(1/2)-6*log(1+x^(1/6)) +--R +--R +--R 6+-+ 6+-+ 3+-+ +-+ +--R (127) - 6log(\|x + 1) + 6\|x - 3\|x + 2\|x +--R Type: Expression Integer +--E 127 + +--S 128 of 324 +a0425:= integrate(t0425,x) +--R +--R +--R 6+-+ 6+-+3 6+-+2 6+-+ +--R (128) - 6log(\|x + 1) + 2\|x - 3\|x + 6\|x +--R Type: Union(Expression Integer,...) +--E 128 + +--S 129 of 324 +m0425:= a0425-r0425 +--R +--R +--R 6+-+3 6+-+2 3+-+ +-+ +--R (129) 2\|x - 3\|x + 3\|x - 2\|x +--R Type: Expression Integer +--E 129 + +--S 130 of 324 +d0425:= D(m0425,x) +--R +--R +--R 3+-+2 +-+ 6+-+4 +-+3+-+2 6+-+ +-+3+-+2 +--R (- \|x + \|x )\|x + \|x \|x \|x - \|x \|x +--R (130) ------------------------------------------------- +--R +-+3+-+2 6+-+4 +--R \|x \|x \|x +--R Type: Expression Integer +--E 130 + +--S 131 of 324 +t0426:= 1/(x^(1/4)+x^(1/2)) +--R +--R +--R 1 +--R (131) ----------- +--R 4+-+ +-+ +--R \|x + \|x +--R Type: Expression Integer +--E 131 + +--S 132 of 324 +r0426:= -4*x^(1/4)+2*x^(1/2)+4*log(1+x^(1/4)) +--R +--R +--R 4+-+ 4+-+ +-+ +--R (132) 4log(\|x + 1) - 4\|x + 2\|x +--R Type: Expression Integer +--E 132 + +--S 133 of 324 +a0426:= integrate(t0426,x) +--R +--R +--R 4+-+ 4+-+2 4+-+ +--R (133) 4log(\|x + 1) + 2\|x - 4\|x +--R Type: Union(Expression Integer,...) +--E 133 + +--S 134 of 324 +m0426:= a0426-r0426 +--R +--R +--R 4+-+2 +-+ +--R (134) 2\|x - 2\|x +--R Type: Expression Integer +--E 134 + +--S 135 of 324 +d0426:= D(m0426,x) +--R +--R +--R 4+-+2 +-+ +--R - \|x + \|x +--R (135) -------------- +--R +-+4+-+2 +--R \|x \|x +--R Type: Expression Integer +--E 135 + +--S 136 of 324 +t0427:= (1+x^(2/3))/(-1+x^(2/3)) +--R +--R +--R 3+-+2 +--R \|x + 1 +--R (136) --------- +--R 3+-+2 +--R \|x - 1 +--R Type: Expression Integer +--E 136 + +--S 137 of 324 +r0427:= 6*x^(1/3)+x-6*atanh(x^(1/3)) +--R +--R +--R 3+-+ 3+-+ +--R (137) - 6atanh(\|x ) + 6\|x + x +--R Type: Expression Integer +--E 137 + +--S 138 of 324 +a0427:= integrate(t0427,x) +--R +--R +--R 3+-+ 3+-+ 3+-+ +--R (138) - 3log(\|x + 1) + 3log(\|x - 1) + 6\|x + x +--R Type: Union(Expression Integer,...) +--E 138 + +--S 139 of 324 +m0427:= a0427-r0427 +--R +--R +--R 3+-+ 3+-+ 3+-+ +--R (139) - 3log(\|x + 1) + 3log(\|x - 1) + 6atanh(\|x ) +--R Type: Expression Integer +--E 139 + +--S 140 of 324 +d0427:= D(m0427,x) +--R +--R +--R (140) 0 +--R Type: Expression Integer +--E 140 + +--S 141 of 324 +t0428:= 1/((a+b*x^3)/x)^(1/2) +--R +--R +--R 1 +--R (141) ----------- +--R +--------+ +--R | 3 +--R |b x + a +--R |-------- +--R \| x +--R Type: Expression Integer +--E 141 + +--S 142 of 324 +r0428:= 2/3*atanh(b^(1/2)*x/((a+b*x^3)/x)^(1/2))/b^(1/2) +--R +--R +--R +-+ +--R x\|b +--R 2atanh(-----------) +--R +--------+ +--R | 3 +--R |b x + a +--R |-------- +--R \| x +--R (142) ------------------- +--R +-+ +--R 3\|b +--R Type: Expression Integer +--E 142 + +--S 143 of 324 +a0428:= integrate(t0428,x) +--R +--R +--R +--------+ +--R +-+ +-+ | 3 +--R |1 2 |1 |b x + a 3 +--R |- log(2b x |- |-------- - 2b x - a) +--R \|b \|b \| x +--R (143) - ----------------------------------------- +--R 3 +--R Type: Union(Expression Integer,...) +--E 143 + +--S 144 of 324 +m0428:= a0428-r0428 +--R +--R +--R (144) +--R +--------+ +--R +-+ +-+ | 3 +-+ +--R |1 +-+ 2 |1 |b x + a 3 x\|b +--R - |- \|b log(2b x |- |-------- - 2b x - a) - 2atanh(-----------) +--R \|b \|b \| x +--------+ +--R | 3 +--R |b x + a +--R |-------- +--R \| x +--R --------------------------------------------------------------------- +--R +-+ +--R 3\|b +--R Type: Expression Integer +--E 144 + +--S 145 of 324 +d0428:= D(m0428,x) +--R +--R +--R (145) 0 +--R Type: Expression Integer +--E 145 + +--S 146 of 324 +t0429:= 1/((a+b*x^4)/x^2)^(1/2) +--R +--R +--R 1 +--R (146) ----------- +--R +--------+ +--R | 4 +--R |b x + a +--R |-------- +--R | 2 +--R \| x +--R Type: Expression Integer +--E 146 + +--S 147 of 324 +r0429:= 1/2*atanh(b^(1/2)*x/((a+b*x^4)/x^2)^(1/2))/b^(1/2) +--R +--R +--R +-+ +--R x\|b +--R atanh(-----------) +--R +--------+ +--R | 4 +--R |b x + a +--R |-------- +--R | 2 +--R \| x +--R (147) ------------------ +--R +-+ +--R 2\|b +--R Type: Expression Integer +--E 147 + +--S 148 of 324 +a0429:= integrate(t0429,x) +--R +--R +--R (148) +--R +--------+ +--R +-+ +-+ 2 | 4 4 +-+ 2 +-+ +--R (\|a \|b - b x )\|b x + a + (- b x - a)\|b + b x \|a +--R log(----------------------------------------------------------) +--R +--------+ +--R +-+ | 4 +--R \|a \|b x + a - a +--R [---------------------------------------------------------------, +--R +-+ +--R 2\|b +--R +--------+ +--R +---+ | 4 +---+ +-+ +--R \|- b \|b x + a - \|- b \|a +--R atan(------------------------------) +--R 2 +--R b x +--R ------------------------------------] +--R +---+ +--R \|- b +--R Type: Union(List Expression Integer,...) +--E 148 + +--S 149 of 324 +m0429a:= a0429.1-r0429 +--R +--R +--R (149) +--R +--------+ +--R +-+ +-+ 2 | 4 4 +-+ 2 +-+ +--R (\|a \|b - b x )\|b x + a + (- b x - a)\|b + b x \|a +--R log(----------------------------------------------------------) +--R +--------+ +--R +-+ | 4 +--R \|a \|b x + a - a +--R + +--R +-+ +--R x\|b +--R - atanh(-----------) +--R +--------+ +--R | 4 +--R |b x + a +--R |-------- +--R | 2 +--R \| x +--R / +--R +-+ +--R 2\|b +--R Type: Expression Integer +--E 149 + +--S 150 of 324 +d0429a:= D(m0429a,x) +--R +--R +--R (150) +--R +--------+ +--R | 4 +--R 5 +-+ +-+ 2 7 3 |b x + a +--R ((- 3b x - 4a x)\|a \|b + b x + 4a b x ) |-------- +--R | 2 +--R \| x +--R + +--R 2 8 4 2 +-+ 2 6 2 +-+ +--R (- b x - 5a b x - 4a )\|b + (3b x + 4a b x )\|a +--R * +--R +--------+ +--R | 4 +--R \|b x + a +--R + +--R +--------+ +--R | 4 +--R 2 9 5 2 +-+ 2 7 3 +-+ |b x + a +--R ((b x + 5a b x + 4a x)\|b + (- 3b x - 4a b x )\|a ) |-------- +--R | 2 +--R \| x +--R + +--R 2 8 4 2 +-+ +-+ 3 10 2 6 2 2 +--R (3b x + 7a b x + 4a )\|a \|b - b x - 5a b x - 4a b x +--R / +--R +--------+ +--R | 4 +--R 2 8 4 2 +-+ 2 6 2 +-+ |b x + a +--R ((b x + 5a b x + 4a )\|b + (- 3b x - 4a b x )\|a ) |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 4 +--R \|b x + a +--R + +--R +--------+ +--R | 4 +--R 2 8 4 2 +-+ +-+ 3 10 2 6 2 2 |b x + a +--R ((- 3b x - 7a b x - 4a )\|a \|b + b x + 5a b x + 4a b x ) |-------- +--R | 2 +--R \| x +--R Type: Expression Integer +--E 150 + +--S 151 of 324 +m0429b:= a0429.2-r0429 +--R +--R +--R (151) +--R +--------+ +--R +-+ +---+ | 4 +---+ +-+ +--R +---+ x\|b +-+ \|- b \|b x + a - \|- b \|a +--R - \|- b atanh(-----------) + 2\|b atan(------------------------------) +--R +--------+ 2 +--R | 4 b x +--R |b x + a +--R |-------- +--R | 2 +--R \| x +--R ---------------------------------------------------------------------- +--R +---+ +-+ +--R 2\|- b \|b +--R Type: Expression Integer +--E 151 + +--S 152 of 324 +d0429b:= D(m0429b,x) +--R +--R +--R +--------+ +--R +--------+ | 4 +--R | 4 |b x + a +--R - \|b x + a + x |-------- +--R | 2 +--R \| x +--R (152) ---------------------------- +--R +--------+ +--R | 4 +--------+ +--R |b x + a | 4 +--R |-------- \|b x + a +--R | 2 +--R \| x +--R Type: Expression Integer +--E 152 + +--S 153 of 324 +t0430:= 1/((a+b*x^5)/x^3)^(1/2) +--R +--R +--R 1 +--R (153) ----------- +--R +--------+ +--R | 5 +--R |b x + a +--R |-------- +--R | 3 +--R \| x +--R Type: Expression Integer +--E 153 + +--S 154 of 324 +r0430:= 2/5*atanh(b^(1/2)*x/((a+b*x^5)/x^3)^(1/2))/b^(1/2) +--R +--R +--R +-+ +--R x\|b +--R 2atanh(-----------) +--R +--------+ +--R | 5 +--R |b x + a +--R |-------- +--R | 3 +--R \| x +--R (154) ------------------- +--R +-+ +--R 5\|b +--R Type: Expression Integer +--E 154 + +--S 155 of 324 +a0430:= integrate(t0430,x) +--R +--R +--R +--------+ +--R +-+ +-+ | 5 +--R |1 3 |1 |b x + a 5 +--R |- log(- 2b x |- |-------- + 2b x + a) +--R \|b \|b \| x +--R (155) - ------------------------------------------- +--R 5 +--R Type: Union(Expression Integer,...) +--E 155 + +--S 156 of 324 +m0430:= a0430-r0430 +--R +--R +--R (156) +--R +--------+ +--R +-+ +-+ | 5 +-+ +--R |1 +-+ 3 |1 |b x + a 5 x\|b +--R - |- \|b log(- 2b x |- |-------- + 2b x + a) - 2atanh(-----------) +--R \|b \|b \| x +--------+ +--R | 5 +--R |b x + a +--R |-------- +--R | 3 +--R \| x +--R ----------------------------------------------------------------------- +--R +-+ +--R 5\|b +--R Type: Expression Integer +--E 156 + +--S 157 of 324 +d0430:= D(m0430,x) +--R +--R +--R (157) +--R +--------+ +--------+ +--R +-+ | 5 | 5 +--R 4 |1 |b x + a 5 |b x + a +--R (- 2b x |- |-------- - 2b x - a) |-------- +--R \|b | 3 \| x +--R \| x +--R + +--R +--------+ +--R | 5 +-+ +--R 6 |b x + a 2 7 2 |1 +--R (2b x + a x) |-------- + (2b x + 2a b x ) |- +--R | 3 \|b +--R \| x +--R / +--R +--------+ +--------+ +--------+ +--R | 5 | 5 +-+ | 5 +--R 5 |b x + a |b x + a 2 7 2 |1 |b x + a +--R (2b x + a) |-------- |-------- + (- 2b x - 2a b x ) |- |-------- +--R | 3 \| x \|b | 3 +--R \| x \| x +--R Type: Expression Integer +--E 157 + +--S 158 of 324 +t0431:= 1/((a+b*x^n)/(x^(-2+n)))^(1/2) +--R +--R +--R 1 +--R (158) ----------- +--R +--------+ +--R | n +--R |b x + a +--R |-------- +--R | n - 2 +--R \| x +--R Type: Expression Integer +--E 158 + +--S 159 of 324 +r0431:= 2*atanh(b^(1/2)*x/(x^2*(x^(-n)*a+b))^(1/2))/b^(1/2)/n +--R +--R +--R +-+ +--R x\|b +--R 2atanh(------------------) +--R +---------------+ +--R | 2 - n 2 +--R \|a x x + b x +--R (159) -------------------------- +--R +-+ +--R n\|b +--R Type: Expression Integer +--E 159 + +--S 160 of 324 +a0431:= integrate(t0431,x) +--R +--R +--R (160) +--R +----------------+ +--R | n log(x) +--R n log(x) |b %e + a +-+ n log(x) +-+ +--R log(2b %e |---------------- + 2b\|b %e + a\|b ) +--R | n log(x) +--R \| %e +--R [----------------------------------------------------------------, +--R +-+ +--R n\|b +--R +----------------+ +--R | n log(x) +--R +---+ |b %e + a +--R \|- b |---------------- +--R | n log(x) +--R \| %e +--R 2atan(-------------------------) +--R b +--R --------------------------------] +--R +---+ +--R n\|- b +--R Type: Union(List Expression Integer,...) +--E 160 + +--S 161 of 324 +m0431a:= a0431.1-r0431 +--R +--R +--R (161) +--R +----------------+ +--R | n log(x) +--R n log(x) |b %e + a +-+ n log(x) +-+ +--R log(2b %e |---------------- + 2b\|b %e + a\|b ) +--R | n log(x) +--R \| %e +--R + +--R +-+ +--R x\|b +--R - 2atanh(------------------) +--R +---------------+ +--R | 2 - n 2 +--R \|a x x + b x +--R / +--R +-+ +--R n\|b +--R Type: Expression Integer +--E 161 + +--S 162 of 324 +d0431a:= D(m0431a,x) +--R +--R +--R (162) +--R +---------------+ +--R - n n log(x) | 2 - n 2 2 - n - 1 +-+ n log(x) +--R 2b x %e \|a x x + b x - 2b x x \|b %e +--R + +--R 2 - n - 1 +-+ +--R - a x x \|b +--R * +--R +----------------+ +--R | n log(x) +--R |b %e + a +--R |---------------- +--R | n log(x) +--R \| %e +--R + +--R +---------------+ +--R - n +-+ n log(x) - n +-+ | 2 - n 2 +--R (2b x \|b %e + a x \|b )\|a x x + b x +--R + +--R 2 2 - n - 1 n log(x) 2 - n - 1 +--R - 2b x x %e - 2a b x x +--R / +--R +---------------+ +--R - n +-+ n log(x) - n +-+ | 2 - n 2 +--R (2b x x \|b %e + a x x \|b )\|a x x + b x +--R * +--R +----------------+ +--R | n log(x) +--R |b %e + a +--R |---------------- +--R | n log(x) +--R \| %e +--R + +--R +---------------+ +--R 2 - n n log(x) - n | 2 - n 2 +--R (2b x x %e + 2a b x x )\|a x x + b x +--R Type: Expression Integer +--E 162 + +--S 163 of 324 +m0431b:= a0431.2-r0431 +--R +--R +--R (163) +--R +----------------+ +--R | n log(x) +--R +---+ |b %e + a +--R \|- b |---------------- +--R | n log(x) +-+ +--R +-+ \| %e +---+ x\|b +--R 2\|b atan(-------------------------) - 2\|- b atanh(------------------) +--R b +---------------+ +--R | 2 - n 2 +--R \|a x x + b x +--R ----------------------------------------------------------------------- +--R +---+ +-+ +--R n\|- b \|b +--R Type: Expression Integer +--E 163 + +--S 164 of 324 +d0431b:= D(m0431b,x) +--R +--R +--R +----------------+ +--R | n log(x) +---------------+ +--R 2 - n - 1 |b %e + a - n | 2 - n 2 +--R - x x |---------------- + x \|a x x + b x +--R | n log(x) +--R \| %e +--R (164) -------------------------------------------------------- +--R +----------------+ +--R +---------------+ | n log(x) +--R - n | 2 - n 2 |b %e + a +--R x x \|a x x + b x |---------------- +--R | n log(x) +--R \| %e +--R Type: Expression Integer +--E 164 + +--S 165 of 324 +t0432:= 1/((a-b*x^3)/x)^(1/2) +--R +--R +--R 1 +--R (165) ------------- +--R +----------+ +--R | 3 +--R |- b x + a +--R |---------- +--R \| x +--R Type: Expression Integer +--E 165 + +--S 166 of 324 +r0432:= 2/3*atan(b^(1/2)*x/((a-b*x^3)/x)^(1/2))/b^(1/2) +--R +--R +--R +-+ +--R x\|b +--R 2atan(-------------) +--R +----------+ +--R | 3 +--R |- b x + a +--R |---------- +--R \| x +--R (166) -------------------- +--R +-+ +--R 3\|b +--R Type: Expression Integer +--E 166 + +--S 167 of 324 +a0432:= integrate(t0432,x) +--R +--R +--R +----------+ +--R +---+ | 3 +---+ +--R | 1 2 |- b x + a | 1 3 +--R |- - log(- 2b x |---------- |- - + 2b x - a) +--R \| b \| x \| b +--R (167) - ------------------------------------------------- +--R 3 +--R Type: Union(Expression Integer,...) +--E 167 + +--S 168 of 324 +m0432:= a0432-r0432 +--R +--R +--R (168) +--R +----------+ +--R +---+ | 3 +---+ +--R | 1 +-+ 2 |- b x + a | 1 3 +--R - |- - \|b log(- 2b x |---------- |- - + 2b x - a) +--R \| b \| x \| b +--R + +--R +-+ +--R x\|b +--R - 2atan(-------------) +--R +----------+ +--R | 3 +--R |- b x + a +--R |---------- +--R \| x +--R / +--R +-+ +--R 3\|b +--R Type: Expression Integer +--E 168 + +--S 169 of 324 +d0432:= D(m0432,x) +--R +--R +--R (169) 0 +--R Type: Expression Integer +--E 169 + +--S 170 of 324 +t0433:= 1/((a-b*x^4)/x^2)^(1/2) +--R +--R +--R 1 +--R (170) ------------- +--R +----------+ +--R | 4 +--R |- b x + a +--R |---------- +--R | 2 +--R \| x +--R Type: Expression Integer +--E 170 + +--S 171 of 324 +r0433:= 1/2*atan(b^(1/2)*x/((a-b*x^4)/x^2)^(1/2))/b^(1/2) +--R +--R +--R +-+ +--R x\|b +--R atan(-------------) +--R +----------+ +--R | 4 +--R |- b x + a +--R |---------- +--R | 2 +--R \| x +--R (171) ------------------- +--R +-+ +--R 2\|b +--R Type: Expression Integer +--E 171 + +--S 172 of 324 +a0433:= integrate(t0433,x) +--R +--R +--R (172) +--R +----------+ +----------+ +--R | 4 +---+ 2 +-+ 4 +---+ 2 | 4 +--R (\|- b x + a \|- b - b x )\|a + (b x - a)\|- b + b x \|- b x + a +--R log(-----------------------------------------------------------------------) +--R +----------+ +--R | 4 +-+ +--R \|- b x + a \|a - a +--R [---------------------------------------------------------------------------- +--R +---+ +--R 2\|- b +--R , +--R +----------+ +--R +-+ | 4 +-+ +--R (\|a - \|- b x + a )\|b +--R atan(--------------------------) +--R 2 +--R b x +--R --------------------------------] +--R +-+ +--R \|b +--R Type: Union(List Expression Integer,...) +--E 172 + +--S 173 of 324 +m0433a:= a0433.1-r0433 +--R +--R +--R (173) +--R +-+ +--R \|b +--R * +--R log +--R +----------+ +--R | 4 +---+ 2 +-+ 4 +---+ +--R (\|- b x + a \|- b - b x )\|a + (b x - a)\|- b +--R + +--R +----------+ +--R 2 | 4 +--R b x \|- b x + a +--R / +--R +----------+ +--R | 4 +-+ +--R \|- b x + a \|a - a +--R + +--R +-+ +--R +---+ x\|b +--R - \|- b atan(-------------) +--R +----------+ +--R | 4 +--R |- b x + a +--R |---------- +--R | 2 +--R \| x +--R / +--R +---+ +-+ +--R 2\|- b \|b +--R Type: Expression Integer +--E 173 + +--S 174 of 324 +d0433a:= D(m0433a,x) +--R +--R +--R (174) +--R +----------+ +--R +----------+ | 4 +--R 5 | 4 |- b x + a 2 8 4 +--R (- 3b x + 4a x)\|- b x + a |---------- - 3b x + 7a b x +--R | 2 +--R \| x +--R + +--R 2 +--R - 4a +--R * +--R +---+ +--R \|- b +--R + +--R +----------+ +--R | 4 +----------+ +--R 2 7 3 |- b x + a 2 6 2 | 4 +--R (3b x - 4a b x ) |---------- + (- 3b x + 4a b x )\|- b x + a +--R | 2 +--R \| x +--R * +--R +-+ +--R \|a +--R + +--R +----------+ +--R | 4 +--R 2 9 5 2 |- b x + a +--R (- b x + 5a b x - 4a x) |---------- +--R | 2 +--R \| x +--R + +--R +----------+ +--R 2 8 4 2 | 4 +--R (b x - 5a b x + 4a )\|- b x + a +--R * +--R +---+ +--R \|- b +--R + +--R +----------+ +--R +----------+ | 4 +--R 2 7 3 | 4 |- b x + a 3 10 2 6 2 2 +--R (- b x + 4a b x )\|- b x + a |---------- - b x + 5a b x - 4a b x +--R | 2 +--R \| x +--R / +--R +----------+ +--R | 4 +--R 2 8 4 2 |- b x + a +---+ +--R (3b x - 7a b x + 4a ) |---------- \|- b +--R | 2 +--R \| x +--R + +--R +----------+ +--R +----------+ | 4 +--R 2 6 2 | 4 |- b x + a +--R (3b x - 4a b x )\|- b x + a |---------- +--R | 2 +--R \| x +--R * +--R +-+ +--R \|a +--R + +--R +----------+ +--R +----------+ | 4 +--R 2 8 4 2 | 4 |- b x + a +---+ +--R (- b x + 5a b x - 4a )\|- b x + a |---------- \|- b +--R | 2 +--R \| x +--R + +--R +----------+ +--R | 4 +--R 3 10 2 6 2 2 |- b x + a +--R (b x - 5a b x + 4a b x ) |---------- +--R | 2 +--R \| x +--R Type: Expression Integer +--E 174 + +--S 175 of 324 +m0433b:= a0433.2-r0433 +--R +--R +--R +----------+ +--R +-+ | 4 +-+ +-+ +--R (\|a - \|- b x + a )\|b x\|b +--R 2atan(--------------------------) - atan(-------------) +--R 2 +----------+ +--R b x | 4 +--R |- b x + a +--R |---------- +--R | 2 +--R \| x +--R (175) ------------------------------------------------------- +--R +-+ +--R 2\|b +--R Type: Expression Integer +--E 175 + +--S 176 of 324 +d0433b:= D(m0433b,x) +--R +--R +--R +----------+ +--R | 4 +----------+ +--R |- b x + a | 4 +--R x |---------- - \|- b x + a +--R | 2 +--R \| x +--R (176) ------------------------------ +--R +----------+ +--R +----------+ | 4 +--R | 4 |- b x + a +--R \|- b x + a |---------- +--R | 2 +--R \| x +--R Type: Expression Integer +--E 176 + +--S 177 of 324 +t0434:= 1/((a-b*x^5)/x^3)^(1/2) +--R +--R +--R 1 +--R (177) ------------- +--R +----------+ +--R | 5 +--R |- b x + a +--R |---------- +--R | 3 +--R \| x +--R Type: Expression Integer +--E 177 + +--S 178 of 324 +r0434:= 2/5*atan(b^(1/2)*x/((a-b*x^5)/x^3)^(1/2))/b^(1/2) +--R +--R +--R +-+ +--R x\|b +--R 2atan(-------------) +--R +----------+ +--R | 5 +--R |- b x + a +--R |---------- +--R | 3 +--R \| x +--R (178) -------------------- +--R +-+ +--R 5\|b +--R Type: Expression Integer +--E 178 + +--S 179 of 324 +a0434:= integrate(t0434,x) +--R +--R +--R +----------+ +--R +---+ | 5 +---+ +--R | 1 3 |- b x + a | 1 5 +--R |- - log(2b x |---------- |- - - 2b x + a) +--R \| b \| x \| b +--R (179) - ----------------------------------------------- +--R 5 +--R Type: Union(Expression Integer,...) +--E 179 + +--S 180 of 324 +m0434:= a0434-r0434 +--R +--R +--R (180) +--R +----------+ +--R +---+ | 5 +---+ +-+ +--R | 1 +-+ 3 |- b x + a | 1 5 x\|b +--R - |- - \|b log(2b x |---------- |- - - 2b x + a) - 2atan(-------------) +--R \| b \| x \| b +----------+ +--R | 5 +--R |- b x + a +--R |---------- +--R | 3 +--R \| x +--R ---------------------------------------------------------------------------- +--R +-+ +--R 5\|b +--R Type: Expression Integer +--E 180 + +--S 181 of 324 +d0434:= D(m0434,x) +--R +--R +--R (181) +--R +----------+ +----------+ +--R | 5 | 5 +---+ +--R 4 |- b x + a |- b x + a 2 7 2 | 1 +--R (- 2b x |---------- |---------- - 2b x + 2a b x ) |- - +--R \| x | 3 \| b +--R \| x +--R + +--R +----------+ +----------+ +--R | 5 | 5 +--R 6 |- b x + a 5 |- b x + a +--R (2b x - a x) |---------- + (- 2b x + a) |---------- +--R | 3 \| x +--R \| x +--R / +--R +----------+ +--R | 5 +---+ +--R 2 7 2 |- b x + a | 1 +--R (2b x - 2a b x ) |---------- |- - +--R | 3 \| b +--R \| x +--R + +--R +----------+ +----------+ +--R | 5 | 5 +--R 5 |- b x + a |- b x + a +--R (2b x - a) |---------- |---------- +--R \| x | 3 +--R \| x +--R Type: Expression Integer +--E 181 + +--S 182 of 324 +t0435:= 1/((a-b*x^n)/(x^(-2+n)))^(1/2) +--R +--R +--R 1 +--R (182) ------------- +--R +----------+ +--R | n +--R |- b x + a +--R |---------- +--R | n - 2 +--R \| x +--R Type: Expression Integer +--E 182 + +--S 183 of 324 +r0435:= 2*atan(b^(1/2)*x/(x^2*(x^(-n)*a-b))^(1/2))/b^(1/2)/n +--R +--R +--R +-+ +--R x\|b +--R 2atan(------------------) +--R +---------------+ +--R | 2 - n 2 +--R \|a x x - b x +--R (183) ------------------------- +--R +-+ +--R n\|b +--R Type: Expression Integer +--E 183 + +--S 184 of 324 +a0435:= integrate(t0435,x) +--R +--R +--R (184) +--R +------------------+ +--R | n log(x) +--R n log(x) |- b %e + a +---+ n log(x) +---+ +--R log(- 2b %e |------------------ - 2b\|- b %e + a\|- b ) +--R | n log(x) +--R \| %e +--R [------------------------------------------------------------------------, +--R +---+ +--R n\|- b +--R +------------------+ +--R | n log(x) +--R +-+ |- b %e + a +--R \|b |------------------ +--R | n log(x) +--R \| %e +--R 2atan(-------------------------) +--R b +--R - --------------------------------] +--R +-+ +--R n\|b +--R Type: Union(List Expression Integer,...) +--E 184 + +--S 185 of 324 +m0435a:= a0435.1-r0435 +--R +--R +--R (185) +--R +-+ +--R \|b +--R * +--R +------------------+ +--R | n log(x) +--R n log(x) |- b %e + a +---+ n log(x) +---+ +--R log(- 2b %e |------------------ - 2b\|- b %e + a\|- b ) +--R | n log(x) +--R \| %e +--R + +--R +-+ +--R +---+ x\|b +--R - 2\|- b atan(------------------) +--R +---------------+ +--R | 2 - n 2 +--R \|a x x - b x +--R / +--R +---+ +-+ +--R n\|- b \|b +--R Type: Expression Integer +--E 185 + +--S 186 of 324 +d0435a:= D(m0435a,x) +--R +--R +--R (186) +--R +---------------+ +--R - n n log(x) | 2 - n 2 2 - n - 1 +---+ n log(x) +--R 2b x %e \|a x x - b x - 2b x x \|- b %e +--R + +--R 2 - n - 1 +---+ +--R a x x \|- b +--R * +--R +------------------+ +--R | n log(x) +--R |- b %e + a +--R |------------------ +--R | n log(x) +--R \| %e +--R + +--R +---------------+ +--R - n +---+ n log(x) - n +---+ | 2 - n 2 +--R (2b x \|- b %e - a x \|- b )\|a x x - b x +--R + +--R 2 2 - n - 1 n log(x) 2 - n - 1 +--R 2b x x %e - 2a b x x +--R / +--R +---------------+ +--R - n +---+ n log(x) - n +---+ | 2 - n 2 +--R (2b x x \|- b %e - a x x \|- b )\|a x x - b x +--R * +--R +------------------+ +--R | n log(x) +--R |- b %e + a +--R |------------------ +--R | n log(x) +--R \| %e +--R + +--R +---------------+ +--R 2 - n n log(x) - n | 2 - n 2 +--R (- 2b x x %e + 2a b x x )\|a x x - b x +--R Type: Expression Integer +--E 186 + +--S 187 of 324 +m0435b:= a0435.2-r0435 +--R +--R +--R +------------------+ +--R | n log(x) +--R +-+ |- b %e + a +--R \|b |------------------ +--R | n log(x) +-+ +--R \| %e x\|b +--R - 2atan(-------------------------) - 2atan(------------------) +--R b +---------------+ +--R | 2 - n 2 +--R \|a x x - b x +--R (187) -------------------------------------------------------------- +--R +-+ +--R n\|b +--R Type: Expression Integer +--E 187 + +--S 188 of 324 +d0435b:= D(m0435b,x) +--R +--R +--R +------------------+ +--R | n log(x) +---------------+ +--R 2 - n - 1 |- b %e + a - n | 2 - n 2 +--R - x x |------------------ + x \|a x x - b x +--R | n log(x) +--R \| %e +--R (188) ---------------------------------------------------------- +--R +------------------+ +--R +---------------+ | n log(x) +--R - n | 2 - n 2 |- b %e + a +--R x x \|a x x - b x |------------------ +--R | n log(x) +--R \| %e +--R Type: Expression Integer +--E 188 + +--S 189 of 324 +t0436:= ((a+b*x^2)/x^2)^(1/2) +--R +--R +--R +--------+ +--R | 2 +--R |b x + a +--R (189) |-------- +--R | 2 +--R \| x +--R Type: Expression Integer +--E 189 + +--S 190 of 324 +r0436:= (b+a/x^2)^(1/2)*x-a^(1/2)*atanh((b+a/x^2)^(1/2)*x/a^(1/2)) +--R +--R +--R +--------+ +--R | 2 +--R |b x + a +--R x |-------- +--------+ +--R | 2 | 2 +--R +-+ \| x |b x + a +--R (190) - \|a atanh(------------) + x |-------- +--R +-+ | 2 +--R \|a \| x +--R Type: Expression Integer +--E 190 + +--S 191 of 324 +a0436:= integrate(t0436,x) +--R +--R +--R +--------+ +--R +--------+ | 2 +-+ +--R | 2 +-+ \|b x + a - \|a 2 +-+ +--R (a\|b x + a - a\|a )log(------------------) + b x \|a +--R x +--R (191) -------------------------------------------------------- +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R Type: Union(Expression Integer,...) +--E 191 + +--S 192 of 324 +m0436:= a0436-r0436 +--R +--R +--R (192) +--R +--------+ +--R +--------+ | 2 +-+ +--R | 2 +-+ \|b x + a - \|a +--R (a\|b x + a - a\|a )log(------------------) +--R x +--R + +--R +--------+ +--R | 2 +--R |b x + a +--R x |-------- +--------+ +--R +--------+ | 2 | 2 +--------+ +--R | 2 +-+ \| x +-+ |b x + a | 2 +--R (a\|b x + a - a\|a )atanh(------------) - x\|a |-------- \|b x + a +--R +-+ | 2 +--R \|a \| x +--R + +--R +--------+ +--R | 2 +--R |b x + a 2 +-+ +--R a x |-------- + b x \|a +--R | 2 +--R \| x +--R / +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R Type: Expression Integer +--E 192 + +--S 193 of 324 +d0436:= D(m0436,x) +--R +--R +--R (193) +--R +--------+ +--R | 2 +--R 2 5 3 2 |b x + a 2 4 2 2 +-+ +--R ((- b x - 5a b x - 4a x) |-------- + (- 3b x - 7a b x - 4a )\|a ) +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R +--------+ +--R | 2 +--R 2 5 3 2 +-+ |b x + a 3 6 2 4 2 2 3 +--R (3b x + 7a b x + 4a x)\|a |-------- + b x + 6a b x + 9a b x + 4a +--R | 2 +--R \| x +--R / +--R +--------+ +--R | 2 +--------+ +--R 4 2 +-+ |b x + a | 2 +--R (3b x + 4a x )\|a |-------- \|b x + a +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 2 6 4 2 2 |b x + a +--R (- b x - 5a b x - 4a x ) |-------- +--R | 2 +--R \| x +--R Type: Expression Integer +--E 193 + +--S 194 of 324 +t0437:= ((a+b*x^n)/x^2)^(1/2) +--R +--R +--R +--------+ +--R | n +--R |b x + a +--R (194) |-------- +--R | 2 +--R \| x +--R Type: Expression Integer +--E 194 + +--S 195 of 324 +r0437:= 2*x*((a+b*x^n)/x^2)^(1/2)*((a+b*x^n)^(1/2)-a^(1/2)*_ + atanh((a+b*x^n)^(1/2)/a^(1/2)))/n/(a+b*x^n)^(1/2) +--R +--R +--R +--------+ +--------+ +--------+ +--R | n | n | n +--------+ +--R +-+ |b x + a \|b x + a |b x + a | n +--R - 2x\|a |-------- atanh(-----------) + 2x |-------- \|b x + a +--R | 2 +-+ | 2 +--R \| x \|a \| x +--R (195) ---------------------------------------------------------------- +--R +--------+ +--R | n +--R n\|b x + a +--R Type: Expression Integer +--E 195 + +--S 196 of 324 +a0437:= integrate(t0437,x) +--R +--R +--R (196) +--R [ +--R +----------------+ +--R +-+ | n log(x) n log(x) +--R +-+ - 2\|a \|b %e + a + b %e + 2a +--R \|a log(----------------------------------------------) +--R n log(x) +--R %e +--R + +--R +----------------+ +--R | n log(x) +--R 2\|b %e + a +--R / +--R n +--R , +--R +----------------+ +--R | n log(x) +----------------+ +--R +---+ \|b %e + a | n log(x) +--R - 2\|- a atan(-------------------) + 2\|b %e + a +--R +---+ +--R \|- a +--R ---------------------------------------------------------] +--R n +--R Type: Union(List Expression Integer,...) +--E 196 + +--S 197 of 324 +m0437a:= a0437.1-r0437 +--R +--R +--R (197) +--R +----------------+ +--R +--------+ +-+ | n log(x) n log(x) +--R +-+ | n - 2\|a \|b %e + a + b %e + 2a +--R \|a \|b x + a log(----------------------------------------------) +--R n log(x) +--R %e +--R + +--R +--------+ +--------+ +--R +--------+ +----------------+ | n | n +--R | n | n log(x) +-+ |b x + a \|b x + a +--R 2\|b x + a \|b %e + a + 2x\|a |-------- atanh(-----------) +--R | 2 +-+ +--R \| x \|a +--R + +--R +--------+ +--R | n +--------+ +--R |b x + a | n +--R - 2x |-------- \|b x + a +--R | 2 +--R \| x +--R / +--R +--------+ +--R | n +--R n\|b x + a +--R Type: Expression Integer +--E 197 + +--S 198 of 324 +d0437a:= D(m0437a,x) +--R +--R +--R (198) +--R +--------+ +--R | n +--R n n log(x) n |b x + a +--R (- b x %e - 2a x ) |-------- +--R | 2 +--R \| x +--R + +--R n - 1 n n - 1 +-+ +--R (- 2b x x - 2a x )\|a +--R * +--R +----------------+ +--R | n log(x) +--R \|b %e + a +--R + +--R +--------+ +--R | n +--R n +-+ n log(x) n +-+ |b x + a +--R (2b x \|a %e + 2a x \|a ) |-------- +--R | 2 +--R \| x +--R + +--R 2 n - 1 n n - 1 n log(x) n - 1 n 2 n - 1 +--R (b x x + a b x )%e + 2a b x x + 2a x +--R / +--R +--------+ +--R | n +----------------+ +--R n +-+ |b x + a | n log(x) +--R 2x x \|a |-------- \|b %e + a +--R | 2 +--R \| x +--R + +--R +--------+ +--R | n +--R n n log(x) n |b x + a +--R (- b x x %e - 2a x x ) |-------- +--R | 2 +--R \| x +--R Type: Expression Integer +--E 198 + +--S 199 of 324 +m0437b:= a0437.2-r0437 +--R +--R +--R (199) +--R +----------------+ +--R +--------+ | n log(x) +--R +---+ | n \|b %e + a +--R - 2\|- a \|b x + a atan(-------------------) +--R +---+ +--R \|- a +--R + +--R +--------+ +--------+ +--R +--------+ +----------------+ | n | n +--R | n | n log(x) +-+ |b x + a \|b x + a +--R 2\|b x + a \|b %e + a + 2x\|a |-------- atanh(-----------) +--R | 2 +-+ +--R \| x \|a +--R + +--R +--------+ +--R | n +--------+ +--R |b x + a | n +--R - 2x |-------- \|b x + a +--R | 2 +--R \| x +--R / +--R +--------+ +--R | n +--R n\|b x + a +--R Type: Expression Integer +--E 199 + +--S 200 of 324 +d0437b:= D(m0437b,x) +--R +--R +--R (200) +--R +----------------+ +--R n - 1 n n - 1 | n log(x) +--R (- b x x - a x )\|b %e + a +--R + +--R +--------+ +--R | n +--R n n log(x) n |b x + a +--R (b x %e + a x ) |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R | n +----------------+ +--R n |b x + a | n log(x) +--R x x |-------- \|b %e + a +--R | 2 +--R \| x +--R Type: Expression Integer +--E 200 + +--S 201 of 324 +t0438:= ((-a+b*x^2)/x^2)^(1/2) +--R +--R +--R +--------+ +--R | 2 +--R |b x - a +--R (201) |-------- +--R | 2 +--R \| x +--R Type: Expression Integer +--E 201 + +--S 202 of 324 +r0438:= (b-a/x^2)^(1/2)*x-a^(1/2)*atan((b-a/x^2)^(1/2)*x/a^(1/2)) +--R +--R +--R +--------+ +--R | 2 +--R |b x - a +--R x |-------- +--------+ +--R | 2 | 2 +--R +-+ \| x |b x - a +--R (202) - \|a atan(------------) + x |-------- +--R +-+ | 2 +--R \|a \| x +--R Type: Expression Integer +--E 202 + +--S 203 of 324 +a0438:= integrate(t0438,x) +--R +--R +--R +--------+ +--R +--------+ | 2 +---+ +--R | 2 +---+ \|b x - a - \|- a 2 +---+ +--R (- a\|b x - a + a\|- a )log(--------------------) + b x \|- a +--R x +--R (203) ---------------------------------------------------------------- +--R +--------+ +--R +---+ | 2 +--R \|- a \|b x - a + a +--R Type: Union(Expression Integer,...) +--E 203 + +--S 204 of 324 +m0438:= a0438-r0438 +--R +--R +--R (204) +--R +--------+ +--R +--------+ | 2 +---+ +--R | 2 +---+ \|b x - a - \|- a +--R (- a\|b x - a + a\|- a )log(--------------------) +--R x +--R + +--R +--------+ +--R | 2 +--R |b x - a +--R x |-------- +--R +--------+ | 2 +--R +---+ +-+ | 2 +-+ \| x +--R (\|- a \|a \|b x - a + a\|a )atan(------------) +--R +-+ +--R \|a +--R + +--R +--------+ +--------+ +--R | 2 +--------+ | 2 +--R +---+ |b x - a | 2 |b x - a 2 +---+ +--R - x\|- a |-------- \|b x - a - a x |-------- + b x \|- a +--R | 2 | 2 +--R \| x \| x +--R / +--R +--------+ +--R +---+ | 2 +--R \|- a \|b x - a + a +--R Type: Expression Integer +--E 204 + +--S 205 of 324 +d0438:= D(m0438,x) +--R +--R +--R (205) +--R +--------+ +--R | 2 +--R 2 5 3 2 |b x - a +--R (- b x + 5a b x - 4a x) |-------- +--R | 2 +--R \| x +--R + +--R 2 4 2 2 +---+ +--R (- 3b x + 7a b x - 4a )\|- a +--R * +--R +--------+ +--R | 2 +--R \|b x - a +--R + +--R +--------+ +--R | 2 +--R 2 5 3 2 +---+ |b x - a 3 6 2 4 2 2 3 +--R (3b x - 7a b x + 4a x)\|- a |-------- + b x - 6a b x + 9a b x - 4a +--R | 2 +--R \| x +--R / +--R +--------+ +--R | 2 +--------+ +--R 4 2 +---+ |b x - a | 2 +--R (3b x - 4a x )\|- a |-------- \|b x - a +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 2 6 4 2 2 |b x - a +--R (- b x + 5a b x - 4a x ) |-------- +--R | 2 +--R \| x +--R Type: Expression Integer +--E 205 + +--S 206 of 324 +t0439:= ((-a+b*x^n)/x^2)^(1/2) +--R +--R +--R +--------+ +--R | n +--R |b x - a +--R (206) |-------- +--R | 2 +--R \| x +--R Type: Expression Integer +--E 206 + +--S 207 of 324 +r0439:= 2*x*(-(a-b*x^n)/x^2)^(1/2)*((-a+b*x^n)^(1/2)-a^(1/2)*_ + atan((-a+b*x^n)^(1/2)/a^(1/2)))/n/(-a+b*x^n)^(1/2) +--R +--R +--R +--------+ +--------+ +--------+ +--R | n | n | n +--------+ +--R +-+ |b x - a \|b x - a |b x - a | n +--R - 2x\|a |-------- atan(-----------) + 2x |-------- \|b x - a +--R | 2 +-+ | 2 +--R \| x \|a \| x +--R (207) --------------------------------------------------------------- +--R +--------+ +--R | n +--R n\|b x - a +--R Type: Expression Integer +--E 207 + +--S 208 of 324 +a0439:= integrate(t0439,x) +--R +--R +--R (208) +--R [ +--R +----------------+ +--R +---+ | n log(x) n log(x) +--R +---+ - 2\|- a \|b %e - a + b %e - 2a +--R \|- a log(------------------------------------------------) +--R n log(x) +--R %e +--R + +--R +----------------+ +--R | n log(x) +--R 2\|b %e - a +--R / +--R n +--R , +--R +----------------+ +--R | n log(x) +----------------+ +--R +-+ \|b %e - a | n log(x) +--R - 2\|a atan(-------------------) + 2\|b %e - a +--R +-+ +--R \|a +--R -------------------------------------------------------] +--R n +--R Type: Union(List Expression Integer,...) +--E 208 + +--S 209 of 324 +m0439a:= a0439.1-r0439 +--R +--R +--R (209) +--R +----------------+ +--R +--------+ +---+ | n log(x) n log(x) +--R +---+ | n - 2\|- a \|b %e - a + b %e - 2a +--R \|- a \|b x - a log(------------------------------------------------) +--R n log(x) +--R %e +--R + +--R +--------+ +--------+ +--R +--------+ +----------------+ | n | n +--R | n | n log(x) +-+ |b x - a \|b x - a +--R 2\|b x - a \|b %e - a + 2x\|a |-------- atan(-----------) +--R | 2 +-+ +--R \| x \|a +--R + +--R +--------+ +--R | n +--------+ +--R |b x - a | n +--R - 2x |-------- \|b x - a +--R | 2 +--R \| x +--R / +--R +--------+ +--R | n +--R n\|b x - a +--R Type: Expression Integer +--E 209 + +--S 210 of 324 +d0439a:= D(m0439a,x) +--R +--R +--R (210) +--R +--------+ +--R | n +--R n n log(x) n |b x - a +--R (- b x %e + 2a x ) |-------- +--R | 2 +--R \| x +--R + +--R n - 1 n n - 1 +---+ +--R (- 2b x x + 2a x )\|- a +--R * +--R +----------------+ +--R | n log(x) +--R \|b %e - a +--R + +--R +--------+ +--R | n +--R n +---+ n log(x) n +---+ |b x - a +--R (2b x \|- a %e - 2a x \|- a ) |-------- +--R | 2 +--R \| x +--R + +--R 2 n - 1 n n - 1 n log(x) n - 1 n 2 n - 1 +--R (b x x - a b x )%e - 2a b x x + 2a x +--R / +--R +--------+ +--R | n +----------------+ +--R n +---+ |b x - a | n log(x) +--R 2x x \|- a |-------- \|b %e - a +--R | 2 +--R \| x +--R + +--R +--------+ +--R | n +--R n n log(x) n |b x - a +--R (- b x x %e + 2a x x ) |-------- +--R | 2 +--R \| x +--R Type: Expression Integer +--E 210 + +--S 211 of 324 +m0439b:= a0439.2-r0439 +--R +--R +--R (211) +--R +----------------+ +--R +--------+ | n log(x) +--R +-+ | n \|b %e - a +--R - 2\|a \|b x - a atan(-------------------) +--R +-+ +--R \|a +--R + +--R +--------+ +--------+ +--R +--------+ +----------------+ | n | n +--R | n | n log(x) +-+ |b x - a \|b x - a +--R 2\|b x - a \|b %e - a + 2x\|a |-------- atan(-----------) +--R | 2 +-+ +--R \| x \|a +--R + +--R +--------+ +--R | n +--------+ +--R |b x - a | n +--R - 2x |-------- \|b x - a +--R | 2 +--R \| x +--R / +--R +--------+ +--R | n +--R n\|b x - a +--R Type: Expression Integer +--E 211 + +--S 212 of 324 +d0439b:= D(m0439b,x) +--R +--R +--R (212) +--R +----------------+ +--R n - 1 n n - 1 | n log(x) +--R (- b x x + a x )\|b %e - a +--R + +--R +--------+ +--R | n +--R n n log(x) n |b x - a +--R (b x %e - a x ) |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R | n +----------------+ +--R n |b x - a | n log(x) +--R x x |-------- \|b %e - a +--R | 2 +--R \| x +--R Type: Expression Integer +--E 212 + +--S 213 of 324 +t0440:= ((a+x)/(a-x))^(1/2) +--R +--R +--R +-------+ +--R |- x - a +--R (213) |------- +--R \| x - a +--R Type: Expression Integer +--E 213 + +--S 214 of 324 +r0440:= (-a+x)*((a+x)/(a-x))^(1/2)+2*a*atan(((a+x)/(a-x))^(1/2)) +--R +--R +--R +-------+ +-------+ +--R |- x - a |- x - a +--R (214) 2a atan( |------- ) + (x - a) |------- +--R \| x - a \| x - a +--R Type: Expression Integer +--E 214 + +--S 215 of 324 +a0440:= integrate(t0440,x) +--R +--R +--R +-------+ +-------+ +--R |- x - a |- x - a +--R (215) 2a atan( |------- ) + (x - a) |------- +--R \| x - a \| x - a +--R Type: Union(Expression Integer,...) +--E 215 + +--S 216 of 324 +m0440:= a0440-r0440 +--R +--R +--R (216) 0 +--R Type: Expression Integer +--E 216 + +--S 217 of 324 +d0440:= D(m0440,x) +--R +--R +--R (217) 0 +--R Type: Expression Integer +--E 217 + +--S 218 of 324 +t0441:= ((-a+x)/(a+x))^(1/2) +--R +--R +--R +-----+ +--R |x - a +--R (218) |----- +--R \|x + a +--R Type: Expression Integer +--E 218 + +--S 219 of 324 +r0441:= (-(a-x)/(a+x))^(1/2)*(a+x)-2*a*atanh((-(a-x)/(a+x))^(1/2)) +--R +--R +--R +-----+ +-----+ +--R |x - a |x - a +--R (219) - 2a atanh( |----- ) + (x + a) |----- +--R \|x + a \|x + a +--R Type: Expression Integer +--E 219 + +--S 220 of 324 +a0441:= integrate(t0441,x) +--R +--R +--R +-----+ +-----+ +-----+ +--R |x - a |x - a |x - a +--R (220) - a log( |----- + 1) + a log( |----- - 1) + (x + a) |----- +--R \|x + a \|x + a \|x + a +--R Type: Union(Expression Integer,...) +--E 220 + +--S 221 of 324 +m0441:= a0441-r0441 +--R +--R +--R +-----+ +-----+ +-----+ +--R |x - a |x - a |x - a +--R (221) - a log( |----- + 1) + a log( |----- - 1) + 2a atanh( |----- ) +--R \|x + a \|x + a \|x + a +--R Type: Expression Integer +--E 221 + +--S 222 of 324 +d0441:= D(m0441,x) +--R +--R +--R (222) 0 +--R Type: Expression Integer +--E 222 + +--S 223 of 324 +t0442:= ((a+b*x)/(c+d*x))^(1/2) +--R +--R +--R +-------+ +--R |b x + a +--R (223) |------- +--R \|d x + c +--R Type: Expression Integer +--E 223 + +--S 224 of 324 +r0442:= ((a+b*x)/(c+d*x))^(1/2)*(c+d*x)/d-(b*c-a*d)*_ + atanh(d^(1/2)*((a+b*x)/(c+d*x))^(1/2)/b^(1/2))/b^(1/2)/d^(3/2) +--R +--R +--R +-------+ +--R |b x + a +-+ +--R |------- \|d +-------+ +--R \|d x + c |b x + a +-+ +-+ +--R (a d - b c)atanh(--------------) + (d x + c) |------- \|b \|d +--R +-+ \|d x + c +--R \|b +--R (224) -------------------------------------------------------------- +--R +-+ +-+ +--R d\|b \|d +--R Type: Expression Integer +--E 224 + +--S 225 of 324 +a0442:= integrate(t0442,x) +--R +--R +--R (225) +--R [ +--R (a d - b c) +--R * +--R +-------+ +--R +---+ 2 |b x + a +--R log((2b d x + a d + b c)\|b d + (2b d x + 2b c d) |------- ) +--R \|d x + c +--R + +--R +-------+ +--R |b x + a +---+ +--R (2d x + 2c) |------- \|b d +--R \|d x + c +--R / +--R +---+ +--R 2d\|b d +--R , +--R +-------+ +--R +-----+ |b x + a +--R \|- b d |------- +-------+ +--R \|d x + c +-----+ |b x + a +--R (a d - b c)atan(------------------) + (d x + c)\|- b d |------- +--R b \|d x + c +--R -----------------------------------------------------------------] +--R +-----+ +--R d\|- b d +--R Type: Union(List Expression Integer,...) +--E 225 + +--S 226 of 324 +m0442a:= a0442.1-r0442 +--R +--R +--R (226) +--R +-+ +-+ +--R (a d - b c)\|b \|d +--R * +--R +-------+ +--R +---+ 2 |b x + a +--R log((2b d x + a d + b c)\|b d + (2b d x + 2b c d) |------- ) +--R \|d x + c +--R + +--R +-------+ +--R |b x + a +-+ +--R |------- \|d +--R +---+ \|d x + c +--R (- 2a d + 2b c)\|b d atanh(--------------) +--R +-+ +--R \|b +--R / +--R +-+ +-+ +---+ +--R 2d\|b \|d \|b d +--R Type: Expression Integer +--E 226 + +--S 227 of 324 +d0442a:= D(m0442a,x) +--R +--R +--R (227) 0 +--R Type: Expression Integer +--E 227 + +--S 228 of 324 +m0442b:= a0442.2-r0442 +--R +--R +--R (228) +--R +-------+ +--R |b x + a +-+ +--R |------- \|d +--R +-----+ \|d x + c +--R (- a d + b c)\|- b d atanh(--------------) +--R +-+ +--R \|b +--R + +--R +-------+ +--R +-----+ |b x + a +--R \|- b d |------- +--R +-+ +-+ \|d x + c +--R (a d - b c)\|b \|d atan(------------------) +--R b +--R / +--R +-----+ +-+ +-+ +--R d\|- b d \|b \|d +--R Type: Expression Integer +--E 228 + +--S 229 of 324 +d0442b:= D(m0442b,x) +--R +--R +--R (229) 0 +--R Type: Expression Integer +--E 229 + +--S 230 of 324 +t0443:= ((-1+5*x)/(1+7*x))^(1/2)/x^2 +--R +--R +--R +------+ +--R |5x - 1 +--R |------ +--R \|7x + 1 +--R (230) --------- +--R 2 +--R x +--R Type: Expression Integer +--E 230 + +--S 231 of 324 +r0443:= -(-(1-5*x)/(1+7*x))^(1/2)*(1+7*x)/x+12*atan((-(1-5*x)/(1+7*x))^(1/2)) +--R +--R +--R +------+ +------+ +--R |5x - 1 |5x - 1 +--R 12x atan( |------ ) + (- 7x - 1) |------ +--R \|7x + 1 \|7x + 1 +--R (231) ----------------------------------------- +--R x +--R Type: Expression Integer +--E 231 + +--S 232 of 324 +a0443:= integrate(t0443,x) +--R +--R +--R +------+ +------+ +--R |5x - 1 |5x - 1 +--R 12x atan( |------ ) + (- 7x - 1) |------ +--R \|7x + 1 \|7x + 1 +--R (232) ----------------------------------------- +--R x +--R Type: Union(Expression Integer,...) +--E 232 + +--S 233 of 324 +m0443:= a0443-r0443 +--R +--R +--R (233) 0 +--R Type: Expression Integer +--E 233 + +--S 234 of 324 +d0443:= D(m0443,x) +--R +--R +--R (234) 0 +--R Type: Expression Integer +--E 234 + +--S 235 of 324 +t0444:= ((-1+x)/(5+3*x))^(1/2) +--R +--R +--R +------+ +--R | x - 1 +--R (235) |------ +--R \|3x + 5 +--R Type: Expression Integer +--E 235 + +--S 236 of 324 +r0444:= 1/3*(-(1-x)/(5+3*x))^(1/2)*(5+3*x)-8/9*_ + atanh(3^(1/2)*(-(1-x)/(5+3*x))^(1/2))*3^(1/2) +--R +--R +--R +------+ +------+ +--R +-+ +-+ | x - 1 | x - 1 +--R - 8\|3 atanh(\|3 |------ ) + (9x + 15) |------ +--R \|3x + 5 \|3x + 5 +--R (236) ------------------------------------------------ +--R 9 +--R Type: Expression Integer +--E 236 + +--S 237 of 324 +a0444:= integrate(t0444,x) +--R +--R +--R +------+ +------+ +--R | x - 1 +-+ +-+ | x - 1 +--R 4log((9x + 15) |------ + (- 3x - 1)\|3 ) + (3x + 5)\|3 |------ +--R \|3x + 5 \|3x + 5 +--R (237) ----------------------------------------------------------------- +--R +-+ +--R 3\|3 +--R Type: Union(Expression Integer,...) +--E 237 + +--S 238 of 324 +m0444:= a0444-r0444 +--R +--R +--R +------+ +------+ +--R | x - 1 +-+ +-+ | x - 1 +--R 4log((9x + 15) |------ + (- 3x - 1)\|3 ) + 8atanh(\|3 |------ ) +--R \|3x + 5 \|3x + 5 +--R (238) ----------------------------------------------------------------- +--R +-+ +--R 3\|3 +--R Type: Expression Integer +--E 238 + +--S 239 of 324 +d0444:= D(m0444,x) +--R +--R +--R (239) 0 +--R Type: Expression Integer +--E 239 + +--S 240 of 324 +t0445:= (1-x^(1/2))/(1+x^(1/4)) +--R +--R +--R +-+ +--R - \|x + 1 +--R (240) ---------- +--R 4+-+ +--R \|x + 1 +--R Type: Expression Integer +--E 240 + +--S 241 of 324 +r0445:= x-4/5*x^(5/4) +--R +--R +--R 4+-+ +--R - 4x\|x + 5x +--R (241) ------------- +--R 5 +--R Type: Expression Integer +--E 241 + +--S 242 of 324 +a0445:= integrate(t0445,x) +--R +--R +--R 4+-+ +--R - 4x\|x + 5x +--R (242) ------------- +--R 5 +--R Type: Union(Expression Integer,...) +--E 242 + +--S 243 of 324 +m0445:= a0445-r0445 +--R +--R +--R (243) 0 +--R Type: Expression Integer +--E 243 + +--S 244 of 324 +d0445:= D(m0445,x) +--R +--R +--R (244) 0 +--R Type: Expression Integer +--E 244 + +--S 245 of 324 +t0446:= (x^6)^(1/2)/x/(1-x^4) +--R +--R +--R +--+ +--R | 6 +--R \|x +--R (245) - ------ +--R 5 +--R x - x +--R Type: Expression Integer +--E 245 + +--S 246 of 324 +r0446:= -1/2*cos(x^3)*(atan(x)-atanh(x)) +--R +--R +--R 3 +--R (atanh(x) - atan(x))cos(x ) +--R (246) --------------------------- +--R 2 +--R Type: Expression Integer +--E 246 + +--S 247 of 324 +a0446:= integrate(t0446,x) +--R +--R +--R log(x + 1) - log(x - 1) - 2atan(x) +--R (247) ---------------------------------- +--R 4 +--R Type: Union(Expression Integer,...) +--E 247 + +--S 248 of 324 +m0446:= a0446-r0446 +--R +--R +--R 3 +--R log(x + 1) - log(x - 1) + (- 2atanh(x) + 2atan(x))cos(x ) - 2atan(x) +--R (248) -------------------------------------------------------------------- +--R 4 +--R Type: Expression Integer +--E 248 + +--S 249 of 324 +d0446:= D(m0446,x) +--R +--R +--R (249) +--R 6 2 6 2 3 2 3 2 +--R ((3x - 3x )atanh(x) + (- 3x + 3x )atan(x))sin(x ) + 2x cos(x ) - 2x +--R ---------------------------------------------------------------------- +--R 4 +--R 2x - 2 +--R Type: Expression Integer +--E 249 + +--S 250 of 324 +t0447:= (x^6)^(1/2)/(x-x^5) +--R +--R +--R +--+ +--R | 6 +--R \|x +--R (250) - ------ +--R 5 +--R x - x +--R Type: Expression Integer +--E 250 + +--S 251 of 324 +r0447:= -1/2*cos(x^3)*(atan(x)-atanh(x)) +--R +--R +--R 3 +--R (atanh(x) - atan(x))cos(x ) +--R (251) --------------------------- +--R 2 +--R Type: Expression Integer +--E 251 + +--S 252 of 324 +a0447:= integrate(t0447,x) +--R +--R +--R log(x + 1) - log(x - 1) - 2atan(x) +--R (252) ---------------------------------- +--R 4 +--R Type: Union(Expression Integer,...) +--E 252 + +--S 253 of 324 +m0447:= a0447-r0447 +--R +--R +--R 3 +--R log(x + 1) - log(x - 1) + (- 2atanh(x) + 2atan(x))cos(x ) - 2atan(x) +--R (253) -------------------------------------------------------------------- +--R 4 +--R Type: Expression Integer +--E 253 + +--S 254 of 324 +d0447:= D(m0447,x) +--R +--R +--R (254) +--R 6 2 6 2 3 2 3 2 +--R ((3x - 3x )atanh(x) + (- 3x + 3x )atan(x))sin(x ) + 2x cos(x ) - 2x +--R ---------------------------------------------------------------------- +--R 4 +--R 2x - 2 +--R Type: Expression Integer +--E 254 + +--S 255 of 324 +t0448:= (x^6)^(3/2)/x/(1-x^4) +--R +--R +--R +--+ +--R 5 | 6 +--R x \|x +--R (255) - ------- +--R 4 +--R x - 1 +--R Type: Expression Integer +--E 255 + +--S 256 of 324 +r0448:= 1/10*cos(x^3)*(-10*x-2*x^5+5*atan(x)+5*atanh(x)) +--R +--R +--R 5 3 +--R (5atanh(x) + 5atan(x) - 2x - 10x)cos(x ) +--R (256) ----------------------------------------- +--R 10 +--R Type: Expression Integer +--E 256 + +--S 257 of 324 +a0448:= integrate(t0448,x) +--R +--R +--R 5 +--R 5log(x + 1) - 5log(x - 1) + 10atan(x) - 4x - 20x +--R (257) ------------------------------------------------- +--R 20 +--R Type: Union(Expression Integer,...) +--E 257 + +--S 258 of 324 +m0448:= a0448-r0448 +--R +--R +--R (258) +--R 5 3 +--R 5log(x + 1) - 5log(x - 1) + (- 10atanh(x) - 10atan(x) + 4x + 20x)cos(x ) +--R + +--R 5 +--R 10atan(x) - 4x - 20x +--R / +--R 20 +--R Type: Expression Integer +--E 258 + +--S 259 of 324 +d0448:= D(m0448,x) +--R +--R +--R (259) +--R 6 2 6 2 11 7 3 +--R ((15x - 15x )atanh(x) + (15x - 15x )atan(x) - 6x - 24x + 30x ) +--R * +--R 3 +--R sin(x ) +--R + +--R 8 3 8 +--R 10x cos(x ) - 10x +--R / +--R 4 +--R 10x - 10 +--R Type: Expression Integer +--E 259 + +--S 260 of 324 +t0449:= (x^3)^(1/2)/(x-x^3) +--R +--R +--R +--+ +--R | 3 +--R \|x +--R (260) - ------ +--R 3 +--R x - x +--R Type: Expression Integer +--E 260 + +--S 261 of 324 +r0449:= -(x^3)^(1/2)*(atan(x^(1/2))-atanh(x^(1/2)))/x^(3/2) +--R +--R +--R +--+ +--+ +--R | 3 +-+ | 3 +-+ +--R \|x atanh(\|x ) - \|x atan(\|x ) +--R (261) ---------------------------------- +--R +-+ +--R x\|x +--R Type: Expression Integer +--E 261 + +--S 262 of 324 +a0449:= integrate(t0449,x) +--R +--R +--R +-+ +-+ +-+ +--R log(\|x + 1) - log(\|x - 1) - 2atan(\|x ) +--R (262) ------------------------------------------- +--R 2 +--R Type: Union(Expression Integer,...) +--E 262 + +--S 263 of 324 +m0449:= a0449-r0449 +--R +--R +--R (263) +--R +--+ +--R +-+ +-+ +-+ +-+ | 3 +-+ +--R x\|x log(\|x + 1) - x\|x log(\|x - 1) - 2\|x atanh(\|x ) +--R + +--R +--+ +--R | 3 +-+ +-+ +--R (2\|x - 2x\|x )atan(\|x ) +--R / +--R +-+ +--R 2x\|x +--R Type: Expression Integer +--E 263 + +--S 264 of 324 +d0449:= D(m0449,x) +--R +--R +--R +--+ +--R | 3 2 +-+ +--R - x\|x + x \|x +--R (264) ----------------- +--R +--+ +--R 2 +-+ | 3 +--R (x - 1)\|x \|x +--R Type: Expression Integer +--E 264 + +--S 265 of 324 +t0450:= (x^(1/2)-(x^3)^(1/2))/(x-x^3) +--R +--R +--R +--+ +--R | 3 +-+ +--R \|x - \|x +--R (265) ------------ +--R 3 +--R x - x +--R Type: Expression Integer +--E 265 + +--S 266 of 324 +r0450:= atan(x^(1/2))+(x^3)^(1/2)*(atan(x^(1/2))-_ + atanh(x^(1/2)))/x^(3/2)+atanh(x^(1/2)) +--R +--R +--R +--+ +--+ +--R | 3 +-+ +-+ | 3 +-+ +-+ +--R (- \|x + x\|x )atanh(\|x ) + (\|x + x\|x )atan(\|x ) +--R (266) -------------------------------------------------------- +--R +-+ +--R x\|x +--R Type: Expression Integer +--E 266 + +--S 267 of 324 +a0450:= integrate(t0450,x) +--R +--R +--R +-+ +--R (267) 2atan(\|x ) +--R Type: Union(Expression Integer,...) +--E 267 + +--S 268 of 324 +m0450:= a0450-r0450 +--R +--R +--R +--+ +--+ +--R | 3 +-+ +-+ | 3 +-+ +-+ +--R (\|x - x\|x )atanh(\|x ) + (- \|x + x\|x )atan(\|x ) +--R (268) -------------------------------------------------------- +--R +-+ +--R x\|x +--R Type: Expression Integer +--E 268 + +--S 269 of 324 +d0450:= D(m0450,x) +--R +--R +--R +--+ +--R | 3 2 +-+ +--R x\|x - x \|x +--R (269) ----------------- +--R +--+ +--R 2 +-+ | 3 +--R (x - 1)\|x \|x +--R Type: Expression Integer +--E 269 + +--S 270 of 324 +t0451:= x^2/(-1+x^2+(1-x^2)^(1/2)) +--R +--R +--R 2 +--R x +--R (270) -------------------- +--R +--------+ +--R | 2 2 +--R \|- x + 1 + x - 1 +--R Type: Expression Integer +--E 270 + +--S 271 of 324 +r0451:= x+asin(x) +--R +--R +--R (271) asin(x) + x +--R Type: Expression Integer +--E 271 + +--S 272 of 324 +a0451:= integrate(t0451,x) +--R +--R +--R +--------+ +--R | 2 +--R \|- x + 1 - 1 +--R (272) - 2atan(---------------) + x +--R x +--R Type: Union(Expression Integer,...) +--E 272 + +--S 273 of 324 +m0451:= a0451-r0451 +--R +--R +--R +--------+ +--R | 2 +--R \|- x + 1 - 1 +--R (273) - 2atan(---------------) - asin(x) +--R x +--R Type: Expression Integer +--E 273 + +--S 274 of 324 +d0451:= D(m0451,x) +--R +--R +--R (274) 0 +--R Type: Expression Integer +--E 274 + +--S 275 of 324 +t0452:= x*(1+x)^(1/2)/(1+x^2) +--R +--R +--R +-----+ +--R x\|x + 1 +--R (275) --------- +--R 2 +--R x + 1 +--R Type: Expression Integer +--E 275 + +--S 276 of 324 +r0452:= 2*(1+x)^(1/2)+atan(((2+2*2^(1/2))^(1/2)-2*(1+x)^(1/2))/_ + (-2+2*2^(1/2))^(1/2))/(2+2*2^(1/2))^(1/2)-_ + atan(((2+2*2^(1/2))^(1/2)+2*(1+x)^(1/2))/_ + (-2+2*2^(1/2))^(1/2))/(2+2*2^(1/2))^(1/2)+_ + 1/4*(2+2^(1/2))*log(1+2^(1/2)+x-_ + (2+2*2^(1/2))^(1/2)*(1+x)^(1/2))/(1+2^(1/2))^(1/2)-_ + 1/4*(2+2^(1/2))*log(1+2^(1/2)+x+(2+2*2^(1/2))^(1/2)*_ + (1+x)^(1/2))/(1+2^(1/2))^(1/2) +--R +--R +--R (276) +--R +---------+ +---------+ +--R +-+ | +-+ +-----+ | +-+ +-+ +--R (- \|2 - 2)\|2\|2 + 2 log(\|x + 1 \|2\|2 + 2 + \|2 + x + 1) +--R + +--R +---------+ +---------+ +--R +-+ | +-+ +-----+ | +-+ +-+ +--R (\|2 + 2)\|2\|2 + 2 log(- \|x + 1 \|2\|2 + 2 + \|2 + x + 1) +--R + +--R +---------+ +--R +--------+ | +-+ +-----+ +--R | +-+ \|2\|2 + 2 + 2\|x + 1 +--R - 4\|\|2 + 1 atan(------------------------) +--R +---------+ +--R | +-+ +--R \|2\|2 - 2 +--R + +--R +---------+ +--R +--------+ | +-+ +-----+ +--R | +-+ \|2\|2 + 2 - 2\|x + 1 +--R 4\|\|2 + 1 atan(------------------------) +--R +---------+ +--R | +-+ +--R \|2\|2 - 2 +--R + +--R +--------+ +---------+ +--R +-----+ | +-+ | +-+ +--R 8\|x + 1 \|\|2 + 1 \|2\|2 + 2 +--R / +--R +--------+ +---------+ +--R | +-+ | +-+ +--R 4\|\|2 + 1 \|2\|2 + 2 +--R Type: Expression Integer +--E 276 + +--S 277 of 324 +a0452:= integrate(t0452,x) +--R +--R +--R (277) +--R - +--R 4+-+ %pi +--R \|2 cos(---) +--R 8 +--R * +--R 4+-+ %pi +-----+ 4+-+2 %pi 2 4+-+2 %pi 2 +--R log(2\|2 cos(---)\|x + 1 + \|2 sin(---) + \|2 cos(---) + x + 1) +--R 8 8 8 +--R + +--R 4+-+ %pi +--R \|2 cos(---) +--R 8 +--R * +--R 4+-+ %pi +-----+ 4+-+2 %pi 2 4+-+2 %pi 2 +--R log(- 2\|2 cos(---)\|x + 1 + \|2 sin(---) + \|2 cos(---) + x + 1) +--R 8 8 8 +--R + +--R 4+-+ %pi +--R \|2 sin(---) +--R 4+-+ %pi 8 +--R 2\|2 sin(---)atan(-----------------------) +--R 8 +-----+ 4+-+ %pi +--R \|x + 1 - \|2 cos(---) +--R 8 +--R + +--R 4+-+ %pi +--R \|2 sin(---) +--R 4+-+ %pi 8 +-----+ +--R 2\|2 sin(---)atan(-----------------------) + 4\|x + 1 +--R 8 +-----+ 4+-+ %pi +--R \|x + 1 + \|2 cos(---) +--R 8 +--R / +--R 2 +--R Type: Union(Expression Integer,...) +--E 277 + +--S 278 of 324 +m0452:= a0452-r0452 +--R +--R +--R (278) +--R +---------+ +---------+ +--R +-+ | +-+ +-----+ | +-+ +-+ +--R (\|2 + 2)\|2\|2 + 2 log(\|x + 1 \|2\|2 + 2 + \|2 + x + 1) +--R + +--R - +--R +--------+ +---------+ +--R 4+-+ %pi | +-+ | +-+ +--R 2\|2 cos(---)\|\|2 + 1 \|2\|2 + 2 +--R 8 +--R * +--R 4+-+ %pi +-----+ 4+-+2 %pi 2 4+-+2 %pi 2 +--R log(2\|2 cos(---)\|x + 1 + \|2 sin(---) + \|2 cos(---) + x + 1) +--R 8 8 8 +--R + +--R +--------+ +---------+ +--R 4+-+ %pi | +-+ | +-+ +--R 2\|2 cos(---)\|\|2 + 1 \|2\|2 + 2 +--R 8 +--R * +--R 4+-+ %pi +-----+ 4+-+2 %pi 2 4+-+2 %pi 2 +--R log(- 2\|2 cos(---)\|x + 1 + \|2 sin(---) + \|2 cos(---) + x + 1) +--R 8 8 8 +--R + +--R +---------+ +---------+ +--R +-+ | +-+ +-----+ | +-+ +-+ +--R (- \|2 - 2)\|2\|2 + 2 log(- \|x + 1 \|2\|2 + 2 + \|2 + x + 1) +--R + +--R +---------+ +--R +--------+ | +-+ +-----+ +--R | +-+ \|2\|2 + 2 + 2\|x + 1 +--R 4\|\|2 + 1 atan(------------------------) +--R +---------+ +--R | +-+ +--R \|2\|2 - 2 +--R + +--R +---------+ +--R +--------+ | +-+ +-----+ +--R | +-+ \|2\|2 + 2 - 2\|x + 1 +--R - 4\|\|2 + 1 atan(------------------------) +--R +---------+ +--R | +-+ +--R \|2\|2 - 2 +--R + +--R 4+-+ %pi +--R +--------+ +---------+ \|2 sin(---) +--R 4+-+ %pi | +-+ | +-+ 8 +--R 4\|2 sin(---)\|\|2 + 1 \|2\|2 + 2 atan(-----------------------) +--R 8 +-----+ 4+-+ %pi +--R \|x + 1 - \|2 cos(---) +--R 8 +--R + +--R 4+-+ %pi +--R +--------+ +---------+ \|2 sin(---) +--R 4+-+ %pi | +-+ | +-+ 8 +--R 4\|2 sin(---)\|\|2 + 1 \|2\|2 + 2 atan(-----------------------) +--R 8 +-----+ 4+-+ %pi +--R \|x + 1 + \|2 cos(---) +--R 8 +--R / +--R +--------+ +---------+ +--R | +-+ | +-+ +--R 4\|\|2 + 1 \|2\|2 + 2 +--R Type: Expression Integer +--E 278 + +--S 279 of 324 +d0452:= D(m0452,x) +--R +--R +--R (279) +--R +-+ %pi 4 +--R ((8x + 16)\|2 + 8x + 24)cos(---) +--R 8 +--R + +--R 2 +-+ 2 4+-+2 %pi 2 +--R ((- 8x - 24x - 16)\|2 - 8x - 32x - 24)\|2 cos(---) +--R 8 +--R + +--R 3 2 +-+ 3 2 +--R (4x + 16x + 20x + 8)\|2 + 4x + 20x + 28x + 12 +--R * +--R %pi 8 +--R sin(---) +--R 8 +--R + +--R +-+ %pi 6 +--R ((32x + 64)\|2 + 32x + 96)cos(---) +--R 8 +--R + +--R 2 +-+ 2 4+-+2 %pi 4 +--R ((- 16x - 48x - 32)\|2 - 16x - 64x - 48)\|2 cos(---) +--R 8 +--R + +--R 3 2 +-+ 3 2 +--R ((- 16x - 64x - 80x - 32)\|2 - 16x - 80x - 112x - 48) +--R * +--R %pi 2 +--R cos(---) +--R 8 +--R + +--R 4 3 2 +-+ 4 3 2 +--R (8x + 40x + 72x + 56x + 16)\|2 + 8x + 48x + 96x +--R + +--R 80x + 24 +--R * +--R 4+-+2 +--R \|2 +--R * +--R %pi 6 +--R sin(---) +--R 8 +--R + +--R +-+ %pi 8 +--R ((48x + 96)\|2 + 48x + 144)cos(---) +--R 8 +--R + +--R 2 +-+ 2 4+-+2 %pi 6 +--R ((- 32x - 96x - 64)\|2 - 32x - 128x - 96)\|2 cos(---) +--R 8 +--R + +--R 3 2 +-+ 3 2 +--R ((16x + 64x + 80x + 32)\|2 + 16x + 80x + 112x + 48) +--R * +--R %pi 4 +--R cos(---) +--R 8 +--R + +--R 4 3 2 +-+ 4 3 +--R (- 16x - 80x - 144x - 112x - 32)\|2 - 16x - 96x +--R + +--R 2 +--R - 192x - 160x - 48 +--R * +--R 4+-+2 %pi 2 +--R \|2 cos(---) +--R 8 +--R + +--R 5 4 3 2 +-+ 5 4 +--R (12x + 72x + 168x + 192x + 108x + 24)\|2 + 12x + 84x +--R + +--R 3 2 +--R 216x + 264x + 156x + 36 +--R * +--R %pi 4 +--R sin(---) +--R 8 +--R + +--R +-+ %pi 10 +--R ((32x + 64)\|2 + 32x + 96)cos(---) +--R 8 +--R + +--R 2 +-+ 2 4+-+2 %pi 8 +--R ((- 48x - 144x - 96)\|2 - 48x - 192x - 144)\|2 cos(---) +--R 8 +--R + +--R 3 2 +-+ 3 2 +--R ((32x + 128x + 160x + 64)\|2 + 32x + 160x + 224x + 96) +--R * +--R %pi 6 +--R cos(---) +--R 8 +--R + +--R 4 3 2 +-+ 4 3 +--R (16x + 80x + 144x + 112x + 32)\|2 + 16x + 96x +--R + +--R 2 +--R 192x + 160x + 48 +--R * +--R 4+-+2 %pi 4 +--R \|2 cos(---) +--R 8 +--R + +--R 5 4 3 2 +-+ 5 +--R (- 24x - 144x - 336x - 384x - 216x - 48)\|2 - 24x +--R + +--R 4 3 2 +--R - 168x - 432x - 528x - 312x - 72 +--R * +--R %pi 2 +--R cos(---) +--R 8 +--R + +--R 6 5 4 3 2 +-+ 6 +--R (4x + 28x + 80x + 120x + 100x + 44x + 8)\|2 + 4x +--R + +--R 5 4 3 2 +--R 32x + 100x + 160x + 140x + 64x + 12 +--R * +--R 4+-+2 +--R \|2 +--R * +--R %pi 2 +--R sin(---) +--R 8 +--R + +--R +-+ %pi 12 +--R ((8x + 16)\|2 + 8x + 24)cos(---) +--R 8 +--R + +--R 2 +-+ 2 4+-+2 %pi 10 +--R ((- 24x - 72x - 48)\|2 - 24x - 96x - 72)\|2 cos(---) +--R 8 +--R + +--R 3 2 +-+ 3 2 +--R ((60x + 240x + 300x + 120)\|2 + 60x + 300x + 420x + 180) +--R * +--R %pi 8 +--R cos(---) +--R 8 +--R + +--R 4 3 2 +-+ 4 3 +--R (- 40x - 200x - 360x - 280x - 80)\|2 - 40x - 240x +--R + +--R 2 +--R - 480x - 400x - 120 +--R * +--R 4+-+2 %pi 6 +--R \|2 cos(---) +--R 8 +--R + +--R 5 4 3 2 +-+ 5 4 +--R (30x + 180x + 420x + 480x + 270x + 60)\|2 + 30x + 210x +--R + +--R 3 2 +--R 540x + 660x + 390x + 90 +--R * +--R %pi 4 +--R cos(---) +--R 8 +--R + +--R 6 5 4 3 2 +-+ 6 +--R (- 6x - 42x - 120x - 180x - 150x - 66x - 12)\|2 - 6x +--R + +--R 5 4 3 2 +--R - 48x - 150x - 240x - 210x - 96x - 18 +--R * +--R 4+-+2 %pi 2 +--R \|2 cos(---) +--R 8 +--R + +--R 7 6 5 4 3 2 +-+ 7 6 +--R (x + 8x + 27x + 50x + 55x + 36x + 13x + 2)\|2 + x + 9x +--R + +--R 5 4 3 2 +--R 33x + 65x + 75x + 51x + 19x + 3 +--R * +--R +---------+ +--R +-----+ | +-+ +--R \|x + 1 \|2\|2 - 2 +--R + +--R +-+ %pi 4 +--R ((- 24x + 8)\|2 - 32x + 16)cos(---) +--R 8 +--R + +--R 2 +-+ 2 4+-+2 %pi 2 +--R ((24x + 16x - 8)\|2 + 32x + 16x - 16)\|2 cos(---) +--R 8 +--R + +--R 3 2 +-+ 3 2 +--R (- 12x - 20x - 4x + 4)\|2 - 16x - 24x + 8 +--R * +--R %pi 8 +--R sin(---) +--R 8 +--R + +--R +-+ %pi 6 +--R ((- 96x + 32)\|2 - 128x + 64)cos(---) +--R 8 +--R + +--R 2 +-+ 2 4+-+2 %pi 4 +--R ((48x + 32x - 16)\|2 + 64x + 32x - 32)\|2 cos(---) +--R 8 +--R + +--R 3 2 +-+ 3 2 %pi 2 +--R ((48x + 80x + 16x - 16)\|2 + 64x + 96x - 32)cos(---) +--R 8 +--R + +--R 4 3 2 +-+ 4 3 2 +--R (- 24x - 64x - 48x + 8)\|2 - 32x - 80x - 48x + 16x +--R + +--R 16 +--R * +--R 4+-+2 +--R \|2 +--R * +--R %pi 6 +--R sin(---) +--R 8 +--R + +--R +-+ %pi 8 +--R ((- 144x + 48)\|2 - 192x + 96)cos(---) +--R 8 +--R + +--R 2 +-+ 2 4+-+2 %pi 6 +--R ((96x + 64x - 32)\|2 + 128x + 64x - 64)\|2 cos(---) +--R 8 +--R + +--R 3 2 +-+ 3 2 %pi 4 +--R ((- 48x - 80x - 16x + 16)\|2 - 64x - 96x + 32)cos(---) +--R 8 +--R + +--R 4 3 2 +-+ 4 3 2 +--R (48x + 128x + 96x - 16)\|2 + 64x + 160x + 96x +--R + +--R - 32x - 32 +--R * +--R 4+-+2 %pi 2 +--R \|2 cos(---) +--R 8 +--R + +--R 5 4 3 2 +-+ 5 4 +--R (- 36x - 132x - 168x - 72x + 12x + 12)\|2 - 48x - 168x +--R + +--R 3 2 +--R - 192x - 48x + 48x + 24 +--R * +--R %pi 4 +--R sin(---) +--R 8 +--R + +--R +-+ %pi 10 +--R ((- 96x + 32)\|2 - 128x + 64)cos(---) +--R 8 +--R + +--R 2 +-+ 2 4+-+2 %pi 8 +--R ((144x + 96x - 48)\|2 + 192x + 96x - 96)\|2 cos(---) +--R 8 +--R + +--R 3 2 +-+ 3 2 +--R ((- 96x - 160x - 32x + 32)\|2 - 128x - 192x + 64) +--R * +--R %pi 6 +--R cos(---) +--R 8 +--R + +--R 4 3 2 +-+ 4 3 2 +--R (- 48x - 128x - 96x + 16)\|2 - 64x - 160x - 96x +--R + +--R 32x + 32 +--R * +--R 4+-+2 %pi 4 +--R \|2 cos(---) +--R 8 +--R + +--R 5 4 3 2 +-+ 5 +--R (72x + 264x + 336x + 144x - 24x - 24)\|2 + 96x +--R + +--R 4 3 2 +--R 336x + 384x + 96x - 96x - 48 +--R * +--R %pi 2 +--R cos(---) +--R 8 +--R + +--R 6 5 4 3 2 +-+ 6 +--R (- 12x - 56x - 100x - 80x - 20x + 8x + 4)\|2 - 16x +--R + +--R 5 4 3 +--R - 72x - 120x - 80x + 24x + 8 +--R * +--R 4+-+2 +--R \|2 +--R * +--R %pi 2 +--R sin(---) +--R 8 +--R + +--R +-+ %pi 12 +--R ((- 24x + 8)\|2 - 32x + 16)cos(---) +--R 8 +--R + +--R 2 +-+ 2 4+-+2 %pi 10 +--R ((72x + 48x - 24)\|2 + 96x + 48x - 48)\|2 cos(---) +--R 8 +--R + +--R 3 2 +-+ 3 2 %pi 8 +--R ((- 180x - 300x - 60x + 60)\|2 - 240x - 360x + 120)cos(---) +--R 8 +--R + +--R 4 3 2 +-+ 4 3 2 +--R (120x + 320x + 240x - 40)\|2 + 160x + 400x + 240x +--R + +--R - 80x - 80 +--R * +--R 4+-+2 %pi 6 +--R \|2 cos(---) +--R 8 +--R + +--R 5 4 3 2 +-+ 5 +--R (- 90x - 330x - 420x - 180x + 30x + 30)\|2 - 120x +--R + +--R 4 3 2 +--R - 420x - 480x - 120x + 120x + 60 +--R * +--R %pi 4 +--R cos(---) +--R 8 +--R + +--R 6 5 4 3 2 +-+ 6 +--R (18x + 84x + 150x + 120x + 30x - 12x - 6)\|2 + 24x +--R + +--R 5 4 3 +--R 108x + 180x + 120x - 36x - 12 +--R * +--R 4+-+2 %pi 2 +--R \|2 cos(---) +--R 8 +--R + +--R 7 6 5 4 3 2 +-+ 7 +--R (- 3x - 17x - 39x - 45x - 25x - 3x + 3x + 1)\|2 - 4x +--R + +--R 6 5 4 3 2 +--R - 22x - 48x - 50x - 20x + 6x + 8x + 2 +--R * +--R +--------+ +--R +-----+ | +-+ +--R \|x + 1 \|\|2 + 1 +--R * +--R +---------+ +--R | +-+ +--R \|2\|2 + 2 +--R + +--R 2 +-+ 2 %pi 4 +--R ((- 64x - 64)\|2 - 96x - 96)cos(---) +--R 8 +--R + +--R 3 2 +-+ 3 2 4+-+2 +--R ((64x + 64x + 64x + 64)\|2 + 96x + 96x + 96x + 96)\|2 +--R * +--R %pi 2 +--R cos(---) +--R 8 +--R + +--R 4 3 2 +-+ 4 3 2 +--R (- 32x - 64x - 64x - 64x - 32)\|2 - 48x - 96x - 96x - 96x +--R + +--R - 48 +--R * +--R %pi 8 +--R sin(---) +--R 8 +--R + +--R 2 +-+ 2 %pi 6 +--R ((- 256x - 256)\|2 - 384x - 384)cos(---) +--R 8 +--R + +--R 3 2 +-+ 3 2 +--R ((160x + 160x + 160x + 160)\|2 + 240x + 240x + 240x + 240) +--R * +--R 4+-+2 %pi 4 +--R \|2 cos(---) +--R 8 +--R + +--R 4 3 2 +-+ 4 3 2 +--R (64x + 128x + 128x + 128x + 64)\|2 + 96x + 192x + 192x +--R + +--R 192x + 96 +--R * +--R %pi 2 +--R cos(---) +--R 8 +--R + +--R 5 4 3 2 +-+ 5 +--R (- 48x - 144x - 192x - 192x - 144x - 48)\|2 - 72x +--R + +--R 4 3 2 +--R - 216x - 288x - 288x - 216x - 72 +--R * +--R 4+-+2 +--R \|2 +--R * +--R %pi 6 +--R sin(---) +--R 8 +--R + +--R 2 +-+ 2 %pi 8 +--R ((- 384x - 384)\|2 - 576x - 576)cos(---) +--R 8 +--R + +--R 3 2 +-+ 3 2 +--R ((288x + 288x + 288x + 288)\|2 + 432x + 432x + 432x + 432) +--R * +--R 4+-+2 %pi 6 +--R \|2 cos(---) +--R 8 +--R + +--R 4 3 2 +-+ 4 3 +--R (- 96x - 192x - 192x - 192x - 96)\|2 - 144x - 288x +--R + +--R 2 +--R - 288x - 288x - 144 +--R * +--R %pi 4 +--R cos(---) +--R 8 +--R + +--R 5 4 3 2 +-+ 5 4 +--R (48x + 144x + 192x + 192x + 144x + 48)\|2 + 72x + 216x +--R + +--R 3 2 +--R 288x + 288x + 216x + 72 +--R * +--R 4+-+2 %pi 2 +--R \|2 cos(---) +--R 8 +--R + +--R 6 5 4 3 2 +-+ 6 +--R (- 48x - 192x - 336x - 384x - 336x - 192x - 48)\|2 - 72x +--R + +--R 5 4 3 2 +--R - 288x - 504x - 576x - 504x - 288x - 72 +--R * +--R %pi 4 +--R sin(---) +--R 8 +--R + +--R 2 +-+ 2 %pi 10 +--R ((- 256x - 256)\|2 - 384x - 384)cos(---) +--R 8 +--R + +--R 3 2 +-+ 3 2 +--R ((352x + 352x + 352x + 352)\|2 + 528x + 528x + 528x + 528) +--R * +--R 4+-+2 %pi 8 +--R \|2 cos(---) +--R 8 +--R + +--R 4 3 2 +-+ 4 3 +--R (- 256x - 512x - 512x - 512x - 256)\|2 - 384x - 768x +--R + +--R 2 +--R - 768x - 768x - 384 +--R * +--R %pi 6 +--R cos(---) +--R 8 +--R + +--R 5 4 3 2 +-+ 5 4 +--R (- 32x - 96x - 128x - 128x - 96x - 32)\|2 - 48x - 144x +--R + +--R 3 2 +--R - 192x - 192x - 144x - 48 +--R * +--R 4+-+2 %pi 4 +--R \|2 cos(---) +--R 8 +--R + +--R 6 5 4 3 2 +-+ 6 +--R (64x + 256x + 448x + 512x + 448x + 256x + 64)\|2 + 96x +--R + +--R 5 4 3 2 +--R 384x + 672x + 768x + 672x + 384x + 96 +--R * +--R %pi 2 +--R cos(---) +--R 8 +--R + +--R 7 6 5 4 3 2 +-+ +--R (- 8x - 40x - 88x - 120x - 120x - 88x - 40x - 8)\|2 +--R + +--R 7 6 5 4 3 2 +--R - 12x - 60x - 132x - 180x - 180x - 132x - 60x - 12 +--R * +--R 4+-+2 +--R \|2 +--R * +--R %pi 2 +--R sin(---) +--R 8 +--R + +--R 2 +-+ 2 %pi 12 +--R ((- 64x - 64)\|2 - 96x - 96)cos(---) +--R 8 +--R + +--R 3 2 +-+ 3 2 +--R ((160x + 160x + 160x + 160)\|2 + 240x + 240x + 240x + 240) +--R * +--R 4+-+2 %pi 10 +--R \|2 cos(---) +--R 8 +--R + +--R 4 3 2 +-+ 4 3 +--R (- 320x - 640x - 640x - 640x - 320)\|2 - 480x - 960x +--R + +--R 2 +--R - 960x - 960x - 480 +--R * +--R %pi 8 +--R cos(---) +--R 8 +--R + +--R 5 4 3 2 +-+ 5 4 +--R (160x + 480x + 640x + 640x + 480x + 160)\|2 + 240x + 720x +--R + +--R 3 2 +--R 960x + 960x + 720x + 240 +--R * +--R 4+-+2 %pi 6 +--R \|2 cos(---) +--R 8 +--R + +--R 6 5 4 3 2 +-+ 6 +--R (- 80x - 320x - 560x - 640x - 560x - 320x - 80)\|2 - 120x +--R + +--R 5 4 3 2 +--R - 480x - 840x - 960x - 840x - 480x - 120 +--R * +--R %pi 4 +--R cos(---) +--R 8 +--R + +--R 7 6 5 4 3 2 +-+ 7 +--R (8x + 40x + 88x + 120x + 120x + 88x + 40x + 8)\|2 + 12x +--R + +--R 6 5 4 3 2 +--R 60x + 132x + 180x + 180x + 132x + 60x + 12 +--R * +--R 4+-+2 %pi 2 +--R \|2 cos(---) +--R 8 +--R * +--R +-----+ +--R \|x + 1 +--R / +--R 3 2 +-+ 3 2 %pi 4 +--R ((64x + 64x + 64x + 64)\|2 + 96x + 96x + 96x + 96)cos(---) +--R 8 +--R + +--R 4 3 2 +-+ 4 3 2 +--R (- 64x - 128x - 128x - 128x - 64)\|2 - 96x - 192x - 192x +--R + +--R - 192x - 96 +--R * +--R 4+-+2 %pi 2 +--R \|2 cos(---) +--R 8 +--R + +--R 5 4 3 2 +-+ 5 4 3 +--R (32x + 96x + 128x + 128x + 96x + 32)\|2 + 48x + 144x + 192x +--R + +--R 2 +--R 192x + 144x + 48 +--R * +--R %pi 8 +--R sin(---) +--R 8 +--R + +--R 3 2 +-+ 3 2 +--R ((256x + 256x + 256x + 256)\|2 + 384x + 384x + 384x + 384) +--R * +--R %pi 6 +--R cos(---) +--R 8 +--R + +--R 4 3 2 +-+ 4 3 +--R (- 128x - 256x - 256x - 256x - 128)\|2 - 192x - 384x +--R + +--R 2 +--R - 384x - 384x - 192 +--R * +--R 4+-+2 %pi 4 +--R \|2 cos(---) +--R 8 +--R + +--R 5 4 3 2 +-+ 5 +--R (- 128x - 384x - 512x - 512x - 384x - 128)\|2 - 192x +--R + +--R 4 3 2 +--R - 576x - 768x - 768x - 576x - 192 +--R * +--R %pi 2 +--R cos(---) +--R 8 +--R + +--R 6 5 4 3 2 +-+ 6 +--R (64x + 256x + 448x + 512x + 448x + 256x + 64)\|2 + 96x +--R + +--R 5 4 3 2 +--R 384x + 672x + 768x + 672x + 384x + 96 +--R * +--R 4+-+2 +--R \|2 +--R * +--R %pi 6 +--R sin(---) +--R 8 +--R + +--R 3 2 +-+ 3 2 +--R ((384x + 384x + 384x + 384)\|2 + 576x + 576x + 576x + 576) +--R * +--R %pi 8 +--R cos(---) +--R 8 +--R + +--R 4 3 2 +-+ 4 3 +--R (- 256x - 512x - 512x - 512x - 256)\|2 - 384x - 768x +--R + +--R 2 +--R - 768x - 768x - 384 +--R * +--R 4+-+2 %pi 6 +--R \|2 cos(---) +--R 8 +--R + +--R 5 4 3 2 +-+ 5 4 +--R (128x + 384x + 512x + 512x + 384x + 128)\|2 + 192x + 576x +--R + +--R 3 2 +--R 768x + 768x + 576x + 192 +--R * +--R %pi 4 +--R cos(---) +--R 8 +--R + +--R 6 5 4 3 2 +-+ +--R (- 128x - 512x - 896x - 1024x - 896x - 512x - 128)\|2 +--R + +--R 6 5 4 3 2 +--R - 192x - 768x - 1344x - 1536x - 1344x - 768x - 192 +--R * +--R 4+-+2 %pi 2 +--R \|2 cos(---) +--R 8 +--R + +--R 7 6 5 4 3 2 +-+ +--R (96x + 480x + 1056x + 1440x + 1440x + 1056x + 480x + 96)\|2 +--R + +--R 7 6 5 4 3 2 +--R 144x + 720x + 1584x + 2160x + 2160x + 1584x + 720x + 144 +--R * +--R %pi 4 +--R sin(---) +--R 8 +--R + +--R 3 2 +-+ 3 2 +--R ((256x + 256x + 256x + 256)\|2 + 384x + 384x + 384x + 384) +--R * +--R %pi 10 +--R cos(---) +--R 8 +--R + +--R 4 3 2 +-+ 4 3 +--R (- 384x - 768x - 768x - 768x - 384)\|2 - 576x - 1152x +--R + +--R 2 +--R - 1152x - 1152x - 576 +--R * +--R 4+-+2 %pi 8 +--R \|2 cos(---) +--R 8 +--R + +--R 5 4 3 2 +-+ 5 +--R (256x + 768x + 1024x + 1024x + 768x + 256)\|2 + 384x +--R + +--R 4 3 2 +--R 1152x + 1536x + 1536x + 1152x + 384 +--R * +--R %pi 6 +--R cos(---) +--R 8 +--R + +--R 6 5 4 3 2 +-+ 6 +--R (128x + 512x + 896x + 1024x + 896x + 512x + 128)\|2 + 192x +--R + +--R 5 4 3 2 +--R 768x + 1344x + 1536x + 1344x + 768x + 192 +--R * +--R 4+-+2 %pi 4 +--R \|2 cos(---) +--R 8 +--R + +--R 7 6 5 4 3 2 +--R - 192x - 960x - 2112x - 2880x - 2880x - 2112x - 960x +--R + +--R - 192 +--R * +--R +-+ +--R \|2 +--R + +--R 7 6 5 4 3 2 +--R - 288x - 1440x - 3168x - 4320x - 4320x - 3168x - 1440x - 288 +--R * +--R %pi 2 +--R cos(---) +--R 8 +--R + +--R 8 7 6 5 4 3 2 +--R 32x + 192x + 512x + 832x + 960x + 832x + 512x + 192x +--R + +--R 32 +--R * +--R +-+ +--R \|2 +--R + +--R 8 7 6 5 4 3 2 +--R 48x + 288x + 768x + 1248x + 1440x + 1248x + 768x + 288x + 48 +--R * +--R 4+-+2 +--R \|2 +--R * +--R %pi 2 +--R sin(---) +--R 8 +--R + +--R 3 2 +-+ 3 2 %pi 12 +--R ((64x + 64x + 64x + 64)\|2 + 96x + 96x + 96x + 96)cos(---) +--R 8 +--R + +--R 4 3 2 +-+ 4 3 2 +--R (- 192x - 384x - 384x - 384x - 192)\|2 - 288x - 576x - 576x +--R + +--R - 576x - 288 +--R * +--R 4+-+2 %pi 10 +--R \|2 cos(---) +--R 8 +--R + +--R 5 4 3 2 +-+ 5 4 +--R (480x + 1440x + 1920x + 1920x + 1440x + 480)\|2 + 720x + 2160x +--R + +--R 3 2 +--R 2880x + 2880x + 2160x + 720 +--R * +--R %pi 8 +--R cos(---) +--R 8 +--R + +--R 6 5 4 3 2 +-+ +--R (- 320x - 1280x - 2240x - 2560x - 2240x - 1280x - 320)\|2 +--R + +--R 6 5 4 3 2 +--R - 480x - 1920x - 3360x - 3840x - 3360x - 1920x - 480 +--R * +--R 4+-+2 %pi 6 +--R \|2 cos(---) +--R 8 +--R + +--R 7 6 5 4 3 2 +--R (240x + 1200x + 2640x + 3600x + 3600x + 2640x + 1200x + 240) +--R * +--R +-+ +--R \|2 +--R + +--R 7 6 5 4 3 2 +--R 360x + 1800x + 3960x + 5400x + 5400x + 3960x + 1800x + 360 +--R * +--R %pi 4 +--R cos(---) +--R 8 +--R + +--R 8 7 6 5 4 3 2 +--R - 48x - 288x - 768x - 1248x - 1440x - 1248x - 768x - 288x +--R + +--R - 48 +--R * +--R +-+ +--R \|2 +--R + +--R 8 7 6 5 4 3 2 +--R - 72x - 432x - 1152x - 1872x - 2160x - 1872x - 1152x - 432x - 72 +--R * +--R 4+-+2 %pi 2 +--R \|2 cos(---) +--R 8 +--R + +--R 9 8 7 6 5 4 3 2 +--R (8x + 56x + 176x + 336x + 448x + 448x + 336x + 176x + 56x + 8) +--R * +--R +-+ +--R \|2 +--R + +--R 9 8 7 6 5 4 3 2 +--R 12x + 84x + 264x + 504x + 672x + 672x + 504x + 264x + 84x + 12 +--R Type: Expression Integer +--E 279 + +--S 280 of 324 +t0453:= 1/(1+2*x/(1+x^2))^(1/2) +--R +--R +--R 1 +--R (280) -------------- +--R +-----------+ +--R | 2 +--R |x + 2x + 1 +--R |----------- +--R | 2 +--R \| x + 1 +--R Type: Expression Integer +--E 280 + +--S 281 of 324 +r0453:= (1+x)*((1+x^2)^(1/2)-asinh(x)+2*2^(1/2)*_ + atanh(1/2*(-1+tanh(1/2*asinh(x)))*2^(1/2)))/_ + (1+x^2)^(1/2)/((1+x)^2/(1+x^2))^(1/2) +--R +--R +--R (281) +--R +-+ asinh(x) +-+ +--R \|2 tanh(--------) - \|2 +------+ +--R +-+ 2 | 2 +--R (2x + 2)\|2 atanh(-------------------------) + (x + 1)\|x + 1 +--R 2 +--R + +--R (- x - 1)asinh(x) +--R / +--R +-----------+ +--R | 2 +------+ +--R |x + 2x + 1 | 2 +--R |----------- \|x + 1 +--R | 2 +--R \| x + 1 +--R Type: Expression Integer +--E 281 + +--S 282 of 324 +a0453:= integrate(t0453,x) +--R +--R +--R (282) +--R +------+ +------+ +--R | 2 | 2 +--R (\|x + 1 - x)log(\|x + 1 - x) +--R + +--R +------+ +--R +-+ | 2 +-+ +--R (\|2 \|x + 1 - x\|2 ) +--R * +--R +------+ +--R +-+ | 2 +-+ 2 +--R (\|2 + x + 1)\|x + 1 + (- x - 1)\|2 - x - x - 2 +--R log(----------------------------------------------------) +--R +------+ +--R | 2 2 +--R (x + 1)\|x + 1 - x - x +--R + +--R +------+ +--R | 2 2 +--R - x\|x + 1 + x + 1 +--R / +--R +------+ +--R | 2 +--R \|x + 1 - x +--R Type: Union(Expression Integer,...) +--E 282 + +--S 283 of 324 +m0453:= a0453-r0453 +--R +--R +--R (283) +--R +------+ +--R +-+ | 2 2 +-+ +--R ((2x + 2)\|2 \|x + 1 + (- 2x - 2x)\|2 ) +--R * +--R +-+ asinh(x) +-+ +--R \|2 tanh(--------) - \|2 +--R 2 +--R atanh(-------------------------) +--R 2 +--R + +--R +-----------+ +-----------+ +--R | 2 +------+ | 2 +------+ +--R |x + 2x + 1 | 2 2 |x + 2x + 1 | 2 +--R (x |----------- \|x + 1 + (- x - 1) |----------- )log(\|x + 1 - x) +--R | 2 | 2 +--R \| x + 1 \| x + 1 +--R + +--R +-----------+ +-----------+ +--R | 2 +------+ | 2 +--R +-+ |x + 2x + 1 | 2 2 +-+ |x + 2x + 1 +--R (x\|2 |----------- \|x + 1 + (- x - 1)\|2 |----------- ) +--R | 2 | 2 +--R \| x + 1 \| x + 1 +--R * +--R +------+ +--R +-+ | 2 +-+ 2 +--R (\|2 + x + 1)\|x + 1 + (- x - 1)\|2 - x - x - 2 +--R log(----------------------------------------------------) +--R +------+ +--R | 2 2 +--R (x + 1)\|x + 1 - x - x +--R + +--R +-----------+ +--R | 2 +------+ +--R 2 |x + 2x + 1 2 | 2 +--R ((- x - 1) |----------- + (- x - 1)asinh(x) - x - x)\|x + 1 +--R | 2 +--R \| x + 1 +--R + +--R +-----------+ +--R | 2 +--R 3 |x + 2x + 1 2 3 2 +--R (x + x) |----------- + (x + x)asinh(x) + x + x + x + 1 +--R | 2 +--R \| x + 1 +--R / +--R +-----------+ +-----------+ +--R | 2 +------+ | 2 +--R |x + 2x + 1 | 2 2 |x + 2x + 1 +--R x |----------- \|x + 1 + (- x - 1) |----------- +--R | 2 | 2 +--R \| x + 1 \| x + 1 +--R Type: Expression Integer +--E 283 + +--S 284 of 324 +d0453:= D(m0453,x) +--R +--R +--R (284) +--R 8 7 6 5 4 3 2 +--R (- 16x - 8x - 44x - 20x - 41x - 16x - 14x - 4x - 1) +--R * +--R +-+ +--R \|2 +--R + +--R 9 8 7 6 5 4 3 2 +--R - 16x - 16x - 60x - 44x - 81x - 41x - 46x - 14x - 9x +--R + +--R - 1 +--R * +--R +-----------+ +--R | 2 +--R |x + 2x + 1 +--R |----------- +--R | 2 +--R \| x + 1 +--R + +--R 8 7 6 5 4 3 2 +-+ +--R (- 16x - 56x - 92x - 108x - 97x - 60x - 26x - 8x - 1)\|2 +--R + +--R 9 8 7 6 5 4 3 2 +--R - 16x - 64x - 132x - 192x - 205x - 164x - 100x - 42x +--R + +--R - 11x - 2 +--R * +--R +------+ +--R | 2 +--R \|x + 1 +--R + +--R 9 8 7 6 5 4 3 2 +--R (16x + 8x + 52x + 24x + 61x + 25x + 30x + 10x + 5x + 1) +--R * +--R +-+ +--R \|2 +--R + +--R 10 9 8 7 6 5 4 3 2 +--R 16x + 16x + 68x + 52x + 109x + 61x + 80x + 30x + 25x +--R + +--R 5x + 2 +--R * +--R +-----------+ +--R | 2 +--R |x + 2x + 1 +--R |----------- +--R | 2 +--R \| x + 1 +--R + +--R 9 8 7 6 5 4 3 2 +--R 16x + 56x + 100x + 136x + 141x + 107x + 64x + 28x + 7x +--R + +--R 1 +--R * +--R +-+ +--R \|2 +--R + +--R 10 9 8 7 6 5 4 3 2 +--R 16x + 64x + 140x + 224x + 269x + 252x + 187x + 104x + 43x +--R + +--R 12x + 1 +--R * +--R asinh(x) 2 +--R tanh(--------) +--R 2 +--R + +--R 8 7 6 5 4 3 2 +-+ +--R (32x + 16x + 88x + 40x + 82x + 32x + 28x + 8x + 2)\|2 +--R + +--R 9 8 7 6 5 4 3 2 +--R 32x + 32x + 120x + 88x + 162x + 82x + 92x + 28x + 18x +--R + +--R 2 +--R * +--R +-----------+ +--R | 2 +--R |x + 2x + 1 +--R |----------- +--R | 2 +--R \| x + 1 +--R + +--R 8 7 6 5 4 3 2 +-+ +--R (32x + 48x + 24x + 8x - 30x - 44x - 24x - 12x - 2)\|2 +--R + +--R 9 8 7 6 5 4 3 2 +--R 32x + 64x + 72x + 48x - 22x - 60x - 68x - 48x - 14x - 4 +--R * +--R +------+ +--R | 2 +--R \|x + 1 +--R + +--R 9 8 7 6 5 4 3 2 +--R - 32x - 16x - 104x - 48x - 122x - 50x - 60x - 20x +--R + +--R - 10x - 2 +--R * +--R +-+ +--R \|2 +--R + +--R 10 9 8 7 6 5 4 3 +--R - 32x - 32x - 136x - 104x - 218x - 122x - 160x - 60x +--R + +--R 2 +--R - 50x - 10x - 4 +--R * +--R +-----------+ +--R | 2 +--R |x + 2x + 1 +--R |----------- +--R | 2 +--R \| x + 1 +--R + +--R 9 8 7 6 5 4 3 2 +--R (- 32x - 48x - 40x - 32x + 22x + 46x + 40x + 32x + 10x + 2) +--R * +--R +-+ +--R \|2 +--R + +--R 10 9 8 7 6 5 4 3 2 +--R - 32x - 64x - 88x - 80x - 10x + 44x + 86x + 80x + 42x + 20x +--R + +--R 2 +--R * +--R asinh(x) +--R tanh(--------) +--R 2 +--R + +--R 8 7 6 5 4 3 2 +-+ +--R (16x + 8x + 44x + 20x + 41x + 16x + 14x + 4x + 1)\|2 +--R + +--R 9 8 7 6 5 4 3 2 +--R 16x + 16x + 60x + 44x + 81x + 41x + 46x + 14x + 9x + 1 +--R * +--R +-----------+ +--R | 2 +--R |x + 2x + 1 +--R |----------- +--R | 2 +--R \| x + 1 +--R + +--R 8 7 6 5 4 3 2 +-+ 9 +--R (16x + 56x + 92x + 108x + 97x + 60x + 26x + 8x + 1)\|2 + 16x +--R + +--R 8 7 6 5 4 3 2 +--R 64x + 132x + 192x + 205x + 164x + 100x + 42x + 11x + 2 +--R * +--R +------+ +--R | 2 +--R \|x + 1 +--R + +--R 9 8 7 6 5 4 3 2 +-+ +--R (- 16x - 8x - 52x - 24x - 61x - 25x - 30x - 10x - 5x - 1)\|2 +--R + +--R 10 9 8 7 6 5 4 3 2 +--R - 16x - 16x - 68x - 52x - 109x - 61x - 80x - 30x - 25x - 5x +--R + +--R - 2 +--R * +--R +-----------+ +--R | 2 +--R |x + 2x + 1 +--R |----------- +--R | 2 +--R \| x + 1 +--R + +--R 9 8 7 6 5 4 3 2 +--R (- 16x - 56x - 100x - 136x - 141x - 107x - 64x - 28x - 7x - 1) +--R * +--R +-+ +--R \|2 +--R + +--R 10 9 8 7 6 5 4 3 2 +--R - 16x - 64x - 140x - 224x - 269x - 252x - 187x - 104x - 43x +--R + +--R - 12x - 1 +--R / +--R 8 7 6 5 4 3 2 +-+ +--R (16x + 24x + 44x + 52x + 41x + 34x + 14x + 6x + 1)\|2 +--R + +--R 9 8 7 6 5 4 3 2 +--R 16x + 32x + 68x + 88x + 93x + 82x + 48x + 28x + 7x + 2 +--R * +--R +-----------+ +--R | 2 +------+ +--R |x + 2x + 1 | 2 +--R |----------- \|x + 1 +--R | 2 +--R \| x + 1 +--R + +--R 9 8 7 6 5 4 3 2 +--R - 16x - 24x - 52x - 64x - 61x - 57x - 30x - 18x - 5x +--R + +--R - 1 +--R * +--R +-+ +--R \|2 +--R + +--R 10 9 8 7 6 5 4 3 +--R - 16x - 32x - 76x - 104x - 125x - 122x - 87x - 60x +--R + +--R 2 +--R - 23x - 10x - 1 +--R * +--R +-----------+ +--R | 2 +--R |x + 2x + 1 +--R |----------- +--R | 2 +--R \| x + 1 +--R * +--R asinh(x) 2 +--R tanh(--------) +--R 2 +--R + +--R 8 7 6 5 4 3 2 +-+ +--R (- 32x - 48x - 88x - 104x - 82x - 68x - 28x - 12x - 2)\|2 +--R + +--R 9 8 7 6 5 4 3 2 +--R - 32x - 64x - 136x - 176x - 186x - 164x - 96x - 56x - 14x +--R + +--R - 4 +--R * +--R +-----------+ +--R | 2 +------+ +--R |x + 2x + 1 | 2 +--R |----------- \|x + 1 +--R | 2 +--R \| x + 1 +--R + +--R 9 8 7 6 5 4 3 2 +--R 32x + 48x + 104x + 128x + 122x + 114x + 60x + 36x +--R + +--R 10x + 2 +--R * +--R +-+ +--R \|2 +--R + +--R 10 9 8 7 6 5 4 3 +--R 32x + 64x + 152x + 208x + 250x + 244x + 174x + 120x +--R + +--R 2 +--R 46x + 20x + 2 +--R * +--R +-----------+ +--R | 2 +--R |x + 2x + 1 +--R |----------- +--R | 2 +--R \| x + 1 +--R * +--R asinh(x) +--R tanh(--------) +--R 2 +--R + +--R 8 7 6 5 4 3 2 +-+ +--R (- 16x - 24x - 44x - 52x - 41x - 34x - 14x - 6x - 1)\|2 +--R + +--R 9 8 7 6 5 4 3 2 +--R - 16x - 32x - 68x - 88x - 93x - 82x - 48x - 28x - 7x - 2 +--R * +--R +-----------+ +--R | 2 +------+ +--R |x + 2x + 1 | 2 +--R |----------- \|x + 1 +--R | 2 +--R \| x + 1 +--R + +--R 9 8 7 6 5 4 3 2 +-+ +--R (16x + 24x + 52x + 64x + 61x + 57x + 30x + 18x + 5x + 1)\|2 +--R + +--R 10 9 8 7 6 5 4 3 2 +--R 16x + 32x + 76x + 104x + 125x + 122x + 87x + 60x + 23x +--R + +--R 10x + 1 +--R * +--R +-----------+ +--R | 2 +--R |x + 2x + 1 +--R |----------- +--R | 2 +--R \| x + 1 +--R Type: Expression Integer +--E 284 + +--S 285 of 324 +t0454:= x/(1+x)/((2+x)/(3+x))^(1/2) +--R +--R +--R x +--R (285) --------------- +--R +-----+ +--R |x + 2 +--R (x + 1) |----- +--R \|x + 3 +--R Type: Expression Integer +--E 285 + +--S 286 of 324 +r0454:= (2+x)^(1/2)*(3+x)^(1/2)-atanh(((2+x)/(3+x))^(1/2))+2*2^(1/2)*_ + atanh(2^(1/2)*((2+x)/(3+x))^(1/2)) +--R +--R +--R +-----+ +-----+ +--R +-+ +-+ |x + 2 |x + 2 +-----+ +-----+ +--R (286) 2\|2 atanh(\|2 |----- ) - atanh( |----- ) + \|x + 2 \|x + 3 +--R \|x + 3 \|x + 3 +--R Type: Expression Integer +--E 286 + +--S 287 of 324 +a0454:= integrate(t0454,x) +--R +--R +--R (287) +--R +-----+ +--R +-+ |x + 2 +--R (2x + 6)\|2 |----- + 3x + 7 +-----+ +--R +-+ \|x + 3 |x + 2 +--R 2\|2 log(-----------------------------) - log( |----- + 1) +--R x + 1 \|x + 3 +--R + +--R +-----+ +-----+ +--R |x + 2 |x + 2 +--R log( |----- - 1) + (2x + 6) |----- +--R \|x + 3 \|x + 3 +--R / +--R 2 +--R Type: Union(Expression Integer,...) +--E 287 + +--S 288 of 324 +m0454:= a0454-r0454 +--R +--R +--R (288) +--R +-----+ +--R +-+ |x + 2 +--R (2x + 6)\|2 |----- + 3x + 7 +-----+ +--R +-+ \|x + 3 |x + 2 +--R 2\|2 log(-----------------------------) - log( |----- + 1) +--R x + 1 \|x + 3 +--R + +--R +-----+ +-----+ +-----+ +--R |x + 2 +-+ +-+ |x + 2 |x + 2 +--R log( |----- - 1) - 4\|2 atanh(\|2 |----- ) + 2atanh( |----- ) +--R \|x + 3 \|x + 3 \|x + 3 +--R + +--R +-----+ +--R +-----+ +-----+ |x + 2 +--R - 2\|x + 2 \|x + 3 + (2x + 6) |----- +--R \|x + 3 +--R / +--R 2 +--R Type: Expression Integer +--E 288 + +--S 289 of 324 +d0454:= D(m0454,x) +--R +--R +--R +-----+ +--R +-----+ +-----+ 2 |x + 2 +--R (2x + 5)\|x + 2 \|x + 3 + (- 2x - 11x - 15) |----- +--R \|x + 3 +--R (289) ----------------------------------------------------- +--R +-----+ +--R |x + 2 +-----+ +-----+ +--R (2x + 6) |----- \|x + 2 \|x + 3 +--R \|x + 3 +--R Type: Expression Integer +--E 289 + +--S 290 of 324 +t0455:= (x^(1/2)+x)^(1/2) +--R +--R +--R +--------+ +--R | +-+ +--R (290) \|\|x + x +--R Type: Expression Integer +--E 290 + +--S 291 of 324 +r0455:= -1/4*(1+2*x^(1/2))*(x^(1/2)+x)^(1/2)+2/3*(x^(1/2)+x)^(3/2)+_ + 1/8*atanh(2*(x^(1/2)+x)^(1/2)/(1+2*x^(1/2))) +--R +--R +--R +--------+ +--R | +-+ +--------+ +--R 2\|\|x + x +-+ | +-+ +--R 3atanh(------------) + (4\|x + 16x - 6)\|\|x + x +--R +-+ +--R 2\|x + 1 +--R (291) --------------------------------------------------- +--R 24 +--R Type: Expression Integer +--E 291 + +--S 292 of 324 +a0455:= integrate(t0455,x) +--R +--R +--R (292) +--R +--------+ +--R +-+ | +-+ +-+ +--R - 3log((8\|x + 4)\|\|x + x - 8\|x - 8x - 1) +--R + +--R +--------+ +--R +-+ | +-+ +--R (8\|x + 32x - 12)\|\|x + x +--R / +--R 48 +--R Type: Union(Expression Integer,...) +--E 292 + +--S 293 of 324 +m0455:= a0455-r0455 +--R +--R +--R (293) +--R +--------+ +--R +--------+ | +-+ +--R +-+ | +-+ +-+ 2\|\|x + x +--R - log((8\|x + 4)\|\|x + x - 8\|x - 8x - 1) - 2atanh(------------) +--R +-+ +--R 2\|x + 1 +--R --------------------------------------------------------------------- +--R 16 +--R Type: Expression Integer +--E 293 + +--S 294 of 324 +d0455:= D(m0455,x) +--R +--R +--R (294) 0 +--R Type: Expression Integer +--E 294 + +--S 295 of 324 +t0456:= (x-(-4+x^2)^(1/2))^(1/2) +--R +--R +--R +---------------+ +--R | +------+ +--R | | 2 +--R (295) \|- \|x - 4 + x +--R Type: Expression Integer +--E 295 + +--S 296 of 324 +r0456:= 2/3*(x-(-4+x^2)^(1/2))^(1/2)*(2*x+(-4+x^2)^(1/2)) +--R +--R +--R +---------------+ +--R +------+ | +------+ +--R | 2 | | 2 +--R (2\|x - 4 + 4x)\|- \|x - 4 + x +--R (296) ----------------------------------- +--R 3 +--R Type: Expression Integer +--E 296 + +--S 297 of 324 +a0456:= integrate(t0456,x) +--R +--R +--R +------+ +--R | 2 2 +--R - 2x\|x - 4 + 2x + 8 +--R (297) ----------------------- +--R +---------------+ +--R | +------+ +--R | | 2 +--R 3\|- \|x - 4 + x +--R Type: Union(Expression Integer,...) +--E 297 + +--S 298 of 324 +m0456:= a0456-r0456 +--R +--R +--R (298) 0 +--R Type: Expression Integer +--E 298 + +--S 299 of 324 +d0456:= D(m0456,x) +--R +--R +--R (299) 0 +--R Type: Expression Integer +--E 299 + +--S 300 of 324 +t0457:= (1+(1-x^2)^(1/2))^(1/2) +--R +--R +--R +---------------+ +--R | +--------+ +--R | | 2 +--R (300) \|\|- x + 1 + 1 +--R Type: Expression Integer +--E 300 + +--S 301 of 324 +r0457:= 2/3*(1+x^2-(1-x^2)^(1/2))*(1+(1-x^2)^(1/2))^(1/2)/x +--R +--R +--R +---------------+ +--R +--------+ | +--------+ +--R | 2 2 | | 2 +--R (- 2\|- x + 1 + 2x + 2)\|\|- x + 1 + 1 +--R (301) -------------------------------------------- +--R 3x +--R Type: Expression Integer +--E 301 + +--S 302 of 324 +a0457:= integrate(t0457,x) +--R +--R +--R +---------------+ +--R +--------+ | +--------+ +--R | 2 2 | | 2 +--R (- 2\|- x + 1 + 2x + 2)\|\|- x + 1 + 1 +--R (302) -------------------------------------------- +--R 3x +--R Type: Union(Expression Integer,...) +--E 302 + +--S 303 of 324 +m0457:= a0457-r0457 +--R +--R +--R (303) 0 +--R Type: Expression Integer +--E 303 + +--S 304 of 324 +d0457:= D(m0457,x) +--R +--R +--R (304) 0 +--R Type: Expression Integer +--E 304 + +--S 305 of 324 +t0458:= (1-x^(1/2)-x)^(1/2) +--R +--R +--R +--------------+ +--R | +-+ +--R (305) \|- \|x - x + 1 +--R Type: Expression Integer +--E 305 + +--S 306 of 324 +r0458:= -1/4*(1+2*x^(1/2))*(1-x^(1/2)-x)^(1/2)-2/3*(1-x^(1/2)-x)^(3/2)-5/8*_ + asin(1/5*(1+2*x^(1/2))*5^(1/2)) +--R +--R +--R +--------------+ +-+ +-+ +-+ +--R +-+ | +-+ 2\|5 \|x + \|5 +--R (4\|x + 16x - 22)\|- \|x - x + 1 - 15asin(----------------) +--R 5 +--R (306) -------------------------------------------------------------- +--R 24 +--R Type: Expression Integer +--E 306 + +--S 307 of 324 +a0458:= integrate(t0458,x) +--R +--R +--R (307) +--R +-+ +--------------+ +--R 8\|x + 8x - 3 +-+ | +-+ +--R - 15atan(----------------------------) + (8\|x + 32x - 44)\|- \|x - x + 1 +--R +--------------+ +--R +-+ | +-+ +--R (8\|x + 4)\|- \|x - x + 1 +--R ---------------------------------------------------------------------------- +--R 48 +--R Type: Union(Expression Integer,...) +--E 307 + +--S 308 of 324 +m0458:= a0458-r0458 +--R +--R +--R +-+ +-+ +-+ +-+ +--R 8\|x + 8x - 3 2\|5 \|x + \|5 +--R - 5atan(----------------------------) + 10asin(----------------) +--R +--------------+ 5 +--R +-+ | +-+ +--R (8\|x + 4)\|- \|x - x + 1 +--R (308) ---------------------------------------------------------------- +--R 16 +--R Type: Expression Integer +--E 308 + +--S 309 of 324 +d0458:= D(m0458,x) +--R +--R +--R (309) +--R +--------------+ +--R 2 +-+ 2 | +-+ +--R ((40x + 10x - 10)\|x + 80x - 30x)\|- \|x - x + 1 +--R + +--R +----------------+ +--R 2 +-+ 2 | +-+ +--R ((- 20x - 5x + 5)\|x - 40x + 15x)\|- 4\|x - 4x + 4 +--R / +--R +----------------+ +--------------+ +--R 2 +-+ 3 2 | +-+ | +-+ +--R ((128x - 48x)\|x + 64x + 16x - 16x)\|- 4\|x - 4x + 4 \|- \|x - x + 1 +--R Type: Expression Integer +--E 309 + +--S 310 of 324 +t0459:= 1/((-1-x)/x)^(1/2) +--R +--R +--R 1 +--R (310) ---------- +--R +-------+ +--R |- x - 1 +--R |------- +--R \| x +--R Type: Expression Integer +--E 310 + +--S 311 of 324 +r0459:= -x*(-(1+x)/x)^(1/2)+atan((-(1+x)/x)^(1/2)) +--R +--R +--R +-------+ +-------+ +--R |- x - 1 |- x - 1 +--R (311) atan( |------- ) - x |------- +--R \| x \| x +--R Type: Expression Integer +--E 311 + +--S 312 of 324 +a0459:= integrate(t0459,x) +--R +--R +--R +-------+ +-------+ +--R |- x - 1 |- x - 1 +--R (312) atan( |------- ) - x |------- +--R \| x \| x +--R Type: Union(Expression Integer,...) +--E 312 + +--S 313 of 324 +m0459:= a0459-r0459 +--R +--R +--R (313) 0 +--R Type: Expression Integer +--E 313 + +--S 314 of 324 +d0459:= D(m0459,x) +--R +--R +--R (314) 0 +--R Type: Expression Integer +--E 314 + +--S 315 of 324 +t0460:= (x+x^2)^(3/2)/(1+x^2) +--R +--R +--R +------+ +--R 2 | 2 +--R (x + x)\|x + x +--R (315) ----------------- +--R 2 +--R x + 1 +--R Type: Expression Integer +--E 315 + +--S 316 of 324 +r0460:= 5/4*(x+x^2)^(1/2)+1/2*x*(x+x^2)^(1/2)-5/4*_ + atanh((x*(1+x))^(1/2)/x)+1/2*(1-%i)^(3/2)*_ + atanh(2*(1-%i)^(1/2)*(x+x^2)^(1/2)/(1+(2-%i)*x))+1/2*(1+%i)^(3/2)*_ + atanh(2*(1+%i)^(1/2)*(x+x^2)^(1/2)/(1+(2+%i)*x)) +--R +--R +--R (316) +--R +------+ +--R +------+ | 2 +--R +------+ 2\|1 + %i \|x + x +--R (2 + 2%i)\|1 + %i atanh(-------------------) +--R (2 + %i)x + 1 +--R + +--R +------+ +------+ +--R +------+ | 2 | 2 +--R +------+ 2%i\|1 - %i \|x + x \|x + x +--R (2 - 2%i)\|1 - %i atanh(---------------------) - 5atanh(---------) +--R (1 + 2%i)x + %i x +--R + +--R +------+ +--R | 2 +--R (2x + 5)\|x + x +--R / +--R 4 +--R Type: Expression Complex Integer +--E 316 + +--S 317 of 324 +a0460:= integrate(t0460,x) +--R +--R +--R (317) +--R +------+ +--R 4+-+ %pi | 2 2 4+-+ %pi +--R ((- 128x - 64)\|8 cos(---)\|x + x + (128x + 128x + 16)\|8 cos(---)) +--R 8 8 +--R * +--R log +--R +------+ +--R 4+-+ %pi 4+-+ %pi | 2 4+-+2 %pi 2 +--R (2\|8 sin(---) + 2\|8 cos(---) - 4x)\|x + x + \|8 sin(---) +--R 8 8 8 +--R + +--R 4+-+ %pi 4+-+2 %pi 2 4+-+ %pi +--R (- 2x + 2)\|8 sin(---) + \|8 cos(---) + (- 2x - 2)\|8 cos(---) +--R 8 8 8 +--R + +--R 2 +--R 4x + 2x + 2 +--R + +--R +------+ +------+ +--R | 2 2 | 2 +--R ((160x + 80)\|x + x - 160x - 160x - 20)log(2\|x + x - 2x - 1) +--R + +--R +------+ +--R 4+-+ %pi | 2 2 4+-+ %pi +--R ((128x + 64)\|8 cos(---)\|x + x + (- 128x - 128x - 16)\|8 cos(---)) +--R 8 8 +--R * +--R log +--R +------+ +--R 4+-+ %pi 4+-+ %pi | 2 4+-+2 %pi 2 +--R (- 2\|8 sin(---) - 2\|8 cos(---) - 4x)\|x + x + \|8 sin(---) +--R 8 8 8 +--R + +--R 4+-+ %pi 4+-+2 %pi 2 4+-+ %pi 2 +--R (2x - 2)\|8 sin(---) + \|8 cos(---) + (2x + 2)\|8 cos(---) + 4x +--R 8 8 8 +--R + +--R 2x + 2 +--R + +--R +------+ +--R 4+-+ %pi | 2 2 4+-+ %pi +--R ((256x + 128)\|8 sin(---)\|x + x + (- 256x - 256x - 32)\|8 sin(---)) +--R 8 8 +--R * +--R 4+-+ %pi 4+-+ %pi +--R \|8 sin(---) - \|8 cos(---) + 2 +--R 8 8 +--R atan(---------------------------------------------) +--R +------+ +--R | 2 4+-+ %pi 4+-+ %pi +--R 2\|x + x + \|8 sin(---) + \|8 cos(---) - 2x +--R 8 8 +--R + +--R +------+ +--R 4+-+ %pi | 2 2 4+-+ %pi +--R ((256x + 128)\|8 sin(---)\|x + x + (- 256x - 256x - 32)\|8 sin(---)) +--R 8 8 +--R * +--R 4+-+ %pi 4+-+ %pi +--R \|8 sin(---) - \|8 cos(---) - 2 +--R 8 8 +--R atan(---------------------------------------------) +--R +------+ +--R | 2 4+-+ %pi 4+-+ %pi +--R 2\|x + x - \|8 sin(---) - \|8 cos(---) - 2x +--R 8 8 +--R + +--R +------+ +--R 3 2 | 2 4 3 2 +--R (- 128x - 448x - 264x - 4)\|x + x + 128x + 512x + 472x + 88x - 9 +--R / +--R +------+ +--R | 2 2 +--R (256x + 128)\|x + x - 256x - 256x - 32 +--R Type: Union(Expression Integer,...) +--E 317 + +--S 318 of 324 +m0460:= a0460-r0460 +--R +--R +--R (318) +--R - +--R 4+-+ %pi +--R 16\|8 cos(---) +--R 8 +--R * +--R log +--R +------+ +--R 4+-+ %pi 4+-+ %pi | 2 4+-+2 %pi 2 +--R (2\|8 sin(---) + 2\|8 cos(---) - 4x)\|x + x + \|8 sin(---) +--R 8 8 8 +--R + +--R 4+-+ %pi 4+-+2 %pi 2 +--R (- 2x + 2)\|8 sin(---) + \|8 cos(---) +--R 8 8 +--R + +--R 4+-+ %pi 2 +--R (- 2x - 2)\|8 cos(---) + 4x + 2x + 2 +--R 8 +--R + +--R +------+ +--R | 2 +--R 20log(2\|x + x - 2x - 1) +--R + +--R 4+-+ %pi +--R 16\|8 cos(---) +--R 8 +--R * +--R log +--R +------+ +--R 4+-+ %pi 4+-+ %pi | 2 4+-+2 %pi 2 +--R (- 2\|8 sin(---) - 2\|8 cos(---) - 4x)\|x + x + \|8 sin(---) +--R 8 8 8 +--R + +--R 4+-+ %pi 4+-+2 %pi 2 4+-+ %pi 2 +--R (2x - 2)\|8 sin(---) + \|8 cos(---) + (2x + 2)\|8 cos(---) + 4x +--R 8 8 8 +--R + +--R 2x + 2 +--R + +--R +------+ +--R +------+ | 2 +--R +------+ 2\|1 + %i \|x + x +--R (- 16 - 16%i)\|1 + %i atanh(-------------------) +--R (2 + %i)x + 1 +--R + +--R +------+ +------+ +--R +------+ | 2 | 2 +--R +------+ 2%i\|1 - %i \|x + x \|x + x +--R (- 16 + 16%i)\|1 - %i atanh(---------------------) + 40atanh(---------) +--R (1 + 2%i)x + %i x +--R + +--R 4+-+ %pi 4+-+ %pi +--R \|8 sin(---) - \|8 cos(---) + 2 +--R 4+-+ %pi 8 8 +--R 32\|8 sin(---)atan(---------------------------------------------) +--R 8 +------+ +--R | 2 4+-+ %pi 4+-+ %pi +--R 2\|x + x + \|8 sin(---) + \|8 cos(---) - 2x +--R 8 8 +--R + +--R 4+-+ %pi 4+-+ %pi +--R \|8 sin(---) - \|8 cos(---) - 2 +--R 4+-+ %pi 8 8 +--R 32\|8 sin(---)atan(---------------------------------------------) + 9 +--R 8 +------+ +--R | 2 4+-+ %pi 4+-+ %pi +--R 2\|x + x - \|8 sin(---) - \|8 cos(---) - 2x +--R 8 8 +--R / +--R 32 +--R Type: Expression Complex Integer +--E 318 + +--S 319 of 324 +d0460:= D(m0460,x) +--R +--R +--R (319) +--R 3 2 %pi 12 3 2 %pi %pi 11 +--R (- 16x - 8x - 8)sin(---) + (- 64x - 32x - 32)cos(---)sin(---) +--R 8 8 8 +--R + +--R 3 2 %pi 2 +--R (- 160x - 80x - 80)cos(---) +--R 8 +--R + +--R 5 3 2 4+-+2 +--R (48x - 10x + 18x - 26x + 2)\|8 +--R * +--R %pi 10 +--R sin(---) +--R 8 +--R + +--R 3 2 %pi 3 +--R (- 320x - 160x - 160)cos(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 %pi +--R (160x - 64x - 124x - 4x - 124x - 4)\|8 cos(---) +--R 8 +--R * +--R %pi 9 +--R sin(---) +--R 8 +--R + +--R 3 2 %pi 4 +--R (- 496x - 248x - 248)cos(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 %pi 2 7 +--R (592x + 128x - 166x + 110x - 214x - 34)\|8 cos(---) - 128x +--R 8 +--R + +--R 6 5 4 3 2 +--R 1088x + 1336x + 460x + 664x + 168x - 4 +--R * +--R %pi 8 +--R sin(---) +--R 8 +--R + +--R 3 2 %pi 5 +--R (- 640x - 320x - 320)cos(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 %pi 3 +--R (1152x + 512x - 112x + 304x - 240x - 80)\|8 cos(---) +--R 8 +--R + +--R 7 6 5 4 3 2 +--R (- 2048x + 1024x + 2944x + 192x + 1024x + 320x - 128x) +--R * +--R %pi +--R cos(---) +--R 8 +--R * +--R %pi 7 +--R sin(---) +--R 8 +--R + +--R 3 2 %pi 6 +--R (- 704x - 352x - 352)cos(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 %pi 4 +--R (1696x + 1024x + 52x + 540x - 172x - 132)\|8 cos(---) +--R 8 +--R + +--R 7 6 5 4 3 2 +--R (- 7168x - 1536x + 4672x - 1696x - 160x - 160x - 864x) +--R * +--R %pi 2 +--R cos(---) +--R 8 +--R + +--R 9 8 7 6 5 4 3 +--R - 128x - 896x - 544x + 768x + 471x + 359x + 248x +--R + +--R 2 +--R - 24x + x + 1 +--R * +--R 4+-+2 +--R \|8 +--R * +--R %pi 6 +--R sin(---) +--R 8 +--R + +--R 3 2 %pi 7 +--R (- 640x - 320x - 320)cos(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 %pi 5 +--R (2112x + 1664x + 424x + 856x + 40x - 168)\|8 cos(---) +--R 8 +--R + +--R 7 6 5 4 3 2 +--R - 11264x - 512x + 15168x + 6816x + 4864x + 1984x +--R + +--R - 1344x - 96 +--R * +--R %pi 3 +--R cos(---) +--R 8 +--R + +--R 9 8 7 6 5 4 3 +--R 1792x - 256x - 1472x + 3904x + 4934x + 3310x + 1680x +--R + +--R 2 +--R 144x - 22x + 2 +--R * +--R 4+-+2 %pi +--R \|8 cos(---) +--R 8 +--R * +--R %pi 5 +--R sin(---) +--R 8 +--R + +--R 3 2 %pi 8 +--R (- 496x - 248x - 248)cos(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 %pi 6 +--R (1888x + 1792x + 652x + 900x + 236x - 156)\|8 cos(---) +--R 8 +--R + +--R 7 6 5 4 3 2 +--R - 23296x - 22144x + 5072x + 4424x + 4976x + 5264x +--R + +--R - 160x - 248 +--R * +--R %pi 4 +--R cos(---) +--R 8 +--R + +--R 9 8 7 6 5 4 +--R 1408x - 13696x - 29344x - 20224x - 8797x - 1205x +--R + +--R 3 2 +--R 2552x + 840x - 11x - 3 +--R * +--R 4+-+2 %pi 2 +--R \|8 cos(---) +--R 8 +--R + +--R 10 9 8 7 6 5 +--R - 4096x - 13824x - 24320x - 23040x - 14608x - 5924x +--R + +--R 4 3 2 +--R - 384x + 40x + 16x - 4x +--R * +--R %pi 4 +--R sin(---) +--R 8 +--R + +--R 3 2 %pi 9 +--R (- 320x - 160x - 160)cos(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 %pi 7 +--R (1408x + 1536x + 688x + 784x + 304x - 112)\|8 cos(---) +--R 8 +--R + +--R 7 6 5 4 3 2 +--R - 18432x - 27648x - 8320x - 576x + 1920x + 4672x +--R + +--R 1280x - 256 +--R * +--R %pi 5 +--R cos(---) +--R 8 +--R + +--R 9 8 7 6 5 4 +--R 17920x + 19968x - 13184x - 25728x - 18916x - 11796x +--R + +--R 3 2 +--R - 2400x + 672x + 68x - 12 +--R * +--R 4+-+2 %pi 3 +--R \|8 cos(---) +--R 8 +--R + +--R 11 10 9 8 7 6 +--R 16384x + 90112x + 156672x + 124416x + 59968x + 15584x +--R + +--R 5 4 3 2 +--R - 5424x - 2560x + 736x + 288x + 16x +--R * +--R %pi +--R cos(---) +--R 8 +--R * +--R %pi 3 +--R sin(---) +--R 8 +--R + +--R 3 2 %pi 10 +--R (- 160x - 80x - 80)cos(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 %pi 8 +--R (816x + 1024x + 534x + 530x + 262x - 62)\|8 cos(---) +--R 8 +--R + +--R 7 6 5 4 3 2 +--R - 13312x - 25088x - 16192x - 8928x - 3552x + 1696x +--R + +--R 1248x - 128 +--R * +--R %pi 6 +--R cos(---) +--R 8 +--R + +--R 9 8 7 6 5 4 +--R 11904x + 28032x + 18336x - 512x - 6267x - 6923x +--R + +--R 3 2 +--R - 3656x - 280x + 83x - 13 +--R * +--R 4+-+2 %pi 4 +--R \|8 cos(---) +--R 8 +--R + +--R 11 10 9 8 7 +--R - 57344x - 77824x + 66048x + 186624x + 172320x +--R + +--R 6 5 4 3 2 +--R 107408x + 40024x + 5120x + 336x + 368x + 56x +--R * +--R %pi 2 +--R cos(---) +--R 8 +--R + +--R 13 12 11 10 9 +--R - 4096x - 16384x - 32256x - 36352x - 27408x +--R + +--R 8 7 6 5 4 3 2 +--R - 15840x - 6890x - 2446x - 648x - 128x - 14x - 2x +--R * +--R 4+-+2 +--R \|8 +--R * +--R %pi 2 +--R sin(---) +--R 8 +--R + +--R 3 2 %pi 11 +--R (- 64x - 32x - 32)cos(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 %pi 9 +--R (288x + 448x + 276x + 236x + 148x - 20)\|8 cos(---) +--R 8 +--R + +--R 7 6 5 4 3 2 +--R - 5120x - 11776x - 10048x - 6560x - 3712x - 320x + 448x +--R + +--R - 32 +--R * +--R %pi 7 +--R cos(---) +--R 8 +--R + +--R 9 8 7 6 5 4 +--R 6912x + 19200x + 20288x + 12096x + 4782x - 298x +--R + +--R 3 2 +--R - 1488x - 400x + 34x - 6 +--R * +--R 4+-+2 %pi 5 +--R \|8 cos(---) +--R 8 +--R + +--R 11 10 9 8 7 +--R - 32768x - 114688x - 139264x - 60416x + 11648x +--R + +--R 6 5 4 3 2 +--R 36160x + 31408x + 12288x + 1952x + 192x + 48x +--R * +--R %pi 3 +--R cos(---) +--R 8 +--R + +--R 13 12 11 10 9 8 +--R 8192x + 16384x - 5120x - 41984x - 57568x - 47872x +--R + +--R 7 6 5 4 3 2 +--R - 27964x - 12084x - 3952x - 928x - 148x - 12x +--R * +--R 4+-+2 %pi +--R \|8 cos(---) +--R 8 +--R * +--R %pi +--R sin(---) +--R 8 +--R + +--R 3 2 %pi 12 +--R (- 16x - 8x - 8)cos(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 %pi 10 +--R (80x + 128x + 90x + 78x + 42x - 2)\|8 cos(---) +--R 8 +--R + +--R 7 6 5 4 3 2 +--R (- 1152x - 3520x - 3848x - 2836x - 1928x - 568x + 32x - 4) +--R * +--R %pi 8 +--R cos(---) +--R 8 +--R + +--R 9 8 7 6 5 4 3 +--R 1152x + 4992x + 7968x + 7168x + 4913x + 2409x + 472x +--R + +--R 2 +--R - 24x + 7x - 1 +--R * +--R 4+-+2 %pi 6 +--R \|8 cos(---) +--R 8 +--R + +--R 11 10 9 8 7 6 +--R - 8192x - 32768x - 60416x - 65024x - 46624x - 24640x +--R + +--R 5 4 3 +--R - 8436x - 960x + 136x + 12x +--R * +--R %pi 4 +--R cos(---) +--R 8 +--R + +--R 13 12 11 10 9 8 +--R 4096x + 16384x + 28160x + 26112x + 14352x + 4448x +--R + +--R 7 6 5 4 3 2 +--R - 166x - 890x - 504x - 176x - 34x - 6x +--R * +--R 4+-+2 %pi 2 +--R \|8 cos(---) +--R 8 +--R + +--R 13 12 11 10 9 8 +--R 16384x + 49152x + 71680x + 69632x + 48704x + 25664x +--R + +--R 7 6 5 4 3 +--R 10312x + 3104x + 688x + 96x + 8x +--R * +--R +------+ +--R | 2 +--R \|x + x +--R + +--R 4 3 2 %pi 12 +--R (16x + 16x + 16x + 16x)sin(---) +--R 8 +--R + +--R 4 3 2 %pi %pi 11 +--R (64x + 64x + 64x + 64x)cos(---)sin(---) +--R 8 8 +--R + +--R 4 3 2 %pi 2 +--R (160x + 160x + 160x + 160x)cos(---) +--R 8 +--R + +--R 6 5 4 3 4+-+2 +--R (- 48x - 24x + 16x - 16x + 8x)\|8 +--R * +--R %pi 10 +--R sin(---) +--R 8 +--R + +--R 4 3 2 %pi 3 +--R (320x + 320x + 320x + 320x)cos(---) +--R 8 +--R + +--R 6 5 4 3 2 4+-+2 %pi +--R (- 160x - 16x + 176x + 48x + 80x + 64x)\|8 cos(---) +--R 8 +--R * +--R %pi 9 +--R sin(---) +--R 8 +--R + +--R 4 3 2 %pi 4 +--R (496x + 496x + 496x + 496x)cos(---) +--R 8 +--R + +--R 6 5 4 3 2 4+-+2 %pi 2 8 +--R (- 592x - 424x + 176x - 48x + 128x + 184x)\|8 cos(---) + 128x +--R 8 +--R + +--R 7 6 5 4 3 2 +--R - 1024x - 1896x - 984x - 800x - 480x + 72x - 8x +--R * +--R %pi 8 +--R sin(---) +--R 8 +--R + +--R 4 3 2 %pi 5 +--R (640x + 640x + 640x + 640x)cos(---) +--R 8 +--R + +--R 6 5 3 2 4+-+2 %pi 3 +--R (- 1152x - 1088x - 256x + 128x + 320x)\|8 cos(---) +--R 8 +--R + +--R 8 6 5 4 3 2 %pi +--R (2048x - 3712x - 1408x - 896x - 896x + 256x )cos(---) +--R 8 +--R * +--R %pi 7 +--R sin(---) +--R 8 +--R + +--R 4 3 2 %pi 6 +--R (704x + 704x + 704x + 704x)cos(---) +--R 8 +--R + +--R 6 5 4 3 2 4+-+2 %pi 4 +--R (- 1696x - 1872x - 352x - 544x + 64x + 432x)\|8 cos(---) +--R 8 +--R + +--R 8 7 6 5 4 3 2 +--R (7168x + 5120x - 4800x - 384x + 1408x - 128x + 1088x + 256x) +--R * +--R %pi 2 +--R cos(---) +--R 8 +--R + +--R 10 9 8 7 6 5 4 3 +--R 128x + 960x + 976x - 600x - 872x - 496x - 416x - 56x +--R + +--R 2 +--R - 8x +--R * +--R 4+-+2 +--R \|8 +--R * +--R %pi 6 +--R sin(---) +--R 8 +--R + +--R 4 3 2 %pi 7 +--R (640x + 640x + 640x + 640x)cos(---) +--R 8 +--R + +--R 6 5 4 3 2 4+-+2 %pi 5 +--R (- 2112x - 2720x - 992x - 992x - 160x + 448x)\|8 cos(---) +--R 8 +--R + +--R 8 7 6 5 4 3 2 +--R 11264x + 6144x - 16320x - 13760x - 6784x - 4224x + 832x +--R + +--R 832x +--R * +--R %pi 3 +--R cos(---) +--R 8 +--R + +--R 10 9 8 7 6 5 4 +--R - 1792x - 640x + 1824x - 3312x - 6984x - 5256x - 2976x +--R + +--R 3 2 +--R - 720x + 8x + 8x +--R * +--R 4+-+2 %pi +--R \|8 cos(---) +--R 8 +--R * +--R %pi 5 +--R sin(---) +--R 8 +--R + +--R 4 3 2 %pi 8 +--R (496x + 496x + 496x + 496x)cos(---) +--R 8 +--R + +--R 6 5 4 3 2 4+-+2 %pi 6 +--R (- 1888x - 2736x - 1312x - 1120x - 320x + 336x)\|8 cos(---) +--R 8 +--R + +--R 8 7 6 5 4 3 2 +--R 23296x + 33792x + 3088x - 8272x - 6080x - 7744x - 1488x +--R + +--R 1040x +--R * +--R %pi 4 +--R cos(---) +--R 8 +--R + +--R 10 9 8 7 6 5 +--R - 1408x + 12992x + 36368x + 33096x + 16152x + 4336x +--R + +--R 4 3 2 +--R - 2528x - 2008x - 136x + 32x +--R * +--R 4+-+2 %pi 2 +--R \|8 cos(---) +--R 8 +--R + +--R 11 10 9 8 7 6 5 +--R 4096x + 15872x + 30720x + 33728x + 23792x + 11440x + 2304x +--R + +--R 4 3 2 +--R - 128x + 16x + 16x +--R * +--R %pi 4 +--R sin(---) +--R 8 +--R + +--R 4 3 2 %pi 9 +--R (320x + 320x + 320x + 320x)cos(---) +--R 8 +--R + +--R 6 5 4 3 2 4+-+2 %pi 7 +--R (- 1408x - 2240x - 1280x - 1024x - 384x + 192x)\|8 cos(---) +--R 8 +--R + +--R 8 7 6 5 4 3 2 +--R 18432x + 36864x + 19840x + 2432x - 1664x - 5760x - 2560x +--R + +--R 512x +--R * +--R %pi 5 +--R cos(---) +--R 8 +--R + +--R 10 9 8 7 6 5 +--R - 17920x - 28928x + 5440x + 33696x + 29584x + 19152x +--R + +--R 4 3 2 +--R 6848x - 288x - 272x + 48x +--R * +--R 4+-+2 %pi 3 +--R \|8 cos(---) +--R 8 +--R + +--R 12 11 10 9 8 7 +--R - 16384x - 98304x - 199680x - 192512x - 107584x - 36736x +--R + +--R 6 5 4 3 2 +--R 1344x + 5632x - 192x - 640x - 64x +--R * +--R %pi +--R cos(---) +--R 8 +--R * +--R %pi 3 +--R sin(---) +--R 8 +--R + +--R 4 3 2 %pi 10 +--R (160x + 160x + 160x + 160x)cos(---) +--R 8 +--R + +--R 6 5 4 3 2 4+-+2 %pi 8 +--R (- 816x - 1432x - 944x - 720x - 320x + 72x)\|8 cos(---) +--R 8 +--R + +--R 8 7 6 5 4 3 2 +--R (13312x + 31744x + 27072x + 14720x + 7040x - 640x - 1600x ) +--R * +--R %pi 6 +--R cos(---) +--R 8 +--R + +--R 10 9 8 7 6 5 +--R - 11904x - 33984x - 30864x - 5896x + 7528x + 9616x +--R + +--R 4 3 2 +--R 6560x + 1496x - 56x + 32x +--R * +--R 4+-+2 %pi 4 +--R \|8 cos(---) +--R 8 +--R + +--R 12 11 10 9 8 7 +--R 57344x + 106496x - 34304x - 225792x - 254752x - 175840x +--R + +--R 6 5 4 3 2 +--R - 80320x - 17664x - 1120x - 544x - 192x +--R * +--R %pi 2 +--R cos(---) +--R 8 +--R + +--R 14 13 12 11 10 9 +--R 4096x + 18432x + 39936x + 50688x + 42416x + 26488x +--R + +--R 8 7 6 5 4 +--R 12760x + 4816x + 1472x + 312x + 56x +--R * +--R 4+-+2 +--R \|8 +--R * +--R %pi 2 +--R sin(---) +--R 8 +--R + +--R 4 3 2 %pi 11 +--R (64x + 64x + 64x + 64x)cos(---) +--R 8 +--R + +--R 6 5 4 3 2 4+-+2 %pi 9 +--R (- 288x - 592x - 464x - 336x - 176x )\|8 cos(---) +--R 8 +--R + +--R 8 7 6 5 4 3 2 +--R 5120x + 14336x + 15296x + 10432x + 6272x + 1664x - 320x +--R + +--R - 64x +--R * +--R %pi 7 +--R cos(---) +--R 8 +--R + +--R 10 9 8 7 6 5 +--R - 6912x - 22656x - 29024x - 20272x - 9224x - 1288x +--R + +--R 4 3 2 +--R 1888x + 1008x + 72x + 8x +--R * +--R 4+-+2 %pi 5 +--R \|8 cos(---) +--R 8 +--R + +--R 12 11 10 9 8 7 +--R 32768x + 131072x + 192512x + 117760x + 7040x - 44416x +--R + +--R 6 5 4 3 2 +--R - 47232x - 24576x - 5760x - 640x - 128x +--R * +--R %pi 3 +--R cos(---) +--R 8 +--R + +--R 14 13 12 11 10 9 +--R - 8192x - 20480x - 2048x + 46080x + 77216x + 72144x +--R + +--R 8 7 6 5 4 3 +--R 46848x + 22384x + 8128x + 2192x + 416x + 48x +--R * +--R 4+-+2 %pi +--R \|8 cos(---) +--R 8 +--R * +--R %pi +--R sin(---) +--R 8 +--R + +--R 4 3 2 %pi 12 +--R (16x + 16x + 16x + 16x)cos(---) +--R 8 +--R + +--R 6 5 4 3 2 4+-+2 %pi 10 +--R (- 80x - 168x - 144x - 112x - 64x - 8x)\|8 cos(---) +--R 8 +--R + +--R 8 7 6 5 4 3 2 +--R (1152x + 4096x + 5464x + 4392x + 3040x + 1312x + 136x - 8x) +--R * +--R %pi 8 +--R cos(---) +--R 8 +--R + +--R 10 9 8 7 6 5 4 +--R - 1152x - 5568x - 10320x - 10600x - 7768x - 4304x - 1312x +--R + +--R 3 2 +--R - 72x + 8x +--R * +--R 4+-+2 %pi 6 +--R \|8 cos(---) +--R 8 +--R + +--R 12 11 10 9 8 7 6 +--R 8192x + 36864x + 75776x + 91648x + 73312x + 42544x + 17360x +--R + +--R 5 4 3 2 +--R 3584x - 32x - 48x - 16x +--R * +--R %pi 4 +--R cos(---) +--R 8 +--R + +--R 14 13 12 11 10 9 +--R - 4096x - 18432x - 35840x - 38400x - 24752x - 9592x +--R + +--R 8 7 6 5 4 3 +--R - 1160x + 1152x + 864x + 360x + 88x + 16x +--R * +--R 4+-+2 %pi 2 +--R \|8 cos(---) +--R 8 +--R + +--R 14 13 12 11 10 9 +--R - 16384x - 57344x - 94208x - 100352x - 76992x - 44320x +--R + +--R 8 7 6 5 4 +--R - 19616x - 6592x - 1664x - 288x - 32x +--R / +--R 5 4+-+2 %pi 10 5 4+-+2 %pi %pi 9 +--R (16x - 16x)\|8 sin(---) + (64x - 64x)\|8 cos(---)sin(---) +--R 8 8 8 +--R + +--R 5 4 3 2 4+-+2 %pi 2 7 6 +--R (208x + 96x + 96x + 96x - 112x)\|8 cos(---) - 192x + 224x +--R 8 +--R + +--R 5 4 3 2 +--R 192x + 192x + 384x - 32x +--R * +--R %pi 8 +--R sin(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 %pi 3 +--R (384x + 256x + 256x + 256x - 128x)\|8 cos(---) +--R 8 +--R + +--R 7 6 5 4 3 2 %pi +--R (- 1280x - 384x - 384x - 512x + 768x - 128x - 128x)cos(---) +--R 8 +--R * +--R %pi 7 +--R sin(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 %pi 4 +--R (544x + 448x + 448x + 448x - 96x)\|8 cos(---) +--R 8 +--R + +--R 7 6 5 4 3 2 +--R (- 3584x - 2304x - 1536x - 2048x + 1536x + 256x - 512x) +--R * +--R %pi 2 +--R cos(---) +--R 8 +--R + +--R 9 8 7 6 5 4 3 2 +--R 256x - 128x + 80x + 296x + 40x + 416x + 208x - 8x +--R + +--R - 8x +--R * +--R 4+-+2 +--R \|8 +--R * +--R %pi 6 +--R sin(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 %pi 5 +--R (640x + 640x + 640x + 640x )\|8 cos(---) +--R 8 +--R + +--R 7 6 5 4 3 2 +--R (- 5888x - 5248x - 2432x - 3072x + 2816x + 2176x - 640x) +--R * +--R %pi 3 +--R cos(---) +--R 8 +--R + +--R 9 8 7 6 5 4 3 +--R 1792x + 1024x + 528x + 1168x - 544x + 192x + 688x +--R + +--R 2 +--R 48x - 32x +--R * +--R 4+-+2 %pi +--R \|8 cos(---) +--R 8 +--R * +--R %pi 5 +--R sin(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 %pi 6 +--R (544x + 640x + 640x + 640x + 96x)\|8 cos(---) +--R 8 +--R + +--R 7 6 5 4 3 2 %pi 4 +--R (- 8832x - 13248x - 9856x - 9856x - 1024x + 3392x )cos(---) +--R 8 +--R + +--R 9 8 7 6 5 4 3 +--R 3840x + 2432x - 1680x - 1752x - 5304x - 3936x + 176x +--R + +--R 2 +--R 248x - 40x +--R * +--R 4+-+2 %pi 2 +--R \|8 cos(---) +--R 8 +--R + +--R 11 10 9 8 7 6 5 +--R - 2304x - 1664x - 3360x - 5296x - 2624x - 2992x - 1248x +--R + +--R 4 3 2 +--R 688x + 320x + 48x +--R * +--R %pi 4 +--R sin(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 %pi 7 +--R (384x + 512x + 512x + 512x + 128x)\|8 cos(---) +--R 8 +--R + +--R 7 6 5 4 3 2 +--R - 5888x - 12416x - 11392x - 10752x - 4864x + 1664x +--R + +--R 640x +--R * +--R %pi 5 +--R cos(---) +--R 8 +--R + +--R 9 8 7 6 5 4 +--R 8704x + 17408x + 15328x + 13472x + 4992x - 3712x +--R + +--R 3 2 +--R - 1632x + 224x +--R * +--R 4+-+2 %pi 3 +--R \|8 cos(---) +--R 8 +--R + +--R 11 10 9 8 7 6 +--R - 9216x + 1536x + 23424x + 28992x + 38144x + 27968x +--R + +--R 5 4 3 2 +--R 6272x + 704x + 768x + 192x +--R * +--R %pi +--R cos(---) +--R 8 +--R * +--R %pi 3 +--R sin(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 %pi 8 +--R (208x + 320x + 320x + 320x + 112x)\|8 cos(---) +--R 8 +--R + +--R 7 6 5 4 3 2 +--R (- 3584x - 8448x - 9216x - 8704x - 5120x - 256x + 512x) +--R * +--R %pi 6 +--R cos(---) +--R 8 +--R + +--R 9 8 7 6 5 4 +--R 3840x + 12928x + 16688x + 15864x + 11960x + 2912x +--R + +--R 3 2 +--R - 848x - 24x + 40x +--R * +--R 4+-+2 %pi 4 +--R \|8 cos(---) +--R 8 +--R + +--R 11 10 9 8 7 +--R - 38400x - 96000x - 111296x - 104992x - 65792x +--R + +--R 6 5 4 3 2 +--R - 8608x + 6848x + 544x - 256x + 160x +--R * +--R %pi 2 +--R cos(---) +--R 8 +--R + +--R 13 12 11 10 9 8 +--R 1024x - 1024x - 5824x - 9856x - 13036x - 11580x +--R + +--R 7 6 5 4 3 2 +--R - 6868x - 2820x - 660x - 68x + 20x + 4x +--R * +--R 4+-+2 +--R \|8 +--R * +--R %pi 2 +--R sin(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 %pi 9 +--R (64x + 128x + 128x + 128x + 64x)\|8 cos(---) +--R 8 +--R + +--R 7 6 5 4 3 2 +--R (- 1280x - 3456x - 4224x - 4096x - 2816x - 640x + 128x) +--R * +--R %pi 7 +--R cos(---) +--R 8 +--R + +--R 9 8 7 6 5 4 3 +--R 1792x + 6144x + 9488x + 9936x + 8096x + 3776x + 432x +--R + +--R 2 +--R - 16x + 32x +--R * +--R 4+-+2 %pi 5 +--R \|8 cos(---) +--R 8 +--R + +--R 11 10 9 8 7 6 +--R - 9216x - 47616x - 87168x - 100032x - 91648x - 53696x +--R + +--R 5 4 3 2 +--R - 14208x - 1344x - 512x - 64x +--R * +--R %pi 3 +--R cos(---) +--R 8 +--R + +--R 13 12 11 10 9 8 +--R 10240x + 30720x + 48256x + 57600x + 50376x + 30408x +--R + +--R 7 6 5 4 3 2 +--R 12920x + 3576x + 568x + 56x + 8x + 8x +--R * +--R 4+-+2 %pi +--R \|8 cos(---) +--R 8 +--R * +--R %pi +--R sin(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 %pi 10 +--R (16x + 32x + 32x + 32x + 16x)\|8 cos(---) +--R 8 +--R + +--R 7 6 5 4 3 2 %pi 8 +--R (- 192x - 800x - 1088x - 1088x - 896x - 288x )cos(---) +--R 8 +--R + +--R 9 8 7 6 5 4 3 2 +--R 256x + 1152x + 2320x + 2744x + 2520x + 1632x + 464x + 40x +--R + +--R 8x +--R * +--R 4+-+2 %pi 6 +--R \|8 cos(---) +--R 8 +--R + +--R 11 10 9 8 7 6 +--R - 2304x - 9856x - 21792x - 30896x - 31424x - 24368x +--R + +--R 5 4 3 2 +--R - 12512x - 3408x - 576x - 80x +--R * +--R %pi 4 +--R cos(---) +--R 8 +--R + +--R 13 12 11 10 9 8 +--R 1024x + 7168x + 16704x + 24448x + 27668x + 23012x +--R + +--R 7 6 5 4 3 2 +--R 13836x + 6140x + 1900x + 412x + 52x + 4x +--R * +--R 4+-+2 %pi 2 +--R \|8 cos(---) +--R 8 +--R + +--R 15 14 13 12 11 10 +--R - 8192x - 28672x - 55296x - 78848x - 85600x - 72336x +--R + +--R 9 8 7 6 5 4 3 +--R - 48304x - 25456x - 10640x - 3440x - 848x - 144x - 16x +--R * +--R +------+ +--R | 2 +--R \|x + x +--R + +--R 4 3 2 %pi 12 +--R (8x + 8x + 8x + 8x)sin(---) +--R 8 +--R + +--R 4 3 2 %pi %pi 11 +--R (32x + 32x + 32x + 32x)cos(---)sin(---) +--R 8 8 +--R + +--R 4 3 2 %pi 2 +--R (80x + 80x + 80x + 80x)cos(---) +--R 8 +--R + +--R 6 5 4 3 2 4+-+2 +--R (- 16x - 8x - 8x - 8x + 8x )\|8 +--R * +--R %pi 10 +--R sin(---) +--R 8 +--R + +--R 4 3 2 %pi 3 +--R (160x + 160x + 160x + 160x)cos(---) +--R 8 +--R + +--R 6 5 4 3 2 4+-+2 %pi +--R (- 64x - 32x - 16x - 16x + 48x + 16x)\|8 cos(---) +--R 8 +--R * +--R %pi 9 +--R sin(---) +--R 8 +--R + +--R 4 3 2 %pi 4 +--R (248x + 248x + 248x + 248x)cos(---) +--R 8 +--R + +--R 6 5 4 3 2 4+-+2 %pi 2 8 +--R (- 208x - 200x - 136x - 136x + 72x + 64x)\|8 cos(---) + 192x +--R 8 +--R + +--R 7 6 5 4 3 2 +--R - 128x - 328x - 248x - 432x - 112x + 88x + 8x +--R * +--R %pi 8 +--R sin(---) +--R 8 +--R + +--R 4 3 2 %pi 5 +--R (320x + 320x + 320x + 320x)cos(---) +--R 8 +--R + +--R 6 5 4 3 2 4+-+2 %pi 3 +--R (- 384x - 448x - 320x - 320x + 64x + 128x)\|8 cos(---) +--R 8 +--R + +--R 8 7 6 5 4 3 2 %pi +--R (1280x + 1024x + 416x + 736x - 512x - 256x + 352x + 32x)cos(---) +--R 8 +--R * +--R %pi 7 +--R sin(---) +--R 8 +--R + +--R 4 3 2 %pi 6 +--R (352x + 352x + 352x + 352x)cos(---) +--R 8 +--R + +--R 6 5 4 3 2 4+-+2 %pi 4 +--R (- 544x - 720x - 528x - 528x + 16x + 192x)\|8 cos(---) +--R 8 +--R + +--R 8 7 6 5 4 3 2 +--R (3584x + 4096x + 2240x + 2752x - 704x - 1216x + 640x + 128x) +--R * +--R %pi 2 +--R cos(---) +--R 8 +--R + +--R 10 8 7 6 5 4 3 4+-+2 +--R (- 256x + 16x - 368x - 160x - 416x - 432x - 48x )\|8 +--R * +--R %pi 6 +--R sin(---) +--R 8 +--R + +--R 4 3 2 %pi 7 +--R (320x + 320x + 320x + 320x)cos(---) +--R 8 +--R + +--R 6 5 4 3 2 4+-+2 %pi 5 +--R (- 640x - 960x - 736x - 736x - 96x + 224x)\|8 cos(---) +--R 8 +--R + +--R 8 7 6 5 4 3 2 +--R (5888x + 8192x + 4320x + 4000x - 1536x - 3840x + 32x + 352x) +--R * +--R %pi 3 +--R cos(---) +--R 8 +--R + +--R 10 9 8 7 6 5 4 +--R - 1792x - 1920x - 816x - 1416x + 32x + 184x - 912x +--R + +--R 3 2 +--R - 312x + 32x + 8x +--R * +--R 4+-+2 %pi +--R \|8 cos(---) +--R 8 +--R * +--R %pi 5 +--R sin(---) +--R 8 +--R + +--R 4 3 2 %pi 8 +--R (248x + 248x + 248x + 248x)cos(---) +--R 8 +--R + +--R 6 5 4 3 2 4+-+2 %pi 6 +--R (- 544x - 912x - 720x - 720x - 176x + 192x)\|8 cos(---) +--R 8 +--R + +--R 8 7 6 5 4 3 2 +--R 8832x + 17664x + 15376x + 13680x + 5344x - 3488x - 1200x +--R + +--R 496x +--R * +--R %pi 4 +--R cos(---) +--R 8 +--R + +--R 10 9 8 7 6 5 4 +--R - 3840x - 4352x + 944x + 2656x + 5968x + 6464x + 1200x +--R + +--R 3 2 +--R - 512x + 16x + 32x +--R * +--R 4+-+2 %pi 2 +--R \|8 cos(---) +--R 8 +--R + +--R 12 11 10 9 8 7 6 +--R 2304x + 2816x + 3904x + 6912x + 4866x + 3850x + 2614x +--R + +--R 5 4 3 2 +--R - 386x - 642x - 138x + 10x + 2x +--R * +--R %pi 4 +--R sin(---) +--R 8 +--R + +--R 4 3 2 %pi 9 +--R (160x + 160x + 160x + 160x)cos(---) +--R 8 +--R + +--R 6 5 4 3 2 4+-+2 %pi 7 +--R (- 384x - 704x - 576x - 576x - 192x + 128x)\|8 cos(---) +--R 8 +--R + +--R 8 7 6 5 4 3 2 +--R 5888x + 15360x + 16864x + 15264x + 9728x + 256x - 1248x +--R + +--R 352x +--R * +--R %pi 5 +--R cos(---) +--R 8 +--R + +--R 10 9 8 7 6 5 +--R - 8704x - 21760x - 22944x - 19504x - 10560x + 2384x +--R + +--R 4 3 2 +--R 3616x + 176x - 64x + 48x +--R * +--R 4+-+2 %pi 3 +--R \|8 cos(---) +--R 8 +--R + +--R 12 11 10 9 8 7 +--R 9216x + 3072x - 25344x - 39936x - 50168x - 44568x +--R + +--R 6 5 4 3 2 +--R - 16616x - 2056x - 1032x - 488x - 24x + 8x +--R * +--R %pi +--R cos(---) +--R 8 +--R * +--R %pi 3 +--R sin(---) +--R 8 +--R + +--R 4 3 2 %pi 10 +--R (80x + 80x + 80x + 80x)cos(---) +--R 8 +--R + +--R 6 5 4 3 2 4+-+2 %pi 8 +--R (- 208x - 424x - 360x - 360x - 152x + 64x)\|8 cos(---) +--R 8 +--R + +--R 8 7 6 5 4 3 2 +--R 3584x + 10240x + 12992x + 12480x + 9024x + 2368x - 384x +--R + +--R 128x +--R * +--R %pi 6 +--R cos(---) +--R 8 +--R + +--R 10 9 8 7 6 5 +--R - 3840x - 14848x - 22672x - 22832x - 18464x - 7552x +--R + +--R 4 3 2 +--R 304x + 464x - 64x + 32x +--R * +--R 4+-+2 %pi 4 +--R \|8 cos(---) +--R 8 +--R + +--R 12 11 10 9 8 7 +--R 38400x + 115200x + 154496x + 151040x + 108876x + 32636x +--R + +--R 6 5 4 3 2 +--R - 6716x - 3340x + 436x - 124x - 68x + 12x +--R * +--R %pi 2 +--R cos(---) +--R 8 +--R + +--R 14 13 12 11 10 9 +--R - 1024x + 512x + 6464x + 12576x + 17340x + 17162x +--R + +--R 8 7 6 5 4 3 2 +--R 11466x + 5358x + 1606x + 246x - 10x - 14x - 2x +--R * +--R 4+-+2 +--R \|8 +--R * +--R %pi 2 +--R sin(---) +--R 8 +--R + +--R 4 3 2 %pi 11 +--R (32x + 32x + 32x + 32x)cos(---) +--R 8 +--R + +--R 6 5 4 3 2 4+-+2 %pi 9 +--R (- 64x - 160x - 144x - 144x - 80x + 16x)\|8 cos(---) +--R 8 +--R + +--R 8 7 6 5 4 3 2 +--R (1280x + 4096x + 5792x + 5856x + 4608x + 1792x + 96x + 32x) +--R * +--R %pi 7 +--R cos(---) +--R 8 +--R + +--R 10 9 8 7 6 5 +--R - 1792x - 7040x - 12336x - 14024x - 12192x - 6984x +--R + +--R 4 3 2 +--R - 1680x + 8x - 32x + 8x +--R * +--R 4+-+2 %pi 5 +--R \|8 cos(---) +--R 8 +--R + +--R 12 11 10 9 8 7 +--R 9216x + 52224x + 109824x + 138240x + 133384x + 90856x +--R + +--R 6 5 4 3 2 +--R 33560x + 5112x + 760x + 280x - 24x + 8x +--R * +--R %pi 3 +--R cos(---) +--R 8 +--R + +--R 14 13 12 11 10 9 +--R - 10240x - 35840x - 62336x - 78528x - 74664x - 50492x +--R + +--R 8 7 6 5 4 3 2 +--R - 24172x - 7988x - 1620x - 196x - 20x - 12x - 4x +--R * +--R 4+-+2 %pi +--R \|8 cos(---) +--R 8 +--R * +--R %pi +--R sin(---) +--R 8 +--R + +--R 4 3 2 %pi 12 +--R (8x + 8x + 8x + 8x)cos(---) +--R 8 +--R + +--R 6 5 4 3 2 4+-+2 %pi 10 +--R (- 16x - 40x - 40x - 40x - 24x )\|8 cos(---) +--R 8 +--R + +--R 8 7 6 5 4 3 2 %pi 8 +--R (192x + 896x + 1464x + 1544x + 1360x + 656x + 88x + 8x)cos(---) +--R 8 +--R + +--R 10 9 8 7 6 5 4 +--R - 256x - 1280x - 2864x - 3776x - 3664x - 2656x - 1072x +--R + +--R 3 2 +--R - 160x - 16x +--R * +--R 4+-+2 %pi 6 +--R \|8 cos(---) +--R 8 +--R + +--R 12 11 10 9 8 7 6 +--R 2304x + 11008x + 26432x + 40704x + 44674x + 37258x + 22070x +--R + +--R 5 4 3 2 +--R 7806x + 1534x + 246x + 10x + 2x +--R * +--R %pi 4 +--R cos(---) +--R 8 +--R + +--R 14 13 12 11 10 9 +--R - 1024x - 7680x - 20160x - 31968x - 38212x - 34582x +--R + +--R 8 7 6 5 4 3 2 +--R - 22934x - 11282x - 4026x - 1002x - 170x - 14x - 2x +--R * +--R 4+-+2 %pi 2 +--R \|8 cos(---) +--R 8 +--R + +--R 16 15 14 13 12 11 +--R 8192x + 32768x + 68608x + 103424x + 119584x + 107840x +--R + +--R 10 9 8 7 6 5 4 3 +--R 77156x + 43892x + 19884x + 7100x + 1948x + 396x + 52x + 4x +--R Type: Expression Complex Integer +--E 319 + +--S 320 of 324 +t0461:= x^(1/3)/(-1+x^(5/6)) +--R +--R +--R 3+-+ +--R \|x +--R (320) --------- +--R 6+-+5 +--R \|x - 1 +--R Type: Expression Integer +--E 320 + +--S 321 of 324 +r0461:= 2*x^(1/2)+6*2^(1/2)/(25+5*5^(1/2))^(1/2)*_ + atan((1-5^(1/2)+4*x^(1/6))/(10+2*5^(1/2))^(1/2))-_ + 6*2^(1/2)/(25-5*5^(1/2))^(1/2)*_ + atan((1+5^(1/2)+4*x^(1/6))/(10-2*5^(1/2))^(1/2))+_ + 6/5*log(1-x^(1/6))-3/10*(5^(1/2)+1)*log(2+(1-5^(1/2))*x^(1/6)+_ + 2*x^(1/3))-3/10*(1-5^(1/2))*log(2+(5^(1/2)+1)*x^(1/6)+2*x^(1/3)) +--R +--R +--R (321) +--R +-+ +-+ 6+-+ 3+-+ 6+-+ +--R (15\|5 - 15)log((\|5 + 1)\|x + 2\|x + 2) + 60log(- \|x + 1) +--R + +--R +-+ +-+ 6+-+ 3+-+ +--R (- 15\|5 - 15)log((- \|5 + 1)\|x + 2\|x + 2) +--R + +--R +------------+ 6+-+ +-+ +--R +-+ +-+ +-+ | +-+ 4\|x + \|5 + 1 +--R (- 3\|2 \|5 - 15\|2 )\|- 5\|5 + 25 atan(----------------) +--R +------------+ +--R | +-+ +--R \|- 2\|5 + 10 +--R + +--R +----------+ 6+-+ +-+ +--R +-+ +-+ +-+ | +-+ 4\|x - \|5 + 1 +-+ +--R (- 3\|2 \|5 + 15\|2 )\|5\|5 + 25 atan(----------------) + 100\|x +--R +----------+ +--R | +-+ +--R \|2\|5 + 10 +--R / +--R 50 +--R Type: Expression Integer +--E 321 + +--S 322 of 324 +a0461:= integrate(t0461,x) +--R +--R +--R (322) +--R +-------------------------------------------------------------+ +--R | 2 2 +--I \|- 75%%EX1 + (- 50%%EX0 - 60)%%EX1 - 75%%EX0 - 60%%EX0 - 108 +--R + +--I - 5%%EX1 - 5%%EX0 - 6 +--R * +--R log +--I (5%%EX1 + 5%%EX0 + 6) +--R * +--R +-------------------------------------------------------------+ +--R | 2 2 +--I \|- 75%%EX1 + (- 50%%EX0 - 60)%%EX1 - 75%%EX0 - 60%%EX0 - 108 +--R + +--R 2 2 6+-+ +--I 25%%EX1 + 25%%EX0 + 72\|x + 36 +--R + +--R +-------------------------------------------------------------+ +--R | 2 2 +--I - \|- 75%%EX1 + (- 50%%EX0 - 60)%%EX1 - 75%%EX0 - 60%%EX0 - 108 +--R + +--I - 5%%EX1 - 5%%EX0 - 6 +--R * +--R log +--I (- 5%%EX1 - 5%%EX0 - 6) +--R * +--R +-------------------------------------------------------------+ +--R | 2 2 +--I \|- 75%%EX1 + (- 50%%EX0 - 60)%%EX1 - 75%%EX0 - 60%%EX0 - 108 +--R + +--R 2 2 6+-+ +--I 25%%EX1 + 25%%EX0 + 72\|x + 36 +--R + +--R 2 6+-+ 6+-+ +--I 10%%EX1 log(- 25%%EX1 + 36\|x ) + 12log(\|x - 1) +--R + +--R 2 6+-+ 6+-+3 +--I 10%%EX0 log(- 25%%EX0 + 36\|x ) + 20\|x +--R / +--R 10 +--R Type: Union(Expression Integer,...) +--E 322 + +--S 323 of 324 +m0461:= a0461-r0461 +--R +--R +--R (323) +--R +-------------------------------------------------------------+ +--R | 2 2 +--I 5\|- 75%%EX1 + (- 50%%EX0 - 60)%%EX1 - 75%%EX0 - 60%%EX0 - 108 +--R + +--I - 25%%EX1 - 25%%EX0 - 30 +--R * +--R log +--I (5%%EX1 + 5%%EX0 + 6) +--R * +--R +-------------------------------------------------------------+ +--R | 2 2 +--I \|- 75%%EX1 + (- 50%%EX0 - 60)%%EX1 - 75%%EX0 - 60%%EX0 - 108 +--R + +--R 2 2 6+-+ +--I 25%%EX1 + 25%%EX0 + 72\|x + 36 +--R + +--R +-------------------------------------------------------------+ +--R | 2 2 +--I - 5\|- 75%%EX1 + (- 50%%EX0 - 60)%%EX1 - 75%%EX0 - 60%%EX0 - 108 +--R + +--I - 25%%EX1 - 25%%EX0 - 30 +--R * +--R log +--I (- 5%%EX1 - 5%%EX0 - 6) +--R * +--R +-------------------------------------------------------------+ +--R | 2 2 +--I \|- 75%%EX1 + (- 50%%EX0 - 60)%%EX1 - 75%%EX0 - 60%%EX0 - 108 +--R + +--R 2 2 6+-+ +--I 25%%EX1 + 25%%EX0 + 72\|x + 36 +--R + +--R 2 6+-+ +--I 50%%EX1 log(- 25%%EX1 + 36\|x ) +--R + +--R +-+ +-+ 6+-+ 3+-+ 6+-+ +--R (- 15\|5 + 15)log((\|5 + 1)\|x + 2\|x + 2) + 60log(\|x - 1) +--R + +--R 6+-+ +-+ +-+ 6+-+ 3+-+ +--R - 60log(- \|x + 1) + (15\|5 + 15)log((- \|5 + 1)\|x + 2\|x + 2) +--R + +--R 2 6+-+ +--I 50%%EX0 log(- 25%%EX0 + 36\|x ) +--R + +--R +------------+ 6+-+ +-+ +--R +-+ +-+ +-+ | +-+ 4\|x + \|5 + 1 +--R (3\|2 \|5 + 15\|2 )\|- 5\|5 + 25 atan(----------------) +--R +------------+ +--R | +-+ +--R \|- 2\|5 + 10 +--R + +--R +----------+ 6+-+ +-+ +--R +-+ +-+ +-+ | +-+ 4\|x - \|5 + 1 6+-+3 +--R (3\|2 \|5 - 15\|2 )\|5\|5 + 25 atan(----------------) + 100\|x +--R +----------+ +--R | +-+ +--R \|2\|5 + 10 +--R + +--R +-+ +--R - 100\|x +--R / +--R 50 +--R Type: Expression Integer +--E 323 + +--S 324 of 324 +d0461:= D(m0461,x) +--R +--R +--R (324) +--R +-+ +-+ +-+ +-+3+-+2 2 +-+ +-+ 2 +-+ +-+ 6+-+5 +--R ((2x\|2 \|5 - 10x\|2 )\|x \|x + (x \|2 \|5 - 5x \|2 )\|x )\|x +--R + +--R +-+ +-+ +-+ +-+3+-+2 +--R (x\|2 \|5 - 5x\|2 )\|x \|x +--R + +--R 2 +-+ +-+ 2 +-+ +-+3+-+ +--R ((x + 4x)\|2 \|5 + (- 5x - 10x)\|2 )\|x \|x +--R * +--R 6+-+4 +--R \|x +--R + +--R 2 +-+ +-+ 2 +-+ +-+3+-+2 +--R ((- x - x)\|2 \|5 + (5x - 5x)\|2 )\|x \|x +--R + +--R 2 +-+ +-+ 2 +-+ +-+3+-+ +--R ((- 4x - 5x)\|2 \|5 + (10x + 5x)\|2 )\|x \|x +--R + +--R 2 +-+ +-+ 2 +-+ +-+ +--R (x \|2 \|5 - 5x \|2 )\|x +--R * +--R 6+-+3 +--R \|x +--R + +--R 2 +-+ +-+ 2 +-+ +-+3+-+2 +--R ((x - 3x)\|2 \|5 + (5x + 5x)\|2 )\|x \|x +--R + +--R 2 +-+ +-+ 2 +-+ +-+3+-+ +--R ((5x + x)\|2 \|5 + (- 5x - 5x)\|2 )\|x \|x +--R + +--R 3 2 +-+ +-+ 3 2 +-+ +-+ +--R ((- x - 3x )\|2 \|5 + (5x + 5x )\|2 )\|x +--R * +--R 6+-+2 +--R \|x +--R + +--R 2 +-+ +-+ 2 +-+ +-+3+-+2 +--R ((3x + 5x)\|2 \|5 + (- 5x - 5x)\|2 )\|x \|x +--R + +--R 2 +-+ +-+ 2 +-+ +-+3+-+ +--R ((- x + 2x)\|2 \|5 + 5x \|2 )\|x \|x +--R + +--R 3 2 +-+ +-+ 3 2 +-+ +-+ +--R ((3x + 3x )\|2 \|5 + (- 5x - 5x )\|2 )\|x +--R * +--R 6+-+ +--R \|x +--R + +--R 2 +-+ +-+ 2 +-+ +-+3+-+2 +--R ((- 5x - 2x)\|2 \|5 + (5x + 10x)\|2 )\|x \|x +--R + +--R 2 +-+ +-+ +-+ +-+3+-+ +--R ((- 2x - x)\|2 \|5 + 5x\|2 )\|x \|x +--R + +--R 3 2 +-+ +-+ 3 2 +-+ +-+ +--R ((- 3x - x )\|2 \|5 + (5x + 5x )\|2 )\|x +--R * +--R +----------+ +----------+ +--R | +-+ | +-+ +--R \|2\|5 + 10 \|5\|5 + 25 +--R + +--R +------------+ +------------+ +--R +-+ +-+ +-+ | +-+ | +-+ +--R (2x\|2 \|5 + 10x\|2 )\|- 5\|5 + 25 \|- 2\|5 + 10 + 400x +--R + +--R - 80 +--R * +--R +-+ +--R \|x +--R + +--R 2 +--R - 800x + 800x +--R * +--R 3+-+2 +--R \|x +--R + +--R 2 +-+ 3 2 3+-+ +--R ((- 40x - 80x)\|x - 400x - 800x + 400x)\|x +--R + +--R +------------+ +------------+ +--R 2 +-+ +-+ 2 +-+ | +-+ | +-+ 2 +--R ((x \|2 \|5 + 5x \|2 )\|- 5\|5 + 25 \|- 2\|5 + 10 + 80x - 80x) +--R * +--R +-+ +--R \|x +--R + +--R 2 +--R 400x +--R * +--R 6+-+5 +--R \|x +--R + +--R +------------+ +------------+ +--R +-+ +-+ +-+ | +-+ | +-+ 2 +--R (x\|2 \|5 + 5x\|2 )\|- 5\|5 + 25 \|- 2\|5 + 10 - 80x +--R + +--R - 80x +--R * +--R +-+ +--R \|x +--R + +--R 3 2 +--R 400x - 1600x +--R * +--R 3+-+2 +--R \|x +--R + +--R +------------+ +--R 2 +-+ +-+ 2 +-+ | +-+ +--R ((x + 4x)\|2 \|5 + (5x + 10x)\|2 )\|- 5\|5 + 25 +--R * +--R +------------+ +--R | +-+ +--R \|- 2\|5 + 10 +--R + +--R 2 +--R 80x - 80x +--R * +--R +-+ +--R \|x +--R + +--R 3 2 +--R 400x - 800x +--R * +--R 3+-+ +--R \|x +--R + +--R 2 +-+ 3 +--R 80x \|x - 800x +--R * +--R 6+-+4 +--R \|x +--R + +--R +------------+ +--R 2 +-+ +-+ 2 +-+ | +-+ +--R ((- x - x)\|2 \|5 + (- 5x + 5x)\|2 )\|- 5\|5 + 25 +--R * +--R +------------+ +--R | +-+ +--R \|- 2\|5 + 10 +--R + +--R 2 +--R 160x - 240x +--R * +--R +-+ +--R \|x +--R + +--R 3 +--R 800x +--R * +--R 3+-+2 +--R \|x +--R + +--R +------------+ +--R 2 +-+ +-+ 2 +-+ | +-+ +--R ((- 4x - 5x)\|2 \|5 + (- 10x - 5x)\|2 )\|- 5\|5 + 25 +--R * +--R +------------+ +--R | +-+ +--R \|- 2\|5 + 10 +--R + +--R 2 +--R - 320x - 80x +--R * +--R +-+ +--R \|x +--R + +--R 3 +--R 400x +--R * +--R 3+-+ +--R \|x +--R + +--R +------------+ +------------+ +--R 2 +-+ +-+ 2 +-+ | +-+ | +-+ 2 +-+ +--R ((x \|2 \|5 + 5x \|2 )\|- 5\|5 + 25 \|- 2\|5 + 10 - 80x )\|x +--R + +--R 4 +--R 400x +--R * +--R 6+-+3 +--R \|x +--R + +--R +------------+ +--R 2 +-+ +-+ 2 +-+ | +-+ +--R ((x - 3x)\|2 \|5 + (- 5x - 5x)\|2 )\|- 5\|5 + 25 +--R * +--R +------------+ +--R | +-+ +--R \|- 2\|5 + 10 +--R + +--R 2 +--R 640x - 240x +--R * +--R +-+3+-+2 +--R \|x \|x +--R + +--R +------------+ +--R 2 +-+ +-+ 2 +-+ | +-+ +--R ((5x + x)\|2 \|5 + (5x + 5x)\|2 )\|- 5\|5 + 25 +--R * +--R +------------+ +--R | +-+ +--R \|- 2\|5 + 10 +--R + +--R 3 2 +--R 400x + 480x - 80x +--R * +--R +-+3+-+ +--R \|x \|x +--R + +--R +------------+ +--R 3 2 +-+ +-+ 3 2 +-+ | +-+ +--R ((- x - 3x )\|2 \|5 + (- 5x - 5x )\|2 )\|- 5\|5 + 25 +--R * +--R +------------+ +--R | +-+ +--R \|- 2\|5 + 10 +--R + +--R 3 2 +--R 80x - 80x +--R * +--R +-+ +--R \|x +--R * +--R 6+-+2 +--R \|x +--R + +--R +------------+ +--R 2 +-+ +-+ 2 +-+ | +-+ +--R ((3x + 5x)\|2 \|5 + (5x + 5x)\|2 )\|- 5\|5 + 25 +--R * +--R +------------+ +--R | +-+ +--R \|- 2\|5 + 10 +--R + +--R 3 2 +--R - 400x + 1040x - 240x +--R * +--R +-+3+-+2 +--R \|x \|x +--R + +--R +------------+ +------------+ +--R 2 +-+ +-+ 2 +-+ | +-+ | +-+ +--R ((- x + 2x)\|2 \|5 - 5x \|2 )\|- 5\|5 + 25 \|- 2\|5 + 10 +--R + +--R 3 2 +--R - 400x + 480x - 120x +--R * +--R +-+ +--R \|x +--R + +--R 2 +--R - 400x +--R * +--R 3+-+ +--R \|x +--R + +--R +------------+ +--R 3 2 +-+ +-+ 3 2 +-+ | +-+ +--R ((3x + 3x )\|2 \|5 + (5x + 5x )\|2 )\|- 5\|5 + 25 +--R * +--R +------------+ +--R | +-+ +--R \|- 2\|5 + 10 +--R + +--R 3 2 +--R 480x - 80x +--R * +--R +-+ +--R \|x +--R * +--R 6+-+ +--R \|x +--R + +--R +------------+ +--R 2 +-+ +-+ 2 +-+ | +-+ +--R ((- 5x - 2x)\|2 \|5 + (- 5x - 10x)\|2 )\|- 5\|5 + 25 +--R * +--R +------------+ +--R | +-+ +--R \|- 2\|5 + 10 +--R + +--R 3 2 +--R - 800x + 240x - 320x +--R * +--R +-+ +--R \|x +--R + +--R 2 +--R 400x +--R * +--R 3+-+2 +--R \|x +--R + +--R +------------+ +------------+ +--R 2 +-+ +-+ +-+ | +-+ | +-+ +--R ((- 2x - x)\|2 \|5 - 5x\|2 )\|- 5\|5 + 25 \|- 2\|5 + 10 +--R + +--R 3 2 +--R - 400x + 160x +--R * +--R +-+ +--R \|x +--R + +--R 3 2 +--R 800x + 400x +--R * +--R 3+-+ +--R \|x +--R + +--R +------------+ +--R 3 2 +-+ +-+ 3 2 +-+ | +-+ +--R ((- 3x - x )\|2 \|5 + (- 5x - 5x )\|2 )\|- 5\|5 + 25 +--R * +--R +------------+ +--R | +-+ +--R \|- 2\|5 + 10 +--R + +--R 4 3 2 +--R - 400x + 80x - 80x +--R * +--R +-+ +--R \|x +--R / +--R 2 +-+3+-+2 3 2 +-+3+-+ 2 +-+ +--R ((800x - 800x)\|x \|x + (400x + 800x - 400x)\|x \|x - 400x \|x ) +--R * +--R 6+-+5 +--R \|x +--R + +--R 3 2 +-+3+-+2 3 2 +-+3+-+ 3 +-+ +--R ((- 400x + 1600x )\|x \|x + (- 400x + 800x )\|x \|x + 800x \|x ) +--R * +--R 6+-+4 +--R \|x +--R + +--R 3 +-+3+-+2 3 +-+3+-+ 4 +-+ 6+-+3 2 +-+3+-+6+-+ +--R (- 800x \|x \|x - 400x \|x \|x - 400x \|x )\|x + 400x \|x \|x \|x +--R + +--R 2 +-+3+-+2 3 2 +-+3+-+ +--R - 400x \|x \|x + (- 800x - 400x )\|x \|x +--R Type: Expression Integer +--E 324 + +)spool + +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} +Rich, Albert D. ``Rule-based Mathematics'' \verb|www.apmaths.uwo.ca/~arich| +\end{thebibliography} +\end{document}