3.89.84 $\int \frac{-128x^2+160x^3-32x^4+e^5(-640x+128x^2)+(-640x+128x^2)\log (-5+x)}{-320x^3-176x^4-12x^5+7x^6+x^7+e^{15}(-320+64x)+e^{10}(-960x-48x^2+48x^3)+e^5(-960x^2-288x^3+36x^4+12x^5)+(-240x^3-72x^4+9x^5+3x^6+e^{10}(-240x+48x^2)+e^5(-480x^2-24x^3+24x^4))\log (2)+(-60x^3-3x^4+3x^5+e^5(-60x^2+12x^3)){\log }^2(2)+(-5x^3+x^4){\log }^3(2)+(-240x^3-72x^4+9x^5+3x^6+e^{10}(-240x+48x^2)+e^5(-480x^2-24x^3+24x^4)+(-120x^3-6x^4+6x^5+e^5(-120x^2+24x^3))\log (2)+(-15x^3+3x^4){\log }^2(2))\log (3)+(-60x^3-3x^4+3x^5+e^5(-60x^2+12x^3)+(-15x^3+3x^4)\log (2)){\log }^2(3)+(-5x^3+x^4){\log }^3(3)+(-960x^2-288x^3+36x^4+12x^5+e^{10}(-960+192x)+e^5(-1920x-96x^2+96x^3)+(-480x^2-24x^3+24x^4+e^5(-480x+96x^2))\log (2)+(-60x^2+12x^3){\log }^2(2)+(-480x^2-24x^3+24x^4+e^5(-480x+96x^2)+(-120x^2+24x^3)\log (2))\log (3)+(-60x^2+12x^3){\log }^2(3))\log (-5+x)+(-960x-48x^2+48x^3+e^5(-960+192x)+(-240x+48x^2)\log (2)+(-240x+48x^2)\log (3)){\log }^2(-5+x)+(-320+64x){\log }^3(-5+x)}dx$

Optimal. Leaf size=26 $$\frac{1}{{(\frac{1}{4}(x+\log (2)+\log (3))+\frac{e^5+x+\log (-5+x)}{x})}^2}$$

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Rubi [F]  time = 3.85, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, $\frac{\text{number of rules}}{\text{integrand size}}$ = 0.000, Rules used = {} $$\begin{array}{c}\int \frac{-128x^2+160x^3-32x^4+e^5(-640x+128x^2)+(-640x+128x^2)\log (-5+x)}{-320x^3-176x^4-12x^5+7x^6+x^7+e^{15}(-320+64x)+e^{10}(-960x-48x^2+48x^3)+e^5(-960x^2-288x^3+36x^4+12x^5)+(-240x^3-72x^4+9x^5+3x^6+e^{10}(-240x+48x^2)+e^5(-480x^2-24x^3+24x^4))\log (2)+(-60x^3-3x^4+3x^5+e^5(-60x^2+12x^3)){\log }^2(2)+(-5x^3+x^4){\log }^3(2)+(-240x^3-72x^4+9x^5+3x^6+e^{10}(-240x+48x^2)+e^5(-480x^2-24x^3+24x^4)+(-120x^3-6x^4+6x^5+e^5(-120x^2+24x^3))\log (2)+(-15x^3+3x^4){\log }^2(2))\log (3)+(-60x^3-3x^4+3x^5+e^5(-60x^2+12x^3)+(-15x^3+3x^4)\log (2)){\log }^2(3)+(-5x^3+x^4){\log }^3(3)+(-960x^2-288x^3+36x^4+12x^5+e^{10}(-960+192x)+e^5(-1920x-96x^2+96x^3)+(-480x^2-24x^3+24x^4+e^5(-480x+96x^2))\log (2)+(-60x^2+12x^3){\log }^2(2)+(-480x^2-24x^3+24x^4+e^5(-480x+96x^2)+(-120x^2+24x^3)\log (2))\log (3)+(-60x^2+12x^3){\log }^2(3))\log (-5+x)+(-960x-48x^2+48x^3+e^5(-960+192x)+(-240x+48x^2)\log (2)+(-240x+48x^2)\log (3)){\log }^2(-5+x)+(-320+64x){\log }^3(-5+x)}dx\end{array}$$

Verification is not applicable to the result.

[In]

Int[(-128*x^2 + 160*x^3 - 32*x^4 + E^5*(-640*x + 128*x^2) + (-640*x + 128*x^2)*Log[-5 + x])/(-320*x^3 - 176*x^
4 - 12*x^5 + 7*x^6 + x^7 + E^15*(-320 + 64*x) + E^10*(-960*x - 48*x^2 + 48*x^3) + E^5*(-960*x^2 - 288*x^3 + 36
*x^4 + 12*x^5) + (-240*x^3 - 72*x^4 + 9*x^5 + 3*x^6 + E^10*(-240*x + 48*x^2) + E^5*(-480*x^2 - 24*x^3 + 24*x^4
))*Log[2] + (-60*x^3 - 3*x^4 + 3*x^5 + E^5*(-60*x^2 + 12*x^3))*Log[2]^2 + (-5*x^3 + x^4)*Log[2]^3 + (-240*x^3
- 72*x^4 + 9*x^5 + 3*x^6 + E^10*(-240*x + 48*x^2) + E^5*(-480*x^2 - 24*x^3 + 24*x^4) + (-120*x^3 - 6*x^4 + 6*x
^5 + E^5*(-120*x^2 + 24*x^3))*Log[2] + (-15*x^3 + 3*x^4)*Log[2]^2)*Log[3] + (-60*x^3 - 3*x^4 + 3*x^5 + E^5*(-6
0*x^2 + 12*x^3) + (-15*x^3 + 3*x^4)*Log[2])*Log[3]^2 + (-5*x^3 + x^4)*Log[3]^3 + (-960*x^2 - 288*x^3 + 36*x^4
+ 12*x^5 + E^10*(-960 + 192*x) + E^5*(-1920*x - 96*x^2 + 96*x^3) + (-480*x^2 - 24*x^3 + 24*x^4 + E^5*(-480*x +
96*x^2))*Log[2] + (-60*x^2 + 12*x^3)*Log[2]^2 + (-480*x^2 - 24*x^3 + 24*x^4 + E^5*(-480*x + 96*x^2) + (-120*x
^2 + 24*x^3)*Log[2])*Log[3] + (-60*x^2 + 12*x^3)*Log[3]^2)*Log[-5 + x] + (-960*x - 48*x^2 + 48*x^3 + E^5*(-960
+ 192*x) + (-240*x + 48*x^2)*Log[2] + (-240*x + 48*x^2)*Log[3])*Log[-5 + x]^2 + (-320 + 64*x)*Log[-5 + x]^3),
x]

[Out]

640*Defer[Int][(-4*E^5 - x*(4 + x + Log[6]) - 4*Log[-5 + x])^(-3), x] + 128*Defer[Int][x/(-4*E^5 - x*(4 + x +
Log[6]) - 4*Log[-5 + x])^3, x] + 64*Defer[Int][x^3/(-4*E^5 - x*(4 + x + Log[6]) - 4*Log[-5 + x])^3, x] + 3200*
Defer[Int][1/((5 - x)*(4*E^5 + x^2 + 4*x*(1 + Log[6]/4) + 4*Log[-5 + x])^3), x] - 32*(4 + Log[6])*Defer[Int][x
^2/(4*E^5 + x^2 + 4*x*(1 + Log[6]/4) + 4*Log[-5 + x])^3, x] + 32*Defer[Int][x/(4*E^5 + x^2 + 4*x*(1 + Log[6]/4
) + 4*Log[-5 + x])^2, x]

Rubi steps

$$\begin{array}{c}\begin{array}{rl}\text{integral}& =\int \frac{-128x^2+160x^3-32x^4+e^5(-640x+128x^2)+(-640x+128x^2)\log (-5+x)}{-320x^3-176x^4-12x^5+7x^6+x^7+e^{15}(-320+64x)+e^{10}(-960x-48x^2+48x^3)+e^5(-960x^2-288x^3+36x^4+12x^5)+(-240x^3-72x^4+9x^5+3x^6+e^{10}(-240x+48x^2)+e^5(-480x^2-24x^3+24x^4))\log (2)+(-60x^3-3x^4+3x^5+e^5(-60x^2+12x^3)){\log }^2(2)+(-240x^3-72x^4+9x^5+3x^6+e^{10}(-240x+48x^2)+e^5(-480x^2-24x^3+24x^4)+(-120x^3-6x^4+6x^5+e^5(-120x^2+24x^3))\log (2)+(-15x^3+3x^4){\log }^2(2))\log (3)+(-60x^3-3x^4+3x^5+e^5(-60x^2+12x^3)+(-15x^3+3x^4)\log (2)){\log }^2(3)+(-5x^3+x^4)({\log }^3(2)+{\log }^3(3))+(-960x^2-288x^3+36x^4+12x^5+e^{10}(-960+192x)+e^5(-1920x-96x^2+96x^3)+(-480x^2-24x^3+24x^4+e^5(-480x+96x^2))\log (2)+(-60x^2+12x^3){\log }^2(2)+(-480x^2-24x^3+24x^4+e^5(-480x+96x^2)+(-120x^2+24x^3)\log (2))\log (3)+(-60x^2+12x^3){\log }^2(3))\log (-5+x)+(-960x-48x^2+48x^3+e^5(-960+192x)+(-240x+48x^2)\log (2)+(-240x+48x^2)\log (3)){\log }^2(-5+x)+(-320+64x){\log }^3(-5+x)}dx\\ & =\int \frac{32x(-4e^5(-5+x)+x(4-5x+x^2)-4(-5+x)\log (-5+x))}{(5-x){(4e^5+x(4+x+\log (6))+4\log (-5+x))}^3}dx\\ & =32\int \frac{x(-4e^5(-5+x)+x(4-5x+x^2)-4(-5+x)\log (-5+x))}{(5-x){(4e^5+x(4+x+\log (6))+4\log (-5+x))}^3}dx\\ & =32\int (\frac{x^2(-16+2x^2-x(6-\log (6))-5\log (6))}{(5-x){(4e^5+x^2+4x(1+\frac{\log (6)}{4})+4\log (-5+x))}^3}+\frac{x}{{(4e^5+x^2+4x(1+\frac{\log (6)}{4})+4\log (-5+x))}^2})dx\\ & =32\int \frac{x^2(-16+2x^2-x(6-\log (6))-5\log (6))}{(5-x){(4e^5+x^2+4x(1+\frac{\log (6)}{4})+4\log (-5+x))}^3}dx+32\int \frac{x}{{(4e^5+x^2+4x(1+\frac{\log (6)}{4})+4\log (-5+x))}^2}dx\\ & =32\int \frac{x}{{(4e^5+x^2+4x(1+\frac{\log (6)}{4})+4\log (-5+x))}^2}dx+32\int (\frac{20}{{(-4e^5-x^2-4x(1+\frac{\log (6)}{4})-4\log (-5+x))}^3}+\frac{4x}{{(-4e^5-x^2-4x(1+\frac{\log (6)}{4})-4\log (-5+x))}^3}+\frac{2x^3}{{(-4e^5-x^2-4x(1+\frac{\log (6)}{4})-4\log (-5+x))}^3}+\frac{100}{(5-x){(4e^5+x^2+4x(1+\frac{\log (6)}{4})+4\log (-5+x))}^3}+\frac{x^2(-4-\log (6))}{{(4e^5+x^2+4x(1+\frac{\log (6)}{4})+4\log (-5+x))}^3})dx\\ & =32\int \frac{x}{{(4e^5+x^2+4x(1+\frac{\log (6)}{4})+4\log (-5+x))}^2}dx+64\int \frac{x^3}{{(-4e^5-x^2-4x(1+\frac{\log (6)}{4})-4\log (-5+x))}^3}dx+128\int \frac{x}{{(-4e^5-x^2-4x(1+\frac{\log (6)}{4})-4\log (-5+x))}^3}dx+640\int \frac{1}{{(-4e^5-x^2-4x(1+\frac{\log (6)}{4})-4\log (-5+x))}^3}dx+3200\int \frac{1}{(5-x){(4e^5+x^2+4x(1+\frac{\log (6)}{4})+4\log (-5+x))}^3}dx-(32(4+\log (6)))\int \frac{x^2}{{(4e^5+x^2+4x(1+\frac{\log (6)}{4})+4\log (-5+x))}^3}dx\\ & =32\int \frac{x}{{(4e^5+x^2+4x(1+\frac{\log (6)}{4})+4\log (-5+x))}^2}dx+64\int \frac{x^3}{{(-4e^5-x(4+x+\log (6))-4\log (-5+x))}^3}dx+128\int \frac{x}{{(-4e^5-x(4+x+\log (6))-4\log (-5+x))}^3}dx+640\int \frac{1}{{(-4e^5-x(4+x+\log (6))-4\log (-5+x))}^3}dx+3200\int \frac{1}{(5-x){(4e^5+x^2+4x(1+\frac{\log (6)}{4})+4\log (-5+x))}^3}dx-(32(4+\log (6)))\int \frac{x^2}{{(4e^5+x^2+4x(1+\frac{\log (6)}{4})+4\log (-5+x))}^3}dx\end{array}\end{array}$$

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Mathematica [A]  time = 4.19, size = 26, normalized size = 1.00 $$\begin{array}{c}\frac{16x^2}{{(4e^5+x(4+x+\log (6))+4\log (-5+x))}^2}\end{array}$$

Antiderivative was successfully verified.

[In]

Integrate[(-128*x^2 + 160*x^3 - 32*x^4 + E^5*(-640*x + 128*x^2) + (-640*x + 128*x^2)*Log[-5 + x])/(-320*x^3 -
176*x^4 - 12*x^5 + 7*x^6 + x^7 + E^15*(-320 + 64*x) + E^10*(-960*x - 48*x^2 + 48*x^3) + E^5*(-960*x^2 - 288*x^
3 + 36*x^4 + 12*x^5) + (-240*x^3 - 72*x^4 + 9*x^5 + 3*x^6 + E^10*(-240*x + 48*x^2) + E^5*(-480*x^2 - 24*x^3 +
24*x^4))*Log[2] + (-60*x^3 - 3*x^4 + 3*x^5 + E^5*(-60*x^2 + 12*x^3))*Log[2]^2 + (-5*x^3 + x^4)*Log[2]^3 + (-24
0*x^3 - 72*x^4 + 9*x^5 + 3*x^6 + E^10*(-240*x + 48*x^2) + E^5*(-480*x^2 - 24*x^3 + 24*x^4) + (-120*x^3 - 6*x^4
+ 6*x^5 + E^5*(-120*x^2 + 24*x^3))*Log[2] + (-15*x^3 + 3*x^4)*Log[2]^2)*Log[3] + (-60*x^3 - 3*x^4 + 3*x^5 + E
^5*(-60*x^2 + 12*x^3) + (-15*x^3 + 3*x^4)*Log[2])*Log[3]^2 + (-5*x^3 + x^4)*Log[3]^3 + (-960*x^2 - 288*x^3 + 3
6*x^4 + 12*x^5 + E^10*(-960 + 192*x) + E^5*(-1920*x - 96*x^2 + 96*x^3) + (-480*x^2 - 24*x^3 + 24*x^4 + E^5*(-4
80*x + 96*x^2))*Log[2] + (-60*x^2 + 12*x^3)*Log[2]^2 + (-480*x^2 - 24*x^3 + 24*x^4 + E^5*(-480*x + 96*x^2) + (
-120*x^2 + 24*x^3)*Log[2])*Log[3] + (-60*x^2 + 12*x^3)*Log[3]^2)*Log[-5 + x] + (-960*x - 48*x^2 + 48*x^3 + E^5
*(-960 + 192*x) + (-240*x + 48*x^2)*Log[2] + (-240*x + 48*x^2)*Log[3])*Log[-5 + x]^2 + (-320 + 64*x)*Log[-5 +
x]^3),x]

[Out]

(16*x^2)/(4*E^5 + x*(4 + x + Log[6]) + 4*Log[-5 + x])^2

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fricas [B]  time = 0.56, size = 127, normalized size = 4.88 $$\begin{array}{c}\frac{16x^2}{x^4+x^2\log (3{)}^2+x^2\log (2{)}^2+8x^3+16x^2+8(x^2+4x)e^5+2(x^3+x^2\log (2)+4x^2+4x{e}^5)\log (3)+2(x^3+4x^2+4x{e}^5)\log (2)+8(x^2+x\log (3)+x\log (2)+4x+4e^5)\log (x-5)+16\log {(x-5)}^2+16e^{10}}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((128*x^2-640*x)*log(x-5)+(128*x^2-640*x)*exp(5)-32*x^4+160*x^3-128*x^2)/((64*x-320)*log(x-5)^3+((48
*x^2-240*x)*log(3)+(48*x^2-240*x)*log(2)+(192*x-960)*exp(5)+48*x^3-48*x^2-960*x)*log(x-5)^2+((12*x^3-60*x^2)*l
og(3)^2+((24*x^3-120*x^2)*log(2)+(96*x^2-480*x)*exp(5)+24*x^4-24*x^3-480*x^2)*log(3)+(12*x^3-60*x^2)*log(2)^2+
((96*x^2-480*x)*exp(5)+24*x^4-24*x^3-480*x^2)*log(2)+(192*x-960)*exp(5)^2+(96*x^3-96*x^2-1920*x)*exp(5)+12*x^5
+36*x^4-288*x^3-960*x^2)*log(x-5)+(x^4-5*x^3)*log(3)^3+((3*x^4-15*x^3)*log(2)+(12*x^3-60*x^2)*exp(5)+3*x^5-3*x
^4-60*x^3)*log(3)^2+((3*x^4-15*x^3)*log(2)^2+((24*x^3-120*x^2)*exp(5)+6*x^5-6*x^4-120*x^3)*log(2)+(48*x^2-240*
x)*exp(5)^2+(24*x^4-24*x^3-480*x^2)*exp(5)+3*x^6+9*x^5-72*x^4-240*x^3)*log(3)+(x^4-5*x^3)*log(2)^3+((12*x^3-60
*x^2)*exp(5)+3*x^5-3*x^4-60*x^3)*log(2)^2+((48*x^2-240*x)*exp(5)^2+(24*x^4-24*x^3-480*x^2)*exp(5)+3*x^6+9*x^5-
72*x^4-240*x^3)*log(2)+(64*x-320)*exp(5)^3+(48*x^3-48*x^2-960*x)*exp(5)^2+(12*x^5+36*x^4-288*x^3-960*x^2)*exp(
5)+x^7+7*x^6-12*x^5-176*x^4-320*x^3),x, algorithm="fricas")

[Out]

16*x^2/(x^4 + x^2*log(3)^2 + x^2*log(2)^2 + 8*x^3 + 16*x^2 + 8*(x^2 + 4*x)*e^5 + 2*(x^3 + x^2*log(2) + 4*x^2 +
4*x*e^5)*log(3) + 2*(x^3 + 4*x^2 + 4*x*e^5)*log(2) + 8*(x^2 + x*log(3) + x*log(2) + 4*x + 4*e^5)*log(x - 5) +
16*log(x - 5)^2 + 16*e^10)

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giac [B]  time = 0.55, size = 154, normalized size = 5.92 $$\begin{array}{c}\frac{16x^2}{x^4+2x^3\log (3)+x^2\log (3{)}^2+2x^3\log (2)+2x^2\log (3)\log (2)+x^2\log (2{)}^2+8x^3+8x^2{e}^5+8x^2\log (3)+8x{e}^5\log (3)+8x^2\log (2)+8x{e}^5\log (2)+8x^2\log (x-5)+8x\log (3)\log (x-5)+8x\log (2)\log (x-5)+16x^2+32x{e}^5+32x\log (x-5)+32e^5\log (x-5)+16\log {(x-5)}^2+16e^{10}}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((128*x^2-640*x)*log(x-5)+(128*x^2-640*x)*exp(5)-32*x^4+160*x^3-128*x^2)/((64*x-320)*log(x-5)^3+((48
*x^2-240*x)*log(3)+(48*x^2-240*x)*log(2)+(192*x-960)*exp(5)+48*x^3-48*x^2-960*x)*log(x-5)^2+((12*x^3-60*x^2)*l
og(3)^2+((24*x^3-120*x^2)*log(2)+(96*x^2-480*x)*exp(5)+24*x^4-24*x^3-480*x^2)*log(3)+(12*x^3-60*x^2)*log(2)^2+
((96*x^2-480*x)*exp(5)+24*x^4-24*x^3-480*x^2)*log(2)+(192*x-960)*exp(5)^2+(96*x^3-96*x^2-1920*x)*exp(5)+12*x^5
+36*x^4-288*x^3-960*x^2)*log(x-5)+(x^4-5*x^3)*log(3)^3+((3*x^4-15*x^3)*log(2)+(12*x^3-60*x^2)*exp(5)+3*x^5-3*x
^4-60*x^3)*log(3)^2+((3*x^4-15*x^3)*log(2)^2+((24*x^3-120*x^2)*exp(5)+6*x^5-6*x^4-120*x^3)*log(2)+(48*x^2-240*
x)*exp(5)^2+(24*x^4-24*x^3-480*x^2)*exp(5)+3*x^6+9*x^5-72*x^4-240*x^3)*log(3)+(x^4-5*x^3)*log(2)^3+((12*x^3-60
*x^2)*exp(5)+3*x^5-3*x^4-60*x^3)*log(2)^2+((48*x^2-240*x)*exp(5)^2+(24*x^4-24*x^3-480*x^2)*exp(5)+3*x^6+9*x^5-
72*x^4-240*x^3)*log(2)+(64*x-320)*exp(5)^3+(48*x^3-48*x^2-960*x)*exp(5)^2+(12*x^5+36*x^4-288*x^3-960*x^2)*exp(
5)+x^7+7*x^6-12*x^5-176*x^4-320*x^3),x, algorithm="giac")

[Out]

16*x^2/(x^4 + 2*x^3*log(3) + x^2*log(3)^2 + 2*x^3*log(2) + 2*x^2*log(3)*log(2) + x^2*log(2)^2 + 8*x^3 + 8*x^2*
e^5 + 8*x^2*log(3) + 8*x*e^5*log(3) + 8*x^2*log(2) + 8*x*e^5*log(2) + 8*x^2*log(x - 5) + 8*x*log(3)*log(x - 5)
+ 8*x*log(2)*log(x - 5) + 16*x^2 + 32*x*e^5 + 32*x*log(x - 5) + 32*e^5*log(x - 5) + 16*log(x - 5)^2 + 16*e^10
)

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maple [A]  time = 0.12, size = 33, normalized size = 1.27

method	result	size
risch	$\frac{16x^2}{{(x\ln (2)+x\ln (3)+x^2+4{\mathrm{e}}^5+4\ln (x-5)+4x)}^2}$	$33$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((128*x^2-640*x)*ln(x-5)+(128*x^2-640*x)*exp(5)-32*x^4+160*x^3-128*x^2)/((64*x-320)*ln(x-5)^3+((48*x^2-240
*x)*ln(3)+(48*x^2-240*x)*ln(2)+(192*x-960)*exp(5)+48*x^3-48*x^2-960*x)*ln(x-5)^2+((12*x^3-60*x^2)*ln(3)^2+((24
*x^3-120*x^2)*ln(2)+(96*x^2-480*x)*exp(5)+24*x^4-24*x^3-480*x^2)*ln(3)+(12*x^3-60*x^2)*ln(2)^2+((96*x^2-480*x)
*exp(5)+24*x^4-24*x^3-480*x^2)*ln(2)+(192*x-960)*exp(5)^2+(96*x^3-96*x^2-1920*x)*exp(5)+12*x^5+36*x^4-288*x^3-
960*x^2)*ln(x-5)+(x^4-5*x^3)*ln(3)^3+((3*x^4-15*x^3)*ln(2)+(12*x^3-60*x^2)*exp(5)+3*x^5-3*x^4-60*x^3)*ln(3)^2+
((3*x^4-15*x^3)*ln(2)^2+((24*x^3-120*x^2)*exp(5)+6*x^5-6*x^4-120*x^3)*ln(2)+(48*x^2-240*x)*exp(5)^2+(24*x^4-24
*x^3-480*x^2)*exp(5)+3*x^6+9*x^5-72*x^4-240*x^3)*ln(3)+(x^4-5*x^3)*ln(2)^3+((12*x^3-60*x^2)*exp(5)+3*x^5-3*x^4
-60*x^3)*ln(2)^2+((48*x^2-240*x)*exp(5)^2+(24*x^4-24*x^3-480*x^2)*exp(5)+3*x^6+9*x^5-72*x^4-240*x^3)*ln(2)+(64
*x-320)*exp(5)^3+(48*x^3-48*x^2-960*x)*exp(5)^2+(12*x^5+36*x^4-288*x^3-960*x^2)*exp(5)+x^7+7*x^6-12*x^5-176*x^
4-320*x^3),x,method=_RETURNVERBOSE)

[Out]

16*x^2/(x*ln(2)+x*ln(3)+x^2+4*exp(5)+4*ln(x-5)+4*x)^2

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maxima [B]  time = 0.62, size = 97, normalized size = 3.73 $$\begin{array}{c}\frac{16x^2}{x^4+2x^3(\log (3)+\log (2)+4)+(\log (3{)}^2+2(\log (3)+4)\log (2)+\log (2{)}^2+8e^5+8\log (3)+16)x^2+8x(\log (3)+\log (2)+4)e^5+8(x^2+x(\log (3)+\log (2)+4)+4e^5)\log (x-5)+16\log {(x-5)}^2+16e^{10}}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((128*x^2-640*x)*log(x-5)+(128*x^2-640*x)*exp(5)-32*x^4+160*x^3-128*x^2)/((64*x-320)*log(x-5)^3+((48
*x^2-240*x)*log(3)+(48*x^2-240*x)*log(2)+(192*x-960)*exp(5)+48*x^3-48*x^2-960*x)*log(x-5)^2+((12*x^3-60*x^2)*l
og(3)^2+((24*x^3-120*x^2)*log(2)+(96*x^2-480*x)*exp(5)+24*x^4-24*x^3-480*x^2)*log(3)+(12*x^3-60*x^2)*log(2)^2+
((96*x^2-480*x)*exp(5)+24*x^4-24*x^3-480*x^2)*log(2)+(192*x-960)*exp(5)^2+(96*x^3-96*x^2-1920*x)*exp(5)+12*x^5
+36*x^4-288*x^3-960*x^2)*log(x-5)+(x^4-5*x^3)*log(3)^3+((3*x^4-15*x^3)*log(2)+(12*x^3-60*x^2)*exp(5)+3*x^5-3*x
^4-60*x^3)*log(3)^2+((3*x^4-15*x^3)*log(2)^2+((24*x^3-120*x^2)*exp(5)+6*x^5-6*x^4-120*x^3)*log(2)+(48*x^2-240*
x)*exp(5)^2+(24*x^4-24*x^3-480*x^2)*exp(5)+3*x^6+9*x^5-72*x^4-240*x^3)*log(3)+(x^4-5*x^3)*log(2)^3+((12*x^3-60
*x^2)*exp(5)+3*x^5-3*x^4-60*x^3)*log(2)^2+((48*x^2-240*x)*exp(5)^2+(24*x^4-24*x^3-480*x^2)*exp(5)+3*x^6+9*x^5-
72*x^4-240*x^3)*log(2)+(64*x-320)*exp(5)^3+(48*x^3-48*x^2-960*x)*exp(5)^2+(12*x^5+36*x^4-288*x^3-960*x^2)*exp(
5)+x^7+7*x^6-12*x^5-176*x^4-320*x^3),x, algorithm="maxima")

[Out]

16*x^2/(x^4 + 2*x^3*(log(3) + log(2) + 4) + (log(3)^2 + 2*(log(3) + 4)*log(2) + log(2)^2 + 8*e^5 + 8*log(3) +
16)*x^2 + 8*x*(log(3) + log(2) + 4)*e^5 + 8*(x^2 + x*(log(3) + log(2) + 4) + 4*e^5)*log(x - 5) + 16*log(x - 5)
^2 + 16*e^10)

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mupad [F(-1)]  time = 0.00, size = -1, normalized size = -0.04 $$\begin{array}{c}\text{Hanged}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((log(x - 5)*(640*x - 128*x^2) + exp(5)*(640*x - 128*x^2) + 128*x^2 - 160*x^3 + 32*x^4)/(log(2)*(exp(10)*(2
40*x - 48*x^2) + exp(5)*(480*x^2 + 24*x^3 - 24*x^4) + 240*x^3 + 72*x^4 - 9*x^5 - 3*x^6) + log(x - 5)^2*(960*x
+ log(2)*(240*x - 48*x^2) + log(3)*(240*x - 48*x^2) + 48*x^2 - 48*x^3 - exp(5)*(192*x - 960)) - log(x - 5)^3*(
64*x - 320) + log(3)^2*(exp(5)*(60*x^2 - 12*x^3) + log(2)*(15*x^3 - 3*x^4) + 60*x^3 + 3*x^4 - 3*x^5) + log(3)*
(exp(10)*(240*x - 48*x^2) + log(2)*(exp(5)*(120*x^2 - 24*x^3) + 120*x^3 + 6*x^4 - 6*x^5) + exp(5)*(480*x^2 + 2
4*x^3 - 24*x^4) + 240*x^3 + 72*x^4 - 9*x^5 - 3*x^6 + log(2)^2*(15*x^3 - 3*x^4)) + exp(10)*(960*x + 48*x^2 - 48
*x^3) + log(2)^2*(exp(5)*(60*x^2 - 12*x^3) + 60*x^3 + 3*x^4 - 3*x^5) + log(x - 5)*(log(2)*(exp(5)*(480*x - 96*
x^2) + 480*x^2 + 24*x^3 - 24*x^4) + exp(5)*(1920*x + 96*x^2 - 96*x^3) + log(3)*(exp(5)*(480*x - 96*x^2) + log(
2)*(120*x^2 - 24*x^3) + 480*x^2 + 24*x^3 - 24*x^4) + 960*x^2 + 288*x^3 - 36*x^4 - 12*x^5 + log(2)^2*(60*x^2 -
12*x^3) + log(3)^2*(60*x^2 - 12*x^3) - exp(10)*(192*x - 960)) + 320*x^3 + 176*x^4 + 12*x^5 - 7*x^6 - x^7 + log
(2)^3*(5*x^3 - x^4) + log(3)^3*(5*x^3 - x^4) - exp(15)*(64*x - 320) + exp(5)*(960*x^2 + 288*x^3 - 36*x^4 - 12*
x^5)),x)

[Out]

\text{Hanged}

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sympy [B]  time = 0.77, size = 162, normalized size = 6.23 $$\begin{array}{c}\frac{16x^2}{x^4+2x^3\log (2)+2x^3\log (3)+8x^3+x^2\log {(2)}^2+x^2\log {(3)}^2+2x^2\log (2)\log (3)+8x^2\log (2)+8x^2\log (3)+16x^2+8x^2{e}^5+8x{e}^5\log (2)+8x{e}^5\log (3)+32x{e}^5+(8x^2+8x\log (2)+8x\log (3)+32x+32e^5)\log (x-5)+16\log {(x-5)}^2+16e^{10}}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((128*x**2-640*x)*ln(x-5)+(128*x**2-640*x)*exp(5)-32*x**4+160*x**3-128*x**2)/((64*x-320)*ln(x-5)**3+
((48*x**2-240*x)*ln(3)+(48*x**2-240*x)*ln(2)+(192*x-960)*exp(5)+48*x**3-48*x**2-960*x)*ln(x-5)**2+((12*x**3-60
*x**2)*ln(3)**2+((24*x**3-120*x**2)*ln(2)+(96*x**2-480*x)*exp(5)+24*x**4-24*x**3-480*x**2)*ln(3)+(12*x**3-60*x
**2)*ln(2)**2+((96*x**2-480*x)*exp(5)+24*x**4-24*x**3-480*x**2)*ln(2)+(192*x-960)*exp(5)**2+(96*x**3-96*x**2-1
920*x)*exp(5)+12*x**5+36*x**4-288*x**3-960*x**2)*ln(x-5)+(x**4-5*x**3)*ln(3)**3+((3*x**4-15*x**3)*ln(2)+(12*x*
*3-60*x**2)*exp(5)+3*x**5-3*x**4-60*x**3)*ln(3)**2+((3*x**4-15*x**3)*ln(2)**2+((24*x**3-120*x**2)*exp(5)+6*x**
5-6*x**4-120*x**3)*ln(2)+(48*x**2-240*x)*exp(5)**2+(24*x**4-24*x**3-480*x**2)*exp(5)+3*x**6+9*x**5-72*x**4-240
*x**3)*ln(3)+(x**4-5*x**3)*ln(2)**3+((12*x**3-60*x**2)*exp(5)+3*x**5-3*x**4-60*x**3)*ln(2)**2+((48*x**2-240*x)
*exp(5)**2+(24*x**4-24*x**3-480*x**2)*exp(5)+3*x**6+9*x**5-72*x**4-240*x**3)*ln(2)+(64*x-320)*exp(5)**3+(48*x*
*3-48*x**2-960*x)*exp(5)**2+(12*x**5+36*x**4-288*x**3-960*x**2)*exp(5)+x**7+7*x**6-12*x**5-176*x**4-320*x**3),
x)

[Out]

16*x**2/(x**4 + 2*x**3*log(2) + 2*x**3*log(3) + 8*x**3 + x**2*log(2)**2 + x**2*log(3)**2 + 2*x**2*log(2)*log(3
) + 8*x**2*log(2) + 8*x**2*log(3) + 16*x**2 + 8*x**2*exp(5) + 8*x*exp(5)*log(2) + 8*x*exp(5)*log(3) + 32*x*exp
(5) + (8*x**2 + 8*x*log(2) + 8*x*log(3) + 32*x + 32*exp(5))*log(x - 5) + 16*log(x - 5)**2 + 16*exp(10))

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