3.85.76 $\int \frac{e^{-10-2x}(9216-4608x+(4608+6912x-4608x^2+e^{5+x}(576x-288x^2)+e^{5+x}(192-96x)\log (2-x))\log (x)+(e^{5+x}(96x+576x^2-288x^3)+e^{5+x}(192+96x-96x^2)\log (2-x)){\log }^2(x)+(e^{10+2x}(-12x^2+9x^3)+2e^{10+2x}x\log (2-x)+e^{10+2x}(2-x){\log }^2(2-x)){\log }^3(x))}{(-2x^2+x^3){\log }^3(x)}dx$

Optimal. Leaf size=30 $$\frac{{(\log (2-x)+3(x+\frac{16e^{-5-x}}{\log (x)}))}^2}{x}$$

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Rubi [F]  time = 14.58, 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 = {} $$\begin{array}{c}\int \frac{e^{-10-2x}(9216-4608x+(4608+6912x-4608x^2+e^{5+x}(576x-288x^2)+e^{5+x}(192-96x)\log (2-x))\log (x)+(e^{5+x}(96x+576x^2-288x^3)+e^{5+x}(192+96x-96x^2)\log (2-x)){\log }^2(x)+(e^{10+2x}(-12x^2+9x^3)+2e^{10+2x}x\log (2-x)+e^{10+2x}(2-x){\log }^2(2-x)){\log }^3(x))}{(-2x^2+x^3){\log }^3(x)}dx\end{array}$$

Verification is not applicable to the result.

[In]

Int[(E^(-10 - 2*x)*(9216 - 4608*x + (4608 + 6912*x - 4608*x^2 + E^(5 + x)*(576*x - 288*x^2) + E^(5 + x)*(192 -
96*x)*Log[2 - x])*Log[x] + (E^(5 + x)*(96*x + 576*x^2 - 288*x^3) + E^(5 + x)*(192 + 96*x - 96*x^2)*Log[2 - x]
)*Log[x]^2 + (E^(10 + 2*x)*(-12*x^2 + 9*x^3) + 2*E^(10 + 2*x)*x*Log[2 - x] + E^(10 + 2*x)*(2 - x)*Log[2 - x]^2
)*Log[x]^3))/((-2*x^2 + x^3)*Log[x]^3),x]

[Out]

9*x + 6*Log[2 - x] + Log[2 - x]^2/2 + ((2 - x)*Log[2 - x]^2)/(2*x) + (2304*E^(-10 - 2*x))/(x*Log[x]^2) - 288*D
efer[Int][E^(-5 - x)/(x*Log[x]^2), x] - 96*Defer[Int][(E^(-5 - x)*Log[2 - x])/(x^2*Log[x]^2), x] - 288*Defer[I
nt][E^(-5 - x)/Log[x], x] + 48*Defer[Int][E^(-5 - x)/((-2 + x)*Log[x]), x] - 48*Defer[Int][E^(-5 - x)/(x*Log[x
]), x] - 96*Defer[Int][(E^(-5 - x)*Log[2 - x])/(x^2*Log[x]), x] - 96*Defer[Int][(E^(-5 - x)*Log[2 - x])/(x*Log
[x]), x]

Rubi steps

$$\begin{array}{c}\begin{array}{rl}\text{integral}& =\int \frac{e^{-10-2x}(9216-4608x+(4608+6912x-4608x^2+e^{5+x}(576x-288x^2)+e^{5+x}(192-96x)\log (2-x))\log (x)+(e^{5+x}(96x+576x^2-288x^3)+e^{5+x}(192+96x-96x^2)\log (2-x)){\log }^2(x)+(e^{10+2x}(-12x^2+9x^3)+2e^{10+2x}x\log (2-x)+e^{10+2x}(2-x){\log }^2(2-x)){\log }^3(x))}{(-2+x)x^2{\log }^3(x)}dx\\ & =\int (\frac{-12x^2+9x^3+2x\log (2-x)+2{\log }^2(2-x)-x{\log }^2(2-x)}{(-2+x)x^2}-\frac{2304e^{-10-2x}(2+\log (x)+2x\log (x))}{x^2{\log }^3(x)}-\frac{96e^{-5-x}(-6x+3x^2-2\log (2-x)+x\log (2-x)-x\log (x)-6x^2\log (x)+3x^3\log (x)-2\log (2-x)\log (x)-x\log (2-x)\log (x)+x^2\log (2-x)\log (x))}{(-2+x)x^2{\log }^2(x)})dx\\ & =-(96\int \frac{e^{-5-x}(-6x+3x^2-2\log (2-x)+x\log (2-x)-x\log (x)-6x^2\log (x)+3x^3\log (x)-2\log (2-x)\log (x)-x\log (2-x)\log (x)+x^2\log (2-x)\log (x))}{(-2+x)x^2{\log }^2(x)}dx)-2304\int \frac{e^{-10-2x}(2+\log (x)+2x\log (x))}{x^2{\log }^3(x)}dx+\int \frac{-12x^2+9x^3+2x\log (2-x)+2{\log }^2(2-x)-x{\log }^2(2-x)}{(-2+x)x^2}dx\\ & =\frac{2304e^{-10-2x}}{x{\log }^2(x)}-96\int \frac{e^{-5-x}(-((-2+x)\log (2-x)(1+(1+x)\log (x)))-x(3(-2+x)+(-1-6x+3x^2)\log (x)))}{(2-x)x^2{\log }^2(x)}dx+\int (\frac{3(-4+3x)}{-2+x}+\frac{2\log (2-x)}{(-2+x)x}-\frac{{\log }^2(2-x)}{x^2})dx\\ & =\frac{2304e^{-10-2x}}{x{\log }^2(x)}+2\int \frac{\log (2-x)}{(-2+x)x}dx+3\int \frac{-4+3x}{-2+x}dx-96\int (\frac{e^{-5-x}(3x+\log (2-x))}{x^2{\log }^2(x)}+\frac{e^{-5-x}(-x-6x^2+3x^3-2\log (2-x)-x\log (2-x)+x^2\log (2-x))}{(-2+x)x^2\log (x)})dx-\int \frac{{\log }^2(2-x)}{x^2}dx\\ & =\frac{(2-x){\log }^2(2-x)}{2x}+\frac{2304e^{-10-2x}}{x{\log }^2(x)}+2\mathrm{Subst}(\int \frac{\log (x)}{(2-x)x}dx,x,2-x)+3\int (3+\frac{2}{-2+x})dx-96\int \frac{e^{-5-x}(3x+\log (2-x))}{x^2{\log }^2(x)}dx-96\int \frac{e^{-5-x}(-x-6x^2+3x^3-2\log (2-x)-x\log (2-x)+x^2\log (2-x))}{(-2+x)x^2\log (x)}dx+\int \frac{\log (2-x)}{x}dx\\ & =9x+6\log (2-x)+\frac{(2-x){\log }^2(2-x)}{2x}+\frac{2304e^{-10-2x}}{x{\log }^2(x)}+\log (2)\log (x)-96\int (\frac{3e^{-5-x}}{x{\log }^2(x)}+\frac{e^{-5-x}\log (2-x)}{x^2{\log }^2(x)})dx-96\int (\frac{e^{-5-x}(x+6x^2-3x^3+2\log (2-x)+x\log (2-x)-x^2\log (2-x))}{2x^2\log (x)}+\frac{e^{-5-x}(x+6x^2-3x^3+2\log (2-x)+x\log (2-x)-x^2\log (2-x))}{4x\log (x)}+\frac{e^{-5-x}(-x-6x^2+3x^3-2\log (2-x)-x\log (2-x)+x^2\log (2-x))}{4(-2+x)\log (x)})dx+\int \frac{\log (1-\frac{x}{2})}{x}dx+\mathrm{Subst}(\int \frac{\log (x)}{2-x}dx,x,2-x)+\mathrm{Subst}(\int \frac{\log (x)}{x}dx,x,2-x)\\ & =9x+6\log (2-x)+\frac{1}{2}{\log }^2(2-x)+\frac{(2-x){\log }^2(2-x)}{2x}+\frac{2304e^{-10-2x}}{x{\log }^2(x)}-{\text{Li}}_2\left(\frac{x}{2}\right)-24\int \frac{e^{-5-x}(x+6x^2-3x^3+2\log (2-x)+x\log (2-x)-x^2\log (2-x))}{x\log (x)}dx-24\int \frac{e^{-5-x}(-x-6x^2+3x^3-2\log (2-x)-x\log (2-x)+x^2\log (2-x))}{(-2+x)\log (x)}dx-48\int \frac{e^{-5-x}(x+6x^2-3x^3+2\log (2-x)+x\log (2-x)-x^2\log (2-x))}{x^2\log (x)}dx-96\int \frac{e^{-5-x}\log (2-x)}{x^2{\log }^2(x)}dx-288\int \frac{e^{-5-x}}{x{\log }^2(x)}dx+\mathrm{Subst}(\int \frac{\log \left(\frac{x}{2}\right)}{2-x}dx,x,2-x)\\ & =9x+6\log (2-x)+\frac{1}{2}{\log }^2(2-x)+\frac{(2-x){\log }^2(2-x)}{2x}+\frac{2304e^{-10-2x}}{x{\log }^2(x)}-24\int (-\frac{e^{-5-x}x}{(-2+x)\log (x)}-\frac{6e^{-5-x}{x}^2}{(-2+x)\log (x)}+\frac{3e^{-5-x}{x}^3}{(-2+x)\log (x)}-\frac{2e^{-5-x}\log (2-x)}{(-2+x)\log (x)}-\frac{e^{-5-x}x\log (2-x)}{(-2+x)\log (x)}+\frac{e^{-5-x}{x}^2\log (2-x)}{(-2+x)\log (x)})dx-24\int \frac{e^{-5-x}(x+6x^2-3x^3+(2+x-x^2)\log (2-x))}{x\log (x)}dx-48\int \frac{e^{-5-x}(x+6x^2-3x^3+(2+x-x^2)\log (2-x))}{x^2\log (x)}dx-96\int \frac{e^{-5-x}\log (2-x)}{x^2{\log }^2(x)}dx-288\int \frac{e^{-5-x}}{x{\log }^2(x)}dx\\ & =9x+6\log (2-x)+\frac{1}{2}{\log }^2(2-x)+\frac{(2-x){\log }^2(2-x)}{2x}+\frac{2304e^{-10-2x}}{x{\log }^2(x)}-24\int (\frac{e^{-5-x}}{\log (x)}+\frac{6e^{-5-x}x}{\log (x)}-\frac{3e^{-5-x}{x}^2}{\log (x)}+\frac{e^{-5-x}\log (2-x)}{\log (x)}+\frac{2e^{-5-x}\log (2-x)}{x\log (x)}-\frac{e^{-5-x}x\log (2-x)}{\log (x)})dx+24\int \frac{e^{-5-x}x}{(-2+x)\log (x)}dx+24\int \frac{e^{-5-x}x\log (2-x)}{(-2+x)\log (x)}dx-24\int \frac{e^{-5-x}{x}^2\log (2-x)}{(-2+x)\log (x)}dx-48\int (\frac{6e^{-5-x}}{\log (x)}+\frac{e^{-5-x}}{x\log (x)}-\frac{3e^{-5-x}x}{\log (x)}-\frac{e^{-5-x}\log (2-x)}{\log (x)}+\frac{2e^{-5-x}\log (2-x)}{x^2\log (x)}+\frac{e^{-5-x}\log (2-x)}{x\log (x)})dx+48\int \frac{e^{-5-x}\log (2-x)}{(-2+x)\log (x)}dx-72\int \frac{e^{-5-x}{x}^3}{(-2+x)\log (x)}dx-96\int \frac{e^{-5-x}\log (2-x)}{x^2{\log }^2(x)}dx+144\int \frac{e^{-5-x}{x}^2}{(-2+x)\log (x)}dx-288\int \frac{e^{-5-x}}{x{\log }^2(x)}dx\\ & =9x+6\log (2-x)+\frac{1}{2}{\log }^2(2-x)+\frac{(2-x){\log }^2(2-x)}{2x}+\frac{2304e^{-10-2x}}{x{\log }^2(x)}+24\int (\frac{e^{-5-x}}{\log (x)}+\frac{2e^{-5-x}}{(-2+x)\log (x)})dx+24\int (\frac{e^{-5-x}\log (2-x)}{\log (x)}+\frac{2e^{-5-x}\log (2-x)}{(-2+x)\log (x)})dx-24\int (\frac{2e^{-5-x}\log (2-x)}{\log (x)}+\frac{4e^{-5-x}\log (2-x)}{(-2+x)\log (x)}+\frac{e^{-5-x}x\log (2-x)}{\log (x)})dx-24\int \frac{e^{-5-x}}{\log (x)}dx-24\int \frac{e^{-5-x}\log (2-x)}{\log (x)}dx+24\int \frac{e^{-5-x}x\log (2-x)}{\log (x)}dx-48\int \frac{e^{-5-x}}{x\log (x)}dx+48\int \frac{e^{-5-x}\log (2-x)}{\log (x)}dx+48\int \frac{e^{-5-x}\log (2-x)}{(-2+x)\log (x)}dx-2(48\int \frac{e^{-5-x}\log (2-x)}{x\log (x)}dx)-72\int (\frac{4e^{-5-x}}{\log (x)}+\frac{8e^{-5-x}}{(-2+x)\log (x)}+\frac{2e^{-5-x}x}{\log (x)}+\frac{e^{-5-x}{x}^2}{\log (x)})dx+72\int \frac{e^{-5-x}{x}^2}{\log (x)}dx-96\int \frac{e^{-5-x}\log (2-x)}{x^2{\log }^2(x)}dx-96\int \frac{e^{-5-x}\log (2-x)}{x^2\log (x)}dx+144\int (\frac{2e^{-5-x}}{\log (x)}+\frac{4e^{-5-x}}{(-2+x)\log (x)}+\frac{e^{-5-x}x}{\log (x)})dx-288\int \frac{e^{-5-x}}{x{\log }^2(x)}dx-288\int \frac{e^{-5-x}}{\log (x)}dx\\ & =9x+6\log (2-x)+\frac{1}{2}{\log }^2(2-x)+\frac{(2-x){\log }^2(2-x)}{2x}+\frac{2304e^{-10-2x}}{x{\log }^2(x)}+48\int \frac{e^{-5-x}}{(-2+x)\log (x)}dx-48\int \frac{e^{-5-x}}{x\log (x)}dx+2(48\int \frac{e^{-5-x}\log (2-x)}{(-2+x)\log (x)}dx)-2(48\int \frac{e^{-5-x}\log (2-x)}{x\log (x)}dx)-96\int \frac{e^{-5-x}\log (2-x)}{x^2{\log }^2(x)}dx-96\int \frac{e^{-5-x}\log (2-x)}{(-2+x)\log (x)}dx-96\int \frac{e^{-5-x}\log (2-x)}{x^2\log (x)}dx-288\int \frac{e^{-5-x}}{x{\log }^2(x)}dx-288\int \frac{e^{-5-x}}{\log (x)}dx\end{array}\end{array}$$

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Mathematica [C]  time = 0.31, size = 116, normalized size = 3.87 $$\begin{array}{c}9x+6\log (2-x)-\log (2)\log (2-x)+\frac{{\log }^2(2-x)}{x}+\frac{2304e^{-2(5+x)}}{x{\log }^2(x)}+\frac{288e^{-5-x}}{\log (x)}+\frac{96e^{-5-x}\log (2-x)}{x\log (x)}-\log (2)\log (x)+\log (2-x)\log (x)+{\text{Li}}_2(1-\frac{x}{2})+{\text{Li}}_2\left(\frac{x}{2}\right)\end{array}$$

Antiderivative was successfully verified.

[In]

Integrate[(E^(-10 - 2*x)*(9216 - 4608*x + (4608 + 6912*x - 4608*x^2 + E^(5 + x)*(576*x - 288*x^2) + E^(5 + x)*
(192 - 96*x)*Log[2 - x])*Log[x] + (E^(5 + x)*(96*x + 576*x^2 - 288*x^3) + E^(5 + x)*(192 + 96*x - 96*x^2)*Log[
2 - x])*Log[x]^2 + (E^(10 + 2*x)*(-12*x^2 + 9*x^3) + 2*E^(10 + 2*x)*x*Log[2 - x] + E^(10 + 2*x)*(2 - x)*Log[2
- x]^2)*Log[x]^3))/((-2*x^2 + x^3)*Log[x]^3),x]

[Out]

9*x + 6*Log[2 - x] - Log[2]*Log[2 - x] + Log[2 - x]^2/x + 2304/(E^(2*(5 + x))*x*Log[x]^2) + (288*E^(-5 - x))/L
og[x] + (96*E^(-5 - x)*Log[2 - x])/(x*Log[x]) - Log[2]*Log[x] + Log[2 - x]*Log[x] + PolyLog[2, 1 - x/2] + Poly
Log[2, x/2]

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fricas [B]  time = 0.64, size = 86, normalized size = 2.87 $$\begin{array}{c}\frac{((9x^2{e}^{(2x+10)}+6x{e}^{(2x+10)}\log (-x+2)+e^{(2x+10)}\log {(-x+2)}^2)\log (x{)}^2+96(3x{e}^{(x+5)}+e^{(x+5)}\log (-x+2))\log (x)+2304)e^{(-2x-10)}}{x\log (x{)}^2}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((2-x)*exp(5+x)^2*log(2-x)^2+2*x*exp(5+x)^2*log(2-x)+(9*x^3-12*x^2)*exp(5+x)^2)*log(x)^3+((-96*x^2+
96*x+192)*exp(5+x)*log(2-x)+(-288*x^3+576*x^2+96*x)*exp(5+x))*log(x)^2+((-96*x+192)*exp(5+x)*log(2-x)+(-288*x^
2+576*x)*exp(5+x)-4608*x^2+6912*x+4608)*log(x)-4608*x+9216)/(x^3-2*x^2)/exp(5+x)^2/log(x)^3,x, algorithm="fric
as")

[Out]

((9*x^2*e^(2*x + 10) + 6*x*e^(2*x + 10)*log(-x + 2) + e^(2*x + 10)*log(-x + 2)^2)*log(x)^2 + 96*(3*x*e^(x + 5)
+ e^(x + 5)*log(-x + 2))*log(x) + 2304)*e^(-2*x - 10)/(x*log(x)^2)

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giac [B]  time = 0.17, size = 85, normalized size = 2.83 $$\begin{array}{c}\frac{(9x^2{e}^{15}\log (x{)}^2+6x{e}^{15}\log (x-2)\log (x{)}^2+e^{15}\log (x{)}^2\log {(-x+2)}^2+288x{e}^{(-x+10)}\log (x)+96e^{(-x+10)}\log (x)\log (-x+2)+2304e^{(-2x+5)})e^{(-15)}}{x\log (x{)}^2}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((2-x)*exp(5+x)^2*log(2-x)^2+2*x*exp(5+x)^2*log(2-x)+(9*x^3-12*x^2)*exp(5+x)^2)*log(x)^3+((-96*x^2+
96*x+192)*exp(5+x)*log(2-x)+(-288*x^3+576*x^2+96*x)*exp(5+x))*log(x)^2+((-96*x+192)*exp(5+x)*log(2-x)+(-288*x^
2+576*x)*exp(5+x)-4608*x^2+6912*x+4608)*log(x)-4608*x+9216)/(x^3-2*x^2)/exp(5+x)^2/log(x)^3,x, algorithm="giac
")

[Out]

(9*x^2*e^15*log(x)^2 + 6*x*e^15*log(x - 2)*log(x)^2 + e^15*log(x)^2*log(-x + 2)^2 + 288*x*e^(-x + 10)*log(x) +
96*e^(-x + 10)*log(x)*log(-x + 2) + 2304*e^(-2*x + 5))*e^(-15)/(x*log(x)^2)

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maple [B]  time = 0.38, size = 93, normalized size = 3.10

method	result	size
risch	$\frac{\ln {(2-x)}^2}{x}+\frac{96{\mathrm{e}}^{-x-5}\ln (2-x)}{x\ln (x)}+\frac{3(2\ln (x-2)x{\mathrm{e}}^{2x+10}\ln (x{)}^2+3\ln (x{)}^2{x}^2{\mathrm{e}}^{2x+10}+96\ln (x){\mathrm{e}}^{5+x}x+768){\mathrm{e}}^{-2x-10}}{x\ln (x{)}^2}$	$93$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((2-x)*exp(5+x)^2*ln(2-x)^2+2*x*exp(5+x)^2*ln(2-x)+(9*x^3-12*x^2)*exp(5+x)^2)*ln(x)^3+((-96*x^2+96*x+192)
*exp(5+x)*ln(2-x)+(-288*x^3+576*x^2+96*x)*exp(5+x))*ln(x)^2+((-96*x+192)*exp(5+x)*ln(2-x)+(-288*x^2+576*x)*exp
(5+x)-4608*x^2+6912*x+4608)*ln(x)-4608*x+9216)/(x^3-2*x^2)/exp(5+x)^2/ln(x)^3,x,method=_RETURNVERBOSE)

[Out]

1/x*ln(2-x)^2+96/x*exp(-x-5)/ln(x)*ln(2-x)+3*(2*ln(x-2)*x*exp(2*x+10)*ln(x)^2+3*ln(x)^2*x^2*exp(2*x+10)+96*ln(
x)*exp(5+x)*x+768)/x*exp(-2*x-10)/ln(x)^2

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maxima [B]  time = 0.43, size = 81, normalized size = 2.70 $$\begin{array}{c}\frac{(9x^2{e}^{10}\log (x{)}^2+e^{10}\log (x{)}^2\log {(-x+2)}^2+288x{e}^{(-x+5)}\log (x)+6(x{e}^{10}\log (x{)}^2+16e^{(-x+5)}\log (x))\log (-x+2)+2304e^{(-2x)})e^{(-10)}}{x\log (x{)}^2}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((2-x)*exp(5+x)^2*log(2-x)^2+2*x*exp(5+x)^2*log(2-x)+(9*x^3-12*x^2)*exp(5+x)^2)*log(x)^3+((-96*x^2+
96*x+192)*exp(5+x)*log(2-x)+(-288*x^3+576*x^2+96*x)*exp(5+x))*log(x)^2+((-96*x+192)*exp(5+x)*log(2-x)+(-288*x^
2+576*x)*exp(5+x)-4608*x^2+6912*x+4608)*log(x)-4608*x+9216)/(x^3-2*x^2)/exp(5+x)^2/log(x)^3,x, algorithm="maxi
ma")

[Out]

(9*x^2*e^10*log(x)^2 + e^10*log(x)^2*log(-x + 2)^2 + 288*x*e^(-x + 5)*log(x) + 6*(x*e^10*log(x)^2 + 16*e^(-x +
5)*log(x))*log(-x + 2) + 2304*e^(-2*x))*e^(-10)/(x*log(x)^2)

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mupad [F]  time = 0.00, size = -1, normalized size = -0.03 $$\begin{array}{c}\int -\frac{{\mathrm{e}}^{-2x-10}((-{\mathrm{e}}^{2x+10}(x-2){\ln (2-x)}^2+2x{\mathrm{e}}^{2x+10}\ln (2-x)-{\mathrm{e}}^{2x+10}(12x^2-9x^3)){\ln (x)}^3+({\mathrm{e}}^{x+5}(-288x^3+576x^2+96x)+{\mathrm{e}}^{x+5}\ln (2-x)(-96x^2+96x+192)){\ln (x)}^2+(6912x+{\mathrm{e}}^{x+5}(576x-288x^2)-4608x^2-{\mathrm{e}}^{x+5}\ln (2-x)(96x-192)+4608)\ln (x)-4608x+9216)}{{\ln (x)}^3(2x^2-x^3)}dx\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(exp(- 2*x - 10)*(log(x)*(6912*x + exp(x + 5)*(576*x - 288*x^2) - 4608*x^2 - exp(x + 5)*log(2 - x)*(96*x
- 192) + 4608) - 4608*x - log(x)^3*(exp(2*x + 10)*(12*x^2 - 9*x^3) - 2*x*exp(2*x + 10)*log(2 - x) + exp(2*x +
10)*log(2 - x)^2*(x - 2)) + log(x)^2*(exp(x + 5)*(96*x + 576*x^2 - 288*x^3) + exp(x + 5)*log(2 - x)*(96*x - 96
*x^2 + 192)) + 9216))/(log(x)^3*(2*x^2 - x^3)),x)

[Out]

int(-(exp(- 2*x - 10)*(log(x)*(6912*x + exp(x + 5)*(576*x - 288*x^2) - 4608*x^2 - exp(x + 5)*log(2 - x)*(96*x
- 192) + 4608) - 4608*x - log(x)^3*(exp(2*x + 10)*(12*x^2 - 9*x^3) - 2*x*exp(2*x + 10)*log(2 - x) + exp(2*x +
10)*log(2 - x)^2*(x - 2)) + log(x)^2*(exp(x + 5)*(96*x + 576*x^2 - 288*x^3) + exp(x + 5)*log(2 - x)*(96*x - 96
*x^2 + 192)) + 9216))/(log(x)^3*(2*x^2 - x^3)), x)

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sympy [B]  time = 0.71, size = 71, normalized size = 2.37 $$\begin{array}{c}9x+6\log (x-2)+\frac{\log {(2-x)}^2}{x}+\frac{2304x{e}^{-2x-10}\log (x)+(288x^2\log {(x)}^2+96x\log {(x)}^2\log (2-x))e^{-x-5}}{x^2\log {(x)}^3}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((2-x)*exp(5+x)**2*ln(2-x)**2+2*x*exp(5+x)**2*ln(2-x)+(9*x**3-12*x**2)*exp(5+x)**2)*ln(x)**3+((-96*
x**2+96*x+192)*exp(5+x)*ln(2-x)+(-288*x**3+576*x**2+96*x)*exp(5+x))*ln(x)**2+((-96*x+192)*exp(5+x)*ln(2-x)+(-2
88*x**2+576*x)*exp(5+x)-4608*x**2+6912*x+4608)*ln(x)-4608*x+9216)/(x**3-2*x**2)/exp(5+x)**2/ln(x)**3,x)

[Out]

9*x + 6*log(x - 2) + log(2 - x)**2/x + (2304*x*exp(-2*x - 10)*log(x) + (288*x**2*log(x)**2 + 96*x*log(x)**2*lo
g(2 - x))*exp(-x - 5))/(x**2*log(x)**3)

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