3.12.33 \(\int \frac {-41 x^2+40 x^3+e^x (41 x-32 x^2-8 x^3)+(50 x-58 x^2+e^x (-50+40 x+18 x^2)) \log (x)+(10 x-10 e^x x) \log ^2(x)+(-18 x^2+18 x^3+e^x (18 x-16 x^2-2 x^3)+(20 x-22 x^2+e^x (-20+18 x+4 x^2)) \log (x)+(2 x-2 e^x x) \log ^2(x)) \log (-e^x+x)+(-2 x^2+2 x^3+e^x (2 x-2 x^2)+(2 x-2 x^2+e^x (-2+2 x)) \log (x)) \log ^2(-e^x+x)}{e^x x-x^2} \, dx\)

Optimal. Leaf size=26 \[ 1+x-\left (x+(-x+\log (x)) \left (5+\log \left (-e^x+x\right )\right )\right )^2 \]

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Rubi [F]  time = 11.89, 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 {gather*} \int \frac {-41 x^2+40 x^3+e^x \left (41 x-32 x^2-8 x^3\right )+\left (50 x-58 x^2+e^x \left (-50+40 x+18 x^2\right )\right ) \log (x)+\left (10 x-10 e^x x\right ) \log ^2(x)+\left (-18 x^2+18 x^3+e^x \left (18 x-16 x^2-2 x^3\right )+\left (20 x-22 x^2+e^x \left (-20+18 x+4 x^2\right )\right ) \log (x)+\left (2 x-2 e^x x\right ) \log ^2(x)\right ) \log \left (-e^x+x\right )+\left (-2 x^2+2 x^3+e^x \left (2 x-2 x^2\right )+\left (2 x-2 x^2+e^x (-2+2 x)\right ) \log (x)\right ) \log ^2\left (-e^x+x\right )}{e^x x-x^2} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-41*x^2 + 40*x^3 + E^x*(41*x - 32*x^2 - 8*x^3) + (50*x - 58*x^2 + E^x*(-50 + 40*x + 18*x^2))*Log[x] + (10
*x - 10*E^x*x)*Log[x]^2 + (-18*x^2 + 18*x^3 + E^x*(18*x - 16*x^2 - 2*x^3) + (20*x - 22*x^2 + E^x*(-20 + 18*x +
4*x^2))*Log[x] + (2*x - 2*E^x*x)*Log[x]^2)*Log[-E^x + x] + (-2*x^2 + 2*x^3 + E^x*(2*x - 2*x^2) + (2*x - 2*x^2
+ E^x*(-2 + 2*x))*Log[x])*Log[-E^x + x]^2)/(E^x*x - x^2),x]

[Out]

-19*x - 16*x^2 + (5*x^3)/9 + x^4/6 + 60*x*Log[x] - (2*x^3*Log[x])/3 - 25*Log[x]^2 - 10*x*Log[x]^2 - 9*x^2*Log[
-E^x + x] - (2*x^3*Log[-E^x + x])/3 + 18*x*Log[x]*Log[-E^x + x] + 2*x^2*Log[x]*Log[-E^x + x] - 4*Log[x]*Log[-E
^x + x]*Defer[Int][x/(E^x - x), x] - Defer[Int][x^2/(E^x - x), x] + 2*Log[x]*Defer[Int][x^2/(E^x - x), x] + 2*
Log[-E^x + x]*Defer[Int][x^2/(E^x - x), x] + 4*Log[x]*Log[-E^x + x]*Defer[Int][x^2/(E^x - x), x] + Defer[Int][
x^3/(E^x - x), x]/3 - 2*Log[x]*Defer[Int][x^3/(E^x - x), x] - 2*Log[-E^x + x]*Defer[Int][x^3/(E^x - x), x] + (
2*Defer[Int][x^4/(E^x - x), x])/3 + 10*Defer[Int][Log[x]^2/(E^x - x), x] - 10*Defer[Int][(x*Log[x]^2)/(E^x - x
), x] - 20*Defer[Int][(Log[x]*Log[-E^x + x])/x, x] - 2*Defer[Int][Log[x]^2*Log[-E^x + x], x] + 2*Defer[Int][(L
og[x]^2*Log[-E^x + x])/(E^x - x), x] - 2*Defer[Int][(x*Log[x]^2*Log[-E^x + x])/(E^x - x), x] + 2*Defer[Int][Lo
g[-E^x + x]^2, x] - 2*Defer[Int][x*Log[-E^x + x]^2, x] + 2*Defer[Int][Log[x]*Log[-E^x + x]^2, x] - 2*Defer[Int
][(Log[x]*Log[-E^x + x]^2)/x, x] + 4*Log[x]*Defer[Int][Defer[Int][x/(E^x - x), x], x] - 4*Log[x]*Defer[Int][De
fer[Int][x/(E^x - x), x]/(E^x - x), x] + 4*Log[-E^x + x]*Defer[Int][Defer[Int][x/(E^x - x), x]/x, x] + 4*Log[x
]*Defer[Int][(x*Defer[Int][x/(E^x - x), x])/(E^x - x), x] - 2*Defer[Int][Defer[Int][x^2/(E^x - x), x], x] - 4*
Log[x]*Defer[Int][Defer[Int][x^2/(E^x - x), x], x] + 2*Defer[Int][Defer[Int][x^2/(E^x - x), x]/(E^x - x), x] +
4*Log[x]*Defer[Int][Defer[Int][x^2/(E^x - x), x]/(E^x - x), x] - 2*Defer[Int][Defer[Int][x^2/(E^x - x), x]/x,
x] - 4*Log[-E^x + x]*Defer[Int][Defer[Int][x^2/(E^x - x), x]/x, x] - 2*Defer[Int][(x*Defer[Int][x^2/(E^x - x)
, x])/(E^x - x), x] - 4*Log[x]*Defer[Int][(x*Defer[Int][x^2/(E^x - x), x])/(E^x - x), x] + 2*Defer[Int][Defer[
Int][x^3/(E^x - x), x], x] - 2*Defer[Int][Defer[Int][x^3/(E^x - x), x]/(E^x - x), x] + 2*Defer[Int][Defer[Int]
[x^3/(E^x - x), x]/x, x] + 2*Defer[Int][(x*Defer[Int][x^3/(E^x - x), x])/(E^x - x), x] - 4*Defer[Int][Defer[In
t][Defer[Int][x/(E^x - x), x], x]/x, x] + 4*Defer[Int][Defer[Int][Defer[Int][x/(E^x - x), x]/(E^x - x), x]/x,
x] - 4*Defer[Int][Defer[Int][Defer[Int][x/(E^x - x), x]/x, x], x] + 4*Defer[Int][Defer[Int][Defer[Int][x/(E^x
- x), x]/x, x]/(E^x - x), x] - 4*Defer[Int][(x*Defer[Int][Defer[Int][x/(E^x - x), x]/x, x])/(E^x - x), x] - 4*
Defer[Int][Defer[Int][(x*Defer[Int][x/(E^x - x), x])/(E^x - x), x]/x, x] + 4*Defer[Int][Defer[Int][Defer[Int][
x^2/(E^x - x), x], x]/x, x] - 4*Defer[Int][Defer[Int][Defer[Int][x^2/(E^x - x), x]/(E^x - x), x]/x, x] + 4*Def
er[Int][Defer[Int][Defer[Int][x^2/(E^x - x), x]/x, x], x] - 4*Defer[Int][Defer[Int][Defer[Int][x^2/(E^x - x),
x]/x, x]/(E^x - x), x] + 4*Defer[Int][(x*Defer[Int][Defer[Int][x^2/(E^x - x), x]/x, x])/(E^x - x), x] + 4*Defe
r[Int][Defer[Int][(x*Defer[Int][x^2/(E^x - x), x])/(E^x - x), x]/x, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-\frac {2 (-1+x) (x-\log (x)) \left (4 x-5 \log (x)+x \log \left (-e^x+x\right )-\log (x) \log \left (-e^x+x\right )\right )}{e^x-x}+\frac {41 x-32 x^2-8 x^3-50 \log (x)+40 x \log (x)+18 x^2 \log (x)-10 x \log ^2(x)+18 x \log \left (-e^x+x\right )-16 x^2 \log \left (-e^x+x\right )-2 x^3 \log \left (-e^x+x\right )-20 \log (x) \log \left (-e^x+x\right )+18 x \log (x) \log \left (-e^x+x\right )+4 x^2 \log (x) \log \left (-e^x+x\right )-2 x \log ^2(x) \log \left (-e^x+x\right )+2 x \log ^2\left (-e^x+x\right )-2 x^2 \log ^2\left (-e^x+x\right )-2 \log (x) \log ^2\left (-e^x+x\right )+2 x \log (x) \log ^2\left (-e^x+x\right )}{x}\right ) \, dx\\ &=-\left (2 \int \frac {(-1+x) (x-\log (x)) \left (4 x-5 \log (x)+x \log \left (-e^x+x\right )-\log (x) \log \left (-e^x+x\right )\right )}{e^x-x} \, dx\right )+\int \frac {41 x-32 x^2-8 x^3-50 \log (x)+40 x \log (x)+18 x^2 \log (x)-10 x \log ^2(x)+18 x \log \left (-e^x+x\right )-16 x^2 \log \left (-e^x+x\right )-2 x^3 \log \left (-e^x+x\right )-20 \log (x) \log \left (-e^x+x\right )+18 x \log (x) \log \left (-e^x+x\right )+4 x^2 \log (x) \log \left (-e^x+x\right )-2 x \log ^2(x) \log \left (-e^x+x\right )+2 x \log ^2\left (-e^x+x\right )-2 x^2 \log ^2\left (-e^x+x\right )-2 \log (x) \log ^2\left (-e^x+x\right )+2 x \log (x) \log ^2\left (-e^x+x\right )}{x} \, dx\\ &=-\left (2 \int \left (-\frac {(x-\log (x)) \left (4 x-5 \log (x)+x \log \left (-e^x+x\right )-\log (x) \log \left (-e^x+x\right )\right )}{e^x-x}+\frac {x (x-\log (x)) \left (4 x-5 \log (x)+x \log \left (-e^x+x\right )-\log (x) \log \left (-e^x+x\right )\right )}{e^x-x}\right ) \, dx\right )+\int \left (\frac {41 x-32 x^2-8 x^3-50 \log (x)+40 x \log (x)+18 x^2 \log (x)-10 x \log ^2(x)}{x}-\frac {2 \left (-9 x+8 x^2+x^3+10 \log (x)-9 x \log (x)-2 x^2 \log (x)+x \log ^2(x)\right ) \log \left (-e^x+x\right )}{x}-\frac {2 (-1+x) (x-\log (x)) \log ^2\left (-e^x+x\right )}{x}\right ) \, dx\\ &=-\left (2 \int \frac {\left (-9 x+8 x^2+x^3+10 \log (x)-9 x \log (x)-2 x^2 \log (x)+x \log ^2(x)\right ) \log \left (-e^x+x\right )}{x} \, dx\right )-2 \int \frac {(-1+x) (x-\log (x)) \log ^2\left (-e^x+x\right )}{x} \, dx+2 \int \frac {(x-\log (x)) \left (4 x-5 \log (x)+x \log \left (-e^x+x\right )-\log (x) \log \left (-e^x+x\right )\right )}{e^x-x} \, dx-2 \int \frac {x (x-\log (x)) \left (4 x-5 \log (x)+x \log \left (-e^x+x\right )-\log (x) \log \left (-e^x+x\right )\right )}{e^x-x} \, dx+\int \frac {41 x-32 x^2-8 x^3-50 \log (x)+40 x \log (x)+18 x^2 \log (x)-10 x \log ^2(x)}{x} \, dx\\ &=-\left (2 \int \left (-9 \log \left (-e^x+x\right )+8 x \log \left (-e^x+x\right )+x^2 \log \left (-e^x+x\right )-9 \log (x) \log \left (-e^x+x\right )+\frac {10 \log (x) \log \left (-e^x+x\right )}{x}-2 x \log (x) \log \left (-e^x+x\right )+\log ^2(x) \log \left (-e^x+x\right )\right ) \, dx\right )+2 \int \left (\frac {4 x^2}{e^x-x}-\frac {9 x \log (x)}{e^x-x}+\frac {5 \log ^2(x)}{e^x-x}+\frac {x^2 \log \left (-e^x+x\right )}{e^x-x}-\frac {2 x \log (x) \log \left (-e^x+x\right )}{e^x-x}+\frac {\log ^2(x) \log \left (-e^x+x\right )}{e^x-x}\right ) \, dx-2 \int \left (\frac {4 x^3}{e^x-x}-\frac {9 x^2 \log (x)}{e^x-x}+\frac {5 x \log ^2(x)}{e^x-x}+\frac {x^3 \log \left (-e^x+x\right )}{e^x-x}-\frac {2 x^2 \log (x) \log \left (-e^x+x\right )}{e^x-x}+\frac {x \log ^2(x) \log \left (-e^x+x\right )}{e^x-x}\right ) \, dx-2 \int \left ((x-\log (x)) \log ^2\left (-e^x+x\right )-\frac {(x-\log (x)) \log ^2\left (-e^x+x\right )}{x}\right ) \, dx+\int \left (41-32 x-8 x^2+\frac {2 \left (-25+20 x+9 x^2\right ) \log (x)}{x}-10 \log ^2(x)\right ) \, dx\\ &=41 x-16 x^2-\frac {8 x^3}{3}+2 \int \frac {\left (-25+20 x+9 x^2\right ) \log (x)}{x} \, dx-2 \int x^2 \log \left (-e^x+x\right ) \, dx+2 \int \frac {x^2 \log \left (-e^x+x\right )}{e^x-x} \, dx-2 \int \frac {x^3 \log \left (-e^x+x\right )}{e^x-x} \, dx-2 \int \log ^2(x) \log \left (-e^x+x\right ) \, dx+2 \int \frac {\log ^2(x) \log \left (-e^x+x\right )}{e^x-x} \, dx-2 \int \frac {x \log ^2(x) \log \left (-e^x+x\right )}{e^x-x} \, dx-2 \int (x-\log (x)) \log ^2\left (-e^x+x\right ) \, dx+2 \int \frac {(x-\log (x)) \log ^2\left (-e^x+x\right )}{x} \, dx+4 \int x \log (x) \log \left (-e^x+x\right ) \, dx-4 \int \frac {x \log (x) \log \left (-e^x+x\right )}{e^x-x} \, dx+4 \int \frac {x^2 \log (x) \log \left (-e^x+x\right )}{e^x-x} \, dx+8 \int \frac {x^2}{e^x-x} \, dx-8 \int \frac {x^3}{e^x-x} \, dx-10 \int \log ^2(x) \, dx+10 \int \frac {\log ^2(x)}{e^x-x} \, dx-10 \int \frac {x \log ^2(x)}{e^x-x} \, dx-16 \int x \log \left (-e^x+x\right ) \, dx-18 \int \frac {x \log (x)}{e^x-x} \, dx+18 \int \frac {x^2 \log (x)}{e^x-x} \, dx+18 \int \log \left (-e^x+x\right ) \, dx+18 \int \log (x) \log \left (-e^x+x\right ) \, dx-20 \int \frac {\log (x) \log \left (-e^x+x\right )}{x} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [B]  time = 0.21, size = 65, normalized size = 2.50 \begin {gather*} x-16 x^2+40 x \log (x)-25 \log ^2(x)-2 \left (4 x^2-9 x \log (x)+5 \log ^2(x)\right ) \log \left (-e^x+x\right )-(x-\log (x))^2 \log ^2\left (-e^x+x\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-41*x^2 + 40*x^3 + E^x*(41*x - 32*x^2 - 8*x^3) + (50*x - 58*x^2 + E^x*(-50 + 40*x + 18*x^2))*Log[x]
+ (10*x - 10*E^x*x)*Log[x]^2 + (-18*x^2 + 18*x^3 + E^x*(18*x - 16*x^2 - 2*x^3) + (20*x - 22*x^2 + E^x*(-20 +
18*x + 4*x^2))*Log[x] + (2*x - 2*E^x*x)*Log[x]^2)*Log[-E^x + x] + (-2*x^2 + 2*x^3 + E^x*(2*x - 2*x^2) + (2*x -
2*x^2 + E^x*(-2 + 2*x))*Log[x])*Log[-E^x + x]^2)/(E^x*x - x^2),x]

[Out]

x - 16*x^2 + 40*x*Log[x] - 25*Log[x]^2 - 2*(4*x^2 - 9*x*Log[x] + 5*Log[x]^2)*Log[-E^x + x] - (x - Log[x])^2*Lo
g[-E^x + x]^2

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fricas [B]  time = 0.84, size = 68, normalized size = 2.62 \begin {gather*} -{\left (x^{2} - 2 \, x \log \relax (x) + \log \relax (x)^{2}\right )} \log \left (x - e^{x}\right )^{2} - 16 \, x^{2} - 2 \, {\left (4 \, x^{2} - 9 \, x \log \relax (x) + 5 \, \log \relax (x)^{2}\right )} \log \left (x - e^{x}\right ) + 40 \, x \log \relax (x) - 25 \, \log \relax (x)^{2} + x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((((2*x-2)*exp(x)-2*x^2+2*x)*log(x)+(-2*x^2+2*x)*exp(x)+2*x^3-2*x^2)*log(x-exp(x))^2+((-2*exp(x)*x+2
*x)*log(x)^2+((4*x^2+18*x-20)*exp(x)-22*x^2+20*x)*log(x)+(-2*x^3-16*x^2+18*x)*exp(x)+18*x^3-18*x^2)*log(x-exp(
x))+(-10*exp(x)*x+10*x)*log(x)^2+((18*x^2+40*x-50)*exp(x)-58*x^2+50*x)*log(x)+(-8*x^3-32*x^2+41*x)*exp(x)+40*x
^3-41*x^2)/(exp(x)*x-x^2),x, algorithm="fricas")

[Out]

-(x^2 - 2*x*log(x) + log(x)^2)*log(x - e^x)^2 - 16*x^2 - 2*(4*x^2 - 9*x*log(x) + 5*log(x)^2)*log(x - e^x) + 40
*x*log(x) - 25*log(x)^2 + x

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giac [B]  time = 0.55, size = 98, normalized size = 3.77 \begin {gather*} -x^{2} \log \left (x - e^{x}\right )^{2} + 2 \, x \log \left (x - e^{x}\right )^{2} \log \relax (x) - \log \left (x - e^{x}\right )^{2} \log \relax (x)^{2} - 8 \, x^{2} \log \left (x - e^{x}\right ) + 18 \, x \log \left (x - e^{x}\right ) \log \relax (x) - 10 \, \log \left (x - e^{x}\right ) \log \relax (x)^{2} - 16 \, x^{2} + 40 \, x \log \relax (x) - 25 \, \log \relax (x)^{2} + x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((((2*x-2)*exp(x)-2*x^2+2*x)*log(x)+(-2*x^2+2*x)*exp(x)+2*x^3-2*x^2)*log(x-exp(x))^2+((-2*exp(x)*x+2
*x)*log(x)^2+((4*x^2+18*x-20)*exp(x)-22*x^2+20*x)*log(x)+(-2*x^3-16*x^2+18*x)*exp(x)+18*x^3-18*x^2)*log(x-exp(
x))+(-10*exp(x)*x+10*x)*log(x)^2+((18*x^2+40*x-50)*exp(x)-58*x^2+50*x)*log(x)+(-8*x^3-32*x^2+41*x)*exp(x)+40*x
^3-41*x^2)/(exp(x)*x-x^2),x, algorithm="giac")

[Out]

-x^2*log(x - e^x)^2 + 2*x*log(x - e^x)^2*log(x) - log(x - e^x)^2*log(x)^2 - 8*x^2*log(x - e^x) + 18*x*log(x -
e^x)*log(x) - 10*log(x - e^x)*log(x)^2 - 16*x^2 + 40*x*log(x) - 25*log(x)^2 + x

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maple [B]  time = 0.04, size = 71, normalized size = 2.73

method	result	size
risch	\(\left (-x^{2}+2 x \ln \relax (x )-\ln \relax (x )^{2}\right ) \ln \left (x -{\mathrm e}^{x}\right )^{2}+\left (-8 x^{2}+18 x \ln \relax (x )-10 \ln \relax (x )^{2}\right ) \ln \left (x -{\mathrm e}^{x}\right )-16 x^{2}+40 x \ln \relax (x )-25 \ln \relax (x )^{2}+x\)	\(71\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((((2*x-2)*exp(x)-2*x^2+2*x)*ln(x)+(-2*x^2+2*x)*exp(x)+2*x^3-2*x^2)*ln(x-exp(x))^2+((-2*exp(x)*x+2*x)*ln(x
)^2+((4*x^2+18*x-20)*exp(x)-22*x^2+20*x)*ln(x)+(-2*x^3-16*x^2+18*x)*exp(x)+18*x^3-18*x^2)*ln(x-exp(x))+(-10*ex
p(x)*x+10*x)*ln(x)^2+((18*x^2+40*x-50)*exp(x)-58*x^2+50*x)*ln(x)+(-8*x^3-32*x^2+41*x)*exp(x)+40*x^3-41*x^2)/(e
xp(x)*x-x^2),x,method=_RETURNVERBOSE)

[Out]

(-x^2+2*x*ln(x)-ln(x)^2)*ln(x-exp(x))^2+(-8*x^2+18*x*ln(x)-10*ln(x)^2)*ln(x-exp(x))-16*x^2+40*x*ln(x)-25*ln(x)
^2+x

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maxima [B]  time = 0.51, size = 68, normalized size = 2.62 \begin {gather*} -{\left (x^{2} - 2 \, x \log \relax (x) + \log \relax (x)^{2}\right )} \log \left (x - e^{x}\right )^{2} - 16 \, x^{2} - 2 \, {\left (4 \, x^{2} - 9 \, x \log \relax (x) + 5 \, \log \relax (x)^{2}\right )} \log \left (x - e^{x}\right ) + 40 \, x \log \relax (x) - 25 \, \log \relax (x)^{2} + x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((((2*x-2)*exp(x)-2*x^2+2*x)*log(x)+(-2*x^2+2*x)*exp(x)+2*x^3-2*x^2)*log(x-exp(x))^2+((-2*exp(x)*x+2
*x)*log(x)^2+((4*x^2+18*x-20)*exp(x)-22*x^2+20*x)*log(x)+(-2*x^3-16*x^2+18*x)*exp(x)+18*x^3-18*x^2)*log(x-exp(
x))+(-10*exp(x)*x+10*x)*log(x)^2+((18*x^2+40*x-50)*exp(x)-58*x^2+50*x)*log(x)+(-8*x^3-32*x^2+41*x)*exp(x)+40*x
^3-41*x^2)/(exp(x)*x-x^2),x, algorithm="maxima")

[Out]

-(x^2 - 2*x*log(x) + log(x)^2)*log(x - e^x)^2 - 16*x^2 - 2*(4*x^2 - 9*x*log(x) + 5*log(x)^2)*log(x - e^x) + 40
*x*log(x) - 25*log(x)^2 + x

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mupad [B]  time = 1.20, size = 98, normalized size = 3.77 \begin {gather*} x-25\,{\ln \relax (x)}^2-\ln \left (x-{\mathrm {e}}^x\right )\,\left (18\,x-\frac {18\,x^2-8\,x^3}{x}+10\,{\ln \relax (x)}^2-18\,x\,\ln \relax (x)\right )-{\ln \left (x-{\mathrm {e}}^x\right )}^2\,\left (2\,x-\frac {2\,x^2-x^3}{x}+{\ln \relax (x)}^2-2\,x\,\ln \relax (x)\right )+40\,x\,\ln \relax (x)-16\,x^2 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((log(x)*(50*x + exp(x)*(40*x + 18*x^2 - 50) - 58*x^2) + log(x - exp(x))*(log(x)*(20*x + exp(x)*(18*x + 4*x
^2 - 20) - 22*x^2) + log(x)^2*(2*x - 2*x*exp(x)) - 18*x^2 + 18*x^3 - exp(x)*(16*x^2 - 18*x + 2*x^3)) + log(x)^
2*(10*x - 10*x*exp(x)) - 41*x^2 + 40*x^3 + log(x - exp(x))^2*(log(x)*(2*x + exp(x)*(2*x - 2) - 2*x^2) + exp(x)
*(2*x - 2*x^2) - 2*x^2 + 2*x^3) - exp(x)*(32*x^2 - 41*x + 8*x^3))/(x*exp(x) - x^2),x)

[Out]

x - 25*log(x)^2 - log(x - exp(x))*(18*x - (18*x^2 - 8*x^3)/x + 10*log(x)^2 - 18*x*log(x)) - log(x - exp(x))^2*
(2*x - (2*x^2 - x^3)/x + log(x)^2 - 2*x*log(x)) + 40*x*log(x) - 16*x^2

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sympy [B]  time = 0.82, size = 68, normalized size = 2.62 \begin {gather*} - 16 x^{2} + 40 x \log {\relax (x )} + x + \left (- 8 x^{2} + 18 x \log {\relax (x )} - 10 \log {\relax (x )}^{2}\right ) \log {\left (x - e^{x} \right )} + \left (- x^{2} + 2 x \log {\relax (x )} - \log {\relax (x )}^{2}\right ) \log {\left (x - e^{x} \right )}^{2} - 25 \log {\relax (x )}^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((((2*x-2)*exp(x)-2*x**2+2*x)*ln(x)+(-2*x**2+2*x)*exp(x)+2*x**3-2*x**2)*ln(x-exp(x))**2+((-2*exp(x)*
x+2*x)*ln(x)**2+((4*x**2+18*x-20)*exp(x)-22*x**2+20*x)*ln(x)+(-2*x**3-16*x**2+18*x)*exp(x)+18*x**3-18*x**2)*ln
(x-exp(x))+(-10*exp(x)*x+10*x)*ln(x)**2+((18*x**2+40*x-50)*exp(x)-58*x**2+50*x)*ln(x)+(-8*x**3-32*x**2+41*x)*e
xp(x)+40*x**3-41*x**2)/(exp(x)*x-x**2),x)

[Out]

-16*x**2 + 40*x*log(x) + x + (-8*x**2 + 18*x*log(x) - 10*log(x)**2)*log(x - exp(x)) + (-x**2 + 2*x*log(x) - lo
g(x)**2)*log(x - exp(x))**2 - 25*log(x)**2

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