\(\int \frac {e^{e^{5-x}} (4 e^5-4 e^{5-x} x)+e^{e^{5-x}} (-2+2 e^x) \log (e^x-x)+e^{e^{5-x}} (-e^5+e^{5-x} x) \log ^2(e^x-x)}{e^x-x} \, dx\) [7663]

Optimal result

Integrand size = 97, antiderivative size = 22 \[ \int \frac {e^{e^{5-x}} \left (4 e^5-4 e^{5-x} x\right )+e^{e^{5-x}} \left (-2+2 e^x\right ) \log \left (e^x-x\right )+e^{e^{5-x}} \left (-e^5+e^{5-x} x\right ) \log ^2\left (e^x-x\right )}{e^x-x} \, dx=e^{e^{5-x}} \left (-4+\log ^2\left (e^x-x\right )\right ) \]

[Out]

exp(exp(5-x))*(ln(exp(x)-x)^2-4)

Rubi [F]

\[ \int \frac {e^{e^{5-x}} \left (4 e^5-4 e^{5-x} x\right )+e^{e^{5-x}} \left (-2+2 e^x\right ) \log \left (e^x-x\right )+e^{e^{5-x}} \left (-e^5+e^{5-x} x\right ) \log ^2\left (e^x-x\right )}{e^x-x} \, dx=\int \frac {e^{e^{5-x}} \left (4 e^5-4 e^{5-x} x\right )+e^{e^{5-x}} \left (-2+2 e^x\right ) \log \left (e^x-x\right )+e^{e^{5-x}} \left (-e^5+e^{5-x} x\right ) \log ^2\left (e^x-x\right )}{e^x-x} \, dx \]

[In]

Int[(E^E^(5 - x)*(4*E^5 - 4*E^(5 - x)*x) + E^E^(5 - x)*(-2 + 2*E^x)*Log[E^x - x] + E^E^(5 - x)*(-E^5 + E^(5 -
x)*x)*Log[E^x - x]^2)/(E^x - x),x]

[Out]

-4*E^E^(5 - x) + 2*EulerGamma*x + (2*ExpIntegralEi[E^(5 - x)])/E^5 - 2*E^(5 - x)*HypergeometricPFQ[{1, 1, 1},
{2, 2, 2}, E^(5 - x)] - Log[-E^(5 - x)]^2 - 2*(ExpIntegralE[1, -E^(5 - x)] + ExpIntegralEi[E^(5 - x)])*Log[E^(
5 - x)] + 2*E^(-5 + E^(5 - x))*Log[E^x - x] - 2*ExpIntegralEi[E^(5 - x)]*Log[E^x - x] + 2*Defer[Int][E^(-5 + E
^(5 - x))/(E^x - x), x] + 2*Log[E^x - x]*Defer[Int][E^(E^(5 - x) - x)*x, x] - 2*Defer[Int][(E^(-5 + E^(5 - x))
*x)/(E^x - x), x] - 2*Log[E^x - x]*Defer[Int][(E^(E^(5 - x) - x)*x)/(E^x - x), x] + 2*Log[E^x - x]*Defer[Int][
(E^(E^(5 - x) - x)*x^2)/(E^x - x), x] - 2*Defer[Int][ExpIntegralEi[E^(5 - x)]/(E^x - x), x] + 2*Defer[Int][(x*
ExpIntegralEi[E^(5 - x)])/(E^x - x), x] - Defer[Int][E^(5 + E^(5 - x) - x)*Log[E^x - x]^2, x] - 2*Defer[Int][D
efer[Int][E^(E^(5 - x) - x)*x, x], x] + 2*Defer[Int][Defer[Int][E^(E^(5 - x) - x)*x, x]/(E^x - x), x] - 2*Defe
r[Int][(x*Defer[Int][E^(E^(5 - x) - x)*x, x])/(E^x - x), x] + 2*Defer[Int][Defer[Int][(E^(E^(5 - x) - x)*x)/(E
^x - x), x], x] - 2*Defer[Int][Defer[Int][(E^(E^(5 - x) - x)*x)/(E^x - x), x]/(E^x - x), x] + 2*Defer[Int][(x*
Defer[Int][(E^(E^(5 - x) - x)*x)/(E^x - x), x])/(E^x - x), x] - 2*Defer[Int][Defer[Int][(E^(E^(5 - x) - x)*x^2
)/(E^x - x), x], x] + 2*Defer[Int][Defer[Int][(E^(E^(5 - x) - x)*x^2)/(E^x - x), x]/(E^x - x), x] - 2*Defer[In
t][(x*Defer[Int][(E^(E^(5 - x) - x)*x^2)/(E^x - x), x])/(E^x - x), x]

Rubi steps \begin{align*} \text {integral}& = \int \frac {e^{e^{5-x}-x} \left (4 e^{5+x}-4 e^5 x-2 e^x \log \left (e^x-x\right )+2 e^{2 x} \log \left (e^x-x\right )-e^{5+x} \log ^2\left (e^x-x\right )+e^5 x \log ^2\left (e^x-x\right )\right )}{e^x-x} \, dx \\ & = \int \frac {e^{e^{5-x}-x} \left (4 e^5 \left (e^x-x\right )+2 e^x \left (-1+e^x\right ) \log \left (e^x-x\right )-e^5 \left (e^x-x\right ) \log ^2\left (e^x-x\right )\right )}{e^x-x} \, dx \\ & = \int \left (4 e^{5+e^{5-x}-x}+2 e^{e^{5-x}} \log \left (e^x-x\right )-2 e^{e^{5-x}-x} \log \left (e^x-x\right )+2 e^{e^{5-x}-x} x \log \left (e^x-x\right )+\frac {2 e^{e^{5-x}-x} (-1+x) x \log \left (e^x-x\right )}{e^x-x}-e^{5+e^{5-x}-x} \log ^2\left (e^x-x\right )\right ) \, dx \\ & = 2 \int e^{e^{5-x}} \log \left (e^x-x\right ) \, dx-2 \int e^{e^{5-x}-x} \log \left (e^x-x\right ) \, dx+2 \int e^{e^{5-x}-x} x \log \left (e^x-x\right ) \, dx+2 \int \frac {e^{e^{5-x}-x} (-1+x) x \log \left (e^x-x\right )}{e^x-x} \, dx+4 \int e^{5+e^{5-x}-x} \, dx-\int e^{5+e^{5-x}-x} \log ^2\left (e^x-x\right ) \, dx \\ & = 2 e^{-5+e^{5-x}} \log \left (e^x-x\right )-2 \operatorname {ExpIntegralEi}\left (e^{5-x}\right ) \log \left (e^x-x\right )-2 \int \frac {e^{-5+e^{5-x}} \left (-1+e^x\right )}{e^x-x} \, dx+2 \int \frac {\left (-1+e^x\right ) \operatorname {ExpIntegralEi}\left (e^{5-x}\right )}{e^x-x} \, dx-2 \int \frac {\left (-1+e^x\right ) \int e^{e^{5-x}-x} x \, dx}{e^x-x} \, dx-2 \int \frac {\left (-1+e^x\right ) \left (-\int \frac {e^{e^{5-x}-x} x}{e^x-x} \, dx+\int \frac {e^{e^{5-x}-x} x^2}{e^x-x} \, dx\right )}{e^x-x} \, dx-4 \text {Subst}\left (\int e^{5+e^5 x} \, dx,x,e^{-x}\right )+\left (2 \log \left (e^x-x\right )\right ) \int e^{e^{5-x}-x} x \, dx-\left (2 \log \left (e^x-x\right )\right ) \int \frac {e^{e^{5-x}-x} x}{e^x-x} \, dx+\left (2 \log \left (e^x-x\right )\right ) \int \frac {e^{e^{5-x}-x} x^2}{e^x-x} \, dx-\int e^{5+e^{5-x}-x} \log ^2\left (e^x-x\right ) \, dx \\ & = -4 e^{e^{5-x}}+2 e^{-5+e^{5-x}} \log \left (e^x-x\right )-2 \operatorname {ExpIntegralEi}\left (e^{5-x}\right ) \log \left (e^x-x\right )-2 \int \left (e^{-5+e^{5-x}}+\frac {e^{-5+e^{5-x}} (-1+x)}{e^x-x}\right ) \, dx+2 \int \left (\operatorname {ExpIntegralEi}\left (e^{5-x}\right )+\frac {(-1+x) \operatorname {ExpIntegralEi}\left (e^{5-x}\right )}{e^x-x}\right ) \, dx-2 \int \left (\int e^{e^{5-x}-x} x \, dx+\frac {(-1+x) \int e^{e^{5-x}-x} x \, dx}{e^x-x}\right ) \, dx-2 \int \left (-\int \frac {e^{e^{5-x}-x} x}{e^x-x} \, dx-\frac {(-1+x) \left (\int \frac {e^{e^{5-x}-x} x}{e^x-x} \, dx-\int \frac {e^{e^{5-x}-x} x^2}{e^x-x} \, dx\right )}{e^x-x}+\int \frac {e^{e^{5-x}-x} x^2}{e^x-x} \, dx\right ) \, dx+\left (2 \log \left (e^x-x\right )\right ) \int e^{e^{5-x}-x} x \, dx-\left (2 \log \left (e^x-x\right )\right ) \int \frac {e^{e^{5-x}-x} x}{e^x-x} \, dx+\left (2 \log \left (e^x-x\right )\right ) \int \frac {e^{e^{5-x}-x} x^2}{e^x-x} \, dx-\int e^{5+e^{5-x}-x} \log ^2\left (e^x-x\right ) \, dx \\ & = -4 e^{e^{5-x}}+2 e^{-5+e^{5-x}} \log \left (e^x-x\right )-2 \operatorname {ExpIntegralEi}\left (e^{5-x}\right ) \log \left (e^x-x\right )-2 \int e^{-5+e^{5-x}} \, dx-2 \int \frac {e^{-5+e^{5-x}} (-1+x)}{e^x-x} \, dx+2 \int \operatorname {ExpIntegralEi}\left (e^{5-x}\right ) \, dx+2 \int \frac {(-1+x) \operatorname {ExpIntegralEi}\left (e^{5-x}\right )}{e^x-x} \, dx-2 \int \left (\int e^{e^{5-x}-x} x \, dx\right ) \, dx-2 \int \frac {(-1+x) \int e^{e^{5-x}-x} x \, dx}{e^x-x} \, dx+2 \int \left (\int \frac {e^{e^{5-x}-x} x}{e^x-x} \, dx\right ) \, dx+2 \int \frac {(-1+x) \left (\int \frac {e^{e^{5-x}-x} x}{e^x-x} \, dx-\int \frac {e^{e^{5-x}-x} x^2}{e^x-x} \, dx\right )}{e^x-x} \, dx-2 \int \left (\int \frac {e^{e^{5-x}-x} x^2}{e^x-x} \, dx\right ) \, dx+\left (2 \log \left (e^x-x\right )\right ) \int e^{e^{5-x}-x} x \, dx-\left (2 \log \left (e^x-x\right )\right ) \int \frac {e^{e^{5-x}-x} x}{e^x-x} \, dx+\left (2 \log \left (e^x-x\right )\right ) \int \frac {e^{e^{5-x}-x} x^2}{e^x-x} \, dx-\int e^{5+e^{5-x}-x} \log ^2\left (e^x-x\right ) \, dx \\ & = -4 e^{e^{5-x}}+2 e^{-5+e^{5-x}} \log \left (e^x-x\right )-2 \operatorname {ExpIntegralEi}\left (e^{5-x}\right ) \log \left (e^x-x\right )-2 \int \left (-\frac {e^{-5+e^{5-x}}}{e^x-x}+\frac {e^{-5+e^{5-x}} x}{e^x-x}\right ) \, dx+2 \int \left (-\frac {\operatorname {ExpIntegralEi}\left (e^{5-x}\right )}{e^x-x}+\frac {x \operatorname {ExpIntegralEi}\left (e^{5-x}\right )}{e^x-x}\right ) \, dx-2 \int \left (\int e^{e^{5-x}-x} x \, dx\right ) \, dx-2 \int \left (-\frac {\int e^{e^{5-x}-x} x \, dx}{e^x-x}+\frac {x \int e^{e^{5-x}-x} x \, dx}{e^x-x}\right ) \, dx+2 \int \left (\int \frac {e^{e^{5-x}-x} x}{e^x-x} \, dx\right ) \, dx+2 \int \left (-\frac {\int \frac {e^{e^{5-x}-x} x}{e^x-x} \, dx-\int \frac {e^{e^{5-x}-x} x^2}{e^x-x} \, dx}{e^x-x}+\frac {x \left (\int \frac {e^{e^{5-x}-x} x}{e^x-x} \, dx-\int \frac {e^{e^{5-x}-x} x^2}{e^x-x} \, dx\right )}{e^x-x}\right ) \, dx-2 \int \left (\int \frac {e^{e^{5-x}-x} x^2}{e^x-x} \, dx\right ) \, dx+2 \text {Subst}\left (\int \frac {e^{-5+x}}{x} \, dx,x,e^{5-x}\right )-2 \text {Subst}\left (\int \frac {\operatorname {ExpIntegralEi}(x)}{x} \, dx,x,e^{5-x}\right )+\left (2 \log \left (e^x-x\right )\right ) \int e^{e^{5-x}-x} x \, dx-\left (2 \log \left (e^x-x\right )\right ) \int \frac {e^{e^{5-x}-x} x}{e^x-x} \, dx+\left (2 \log \left (e^x-x\right )\right ) \int \frac {e^{e^{5-x}-x} x^2}{e^x-x} \, dx-\int e^{5+e^{5-x}-x} \log ^2\left (e^x-x\right ) \, dx \\ & = -4 e^{e^{5-x}}+\frac {2 \operatorname {ExpIntegralEi}\left (e^{5-x}\right )}{e^5}-2 \left (\operatorname {ExpIntegralE}\left (1,-e^{5-x}\right )+\operatorname {ExpIntegralEi}\left (e^{5-x}\right )\right ) \log \left (e^{5-x}\right )+2 e^{-5+e^{5-x}} \log \left (e^x-x\right )-2 \operatorname {ExpIntegralEi}\left (e^{5-x}\right ) \log \left (e^x-x\right )+2 \int \frac {e^{-5+e^{5-x}}}{e^x-x} \, dx-2 \int \frac {e^{-5+e^{5-x}} x}{e^x-x} \, dx-2 \int \frac {\operatorname {ExpIntegralEi}\left (e^{5-x}\right )}{e^x-x} \, dx+2 \int \frac {x \operatorname {ExpIntegralEi}\left (e^{5-x}\right )}{e^x-x} \, dx-2 \int \left (\int e^{e^{5-x}-x} x \, dx\right ) \, dx+2 \int \frac {\int e^{e^{5-x}-x} x \, dx}{e^x-x} \, dx-2 \int \frac {x \int e^{e^{5-x}-x} x \, dx}{e^x-x} \, dx+2 \int \left (\int \frac {e^{e^{5-x}-x} x}{e^x-x} \, dx\right ) \, dx-2 \int \frac {\int \frac {e^{e^{5-x}-x} x}{e^x-x} \, dx-\int \frac {e^{e^{5-x}-x} x^2}{e^x-x} \, dx}{e^x-x} \, dx+2 \int \frac {x \left (\int \frac {e^{e^{5-x}-x} x}{e^x-x} \, dx-\int \frac {e^{e^{5-x}-x} x^2}{e^x-x} \, dx\right )}{e^x-x} \, dx-2 \int \left (\int \frac {e^{e^{5-x}-x} x^2}{e^x-x} \, dx\right ) \, dx+2 \text {Subst}\left (\int \frac {\operatorname {ExpIntegralE}(1,-x)}{x} \, dx,x,e^{5-x}\right )+\left (2 \log \left (e^x-x\right )\right ) \int e^{e^{5-x}-x} x \, dx-\left (2 \log \left (e^x-x\right )\right ) \int \frac {e^{e^{5-x}-x} x}{e^x-x} \, dx+\left (2 \log \left (e^x-x\right )\right ) \int \frac {e^{e^{5-x}-x} x^2}{e^x-x} \, dx-\int e^{5+e^{5-x}-x} \log ^2\left (e^x-x\right ) \, dx \\ & = -4 e^{e^{5-x}}+2 \gamma x+\frac {2 \operatorname {ExpIntegralEi}\left (e^{5-x}\right )}{e^5}-2 e^{5-x} \, _3F_3\left (1,1,1;2,2,2;e^{5-x}\right )-\log ^2\left (-e^{5-x}\right )-2 \left (\operatorname {ExpIntegralE}\left (1,-e^{5-x}\right )+\operatorname {ExpIntegralEi}\left (e^{5-x}\right )\right ) \log \left (e^{5-x}\right )+2 e^{-5+e^{5-x}} \log \left (e^x-x\right )-2 \operatorname {ExpIntegralEi}\left (e^{5-x}\right ) \log \left (e^x-x\right )+2 \int \frac {e^{-5+e^{5-x}}}{e^x-x} \, dx-2 \int \frac {e^{-5+e^{5-x}} x}{e^x-x} \, dx-2 \int \frac {\operatorname {ExpIntegralEi}\left (e^{5-x}\right )}{e^x-x} \, dx+2 \int \frac {x \operatorname {ExpIntegralEi}\left (e^{5-x}\right )}{e^x-x} \, dx-2 \int \left (\int e^{e^{5-x}-x} x \, dx\right ) \, dx+2 \int \frac {\int e^{e^{5-x}-x} x \, dx}{e^x-x} \, dx-2 \int \frac {x \int e^{e^{5-x}-x} x \, dx}{e^x-x} \, dx+2 \int \left (\int \frac {e^{e^{5-x}-x} x}{e^x-x} \, dx\right ) \, dx-2 \int \left (\int \frac {e^{e^{5-x}-x} x^2}{e^x-x} \, dx\right ) \, dx-2 \int \left (\frac {\int \frac {e^{e^{5-x}-x} x}{e^x-x} \, dx}{e^x-x}-\frac {\int \frac {e^{e^{5-x}-x} x^2}{e^x-x} \, dx}{e^x-x}\right ) \, dx+2 \int \left (\frac {x \int \frac {e^{e^{5-x}-x} x}{e^x-x} \, dx}{e^x-x}-\frac {x \int \frac {e^{e^{5-x}-x} x^2}{e^x-x} \, dx}{e^x-x}\right ) \, dx+\left (2 \log \left (e^x-x\right )\right ) \int e^{e^{5-x}-x} x \, dx-\left (2 \log \left (e^x-x\right )\right ) \int \frac {e^{e^{5-x}-x} x}{e^x-x} \, dx+\left (2 \log \left (e^x-x\right )\right ) \int \frac {e^{e^{5-x}-x} x^2}{e^x-x} \, dx-\int e^{5+e^{5-x}-x} \log ^2\left (e^x-x\right ) \, dx \\ & = -4 e^{e^{5-x}}+2 \gamma x+\frac {2 \operatorname {ExpIntegralEi}\left (e^{5-x}\right )}{e^5}-2 e^{5-x} \, _3F_3\left (1,1,1;2,2,2;e^{5-x}\right )-\log ^2\left (-e^{5-x}\right )-2 \left (\operatorname {ExpIntegralE}\left (1,-e^{5-x}\right )+\operatorname {ExpIntegralEi}\left (e^{5-x}\right )\right ) \log \left (e^{5-x}\right )+2 e^{-5+e^{5-x}} \log \left (e^x-x\right )-2 \operatorname {ExpIntegralEi}\left (e^{5-x}\right ) \log \left (e^x-x\right )+2 \int \frac {e^{-5+e^{5-x}}}{e^x-x} \, dx-2 \int \frac {e^{-5+e^{5-x}} x}{e^x-x} \, dx-2 \int \frac {\operatorname {ExpIntegralEi}\left (e^{5-x}\right )}{e^x-x} \, dx+2 \int \frac {x \operatorname {ExpIntegralEi}\left (e^{5-x}\right )}{e^x-x} \, dx-2 \int \left (\int e^{e^{5-x}-x} x \, dx\right ) \, dx+2 \int \frac {\int e^{e^{5-x}-x} x \, dx}{e^x-x} \, dx-2 \int \frac {x \int e^{e^{5-x}-x} x \, dx}{e^x-x} \, dx+2 \int \left (\int \frac {e^{e^{5-x}-x} x}{e^x-x} \, dx\right ) \, dx-2 \int \frac {\int \frac {e^{e^{5-x}-x} x}{e^x-x} \, dx}{e^x-x} \, dx+2 \int \frac {x \int \frac {e^{e^{5-x}-x} x}{e^x-x} \, dx}{e^x-x} \, dx-2 \int \left (\int \frac {e^{e^{5-x}-x} x^2}{e^x-x} \, dx\right ) \, dx+2 \int \frac {\int \frac {e^{e^{5-x}-x} x^2}{e^x-x} \, dx}{e^x-x} \, dx-2 \int \frac {x \int \frac {e^{e^{5-x}-x} x^2}{e^x-x} \, dx}{e^x-x} \, dx+\left (2 \log \left (e^x-x\right )\right ) \int e^{e^{5-x}-x} x \, dx-\left (2 \log \left (e^x-x\right )\right ) \int \frac {e^{e^{5-x}-x} x}{e^x-x} \, dx+\left (2 \log \left (e^x-x\right )\right ) \int \frac {e^{e^{5-x}-x} x^2}{e^x-x} \, dx-\int e^{5+e^{5-x}-x} \log ^2\left (e^x-x\right ) \, dx \\ \end{align*}

Mathematica [A] (verified)

Time = 2.00 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.00 \[ \int \frac {e^{e^{5-x}} \left (4 e^5-4 e^{5-x} x\right )+e^{e^{5-x}} \left (-2+2 e^x\right ) \log \left (e^x-x\right )+e^{e^{5-x}} \left (-e^5+e^{5-x} x\right ) \log ^2\left (e^x-x\right )}{e^x-x} \, dx=e^{e^{5-x}} \left (-4+\log ^2\left (e^x-x\right )\right ) \]

[In]

Integrate[(E^E^(5 - x)*(4*E^5 - 4*E^(5 - x)*x) + E^E^(5 - x)*(-2 + 2*E^x)*Log[E^x - x] + E^E^(5 - x)*(-E^5 + E
^(5 - x)*x)*Log[E^x - x]^2)/(E^x - x),x]

[Out]

E^E^(5 - x)*(-4 + Log[E^x - x]^2)

Maple [A] (verified)

Time = 0.58 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.27

method	result	size
risch	\({\mathrm e}^{{\mathrm e}^{5-x}} \ln \left ({\mathrm e}^{x}-x \right )^{2}-4 \,{\mathrm e}^{{\mathrm e}^{5-x}}\)	\(28\)
parallelrisch	\({\mathrm e}^{{\mathrm e}^{5-x}} \ln \left ({\mathrm e}^{x}-x \right )^{2}-4 \,{\mathrm e}^{{\mathrm e}^{5-x}}\)	\(28\)

[In]

int(((-exp(5-x)*exp(x)+x*exp(5-x))*exp(exp(5-x))*ln(exp(x)-x)^2+(2*exp(x)-2)*exp(exp(5-x))*ln(exp(x)-x)+(4*exp
(5-x)*exp(x)-4*x*exp(5-x))*exp(exp(5-x)))/(exp(x)-x),x,method=_RETURNVERBOSE)

[Out]

exp(exp(5-x))*ln(exp(x)-x)^2-4*exp(exp(5-x))

Fricas [A] (verification not implemented)

none

Time = 0.30 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.23 \[ \int \frac {e^{e^{5-x}} \left (4 e^5-4 e^{5-x} x\right )+e^{e^{5-x}} \left (-2+2 e^x\right ) \log \left (e^x-x\right )+e^{e^{5-x}} \left (-e^5+e^{5-x} x\right ) \log ^2\left (e^x-x\right )}{e^x-x} \, dx=e^{\left (e^{\left (-x + 5\right )}\right )} \log \left (-x + e^{x}\right )^{2} - 4 \, e^{\left (e^{\left (-x + 5\right )}\right )} \]

[In]

integrate(((-exp(5-x)*exp(x)+x*exp(5-x))*exp(exp(5-x))*log(exp(x)-x)^2+(2*exp(x)-2)*exp(exp(5-x))*log(exp(x)-x
)+(4*exp(5-x)*exp(x)-4*x*exp(5-x))*exp(exp(5-x)))/(exp(x)-x),x, algorithm="fricas")

[Out]

e^(e^(-x + 5))*log(-x + e^x)^2 - 4*e^(e^(-x + 5))

Sympy [F(-1)]

Timed out. \[ \int \frac {e^{e^{5-x}} \left (4 e^5-4 e^{5-x} x\right )+e^{e^{5-x}} \left (-2+2 e^x\right ) \log \left (e^x-x\right )+e^{e^{5-x}} \left (-e^5+e^{5-x} x\right ) \log ^2\left (e^x-x\right )}{e^x-x} \, dx=\text {Timed out} \]

[In]

integrate(((-exp(5-x)*exp(x)+x*exp(5-x))*exp(exp(5-x))*ln(exp(x)-x)**2+(2*exp(x)-2)*exp(exp(5-x))*ln(exp(x)-x)
+(4*exp(5-x)*exp(x)-4*x*exp(5-x))*exp(exp(5-x)))/(exp(x)-x),x)

[Out]

Timed out

Maxima [A] (verification not implemented)

none

Time = 0.27 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.86 \[ \int \frac {e^{e^{5-x}} \left (4 e^5-4 e^{5-x} x\right )+e^{e^{5-x}} \left (-2+2 e^x\right ) \log \left (e^x-x\right )+e^{e^{5-x}} \left (-e^5+e^{5-x} x\right ) \log ^2\left (e^x-x\right )}{e^x-x} \, dx={\left (\log \left (-x + e^{x}\right )^{2} - 4\right )} e^{\left (e^{\left (-x + 5\right )}\right )} \]

[In]

integrate(((-exp(5-x)*exp(x)+x*exp(5-x))*exp(exp(5-x))*log(exp(x)-x)^2+(2*exp(x)-2)*exp(exp(5-x))*log(exp(x)-x
)+(4*exp(5-x)*exp(x)-4*x*exp(5-x))*exp(exp(5-x)))/(exp(x)-x),x, algorithm="maxima")

[Out]

(log(-x + e^x)^2 - 4)*e^(e^(-x + 5))

Giac [F]

\[ \int \frac {e^{e^{5-x}} \left (4 e^5-4 e^{5-x} x\right )+e^{e^{5-x}} \left (-2+2 e^x\right ) \log \left (e^x-x\right )+e^{e^{5-x}} \left (-e^5+e^{5-x} x\right ) \log ^2\left (e^x-x\right )}{e^x-x} \, dx=\int { -\frac {{\left (x e^{\left (-x + 5\right )} - e^{5}\right )} e^{\left (e^{\left (-x + 5\right )}\right )} \log \left (-x + e^{x}\right )^{2} + 2 \, {\left (e^{x} - 1\right )} e^{\left (e^{\left (-x + 5\right )}\right )} \log \left (-x + e^{x}\right ) - 4 \, {\left (x e^{\left (-x + 5\right )} - e^{5}\right )} e^{\left (e^{\left (-x + 5\right )}\right )}}{x - e^{x}} \,d x } \]

[In]

integrate(((-exp(5-x)*exp(x)+x*exp(5-x))*exp(exp(5-x))*log(exp(x)-x)^2+(2*exp(x)-2)*exp(exp(5-x))*log(exp(x)-x
)+(4*exp(5-x)*exp(x)-4*x*exp(5-x))*exp(exp(5-x)))/(exp(x)-x),x, algorithm="giac")

[Out]

integrate(-((x*e^(-x + 5) - e^5)*e^(e^(-x + 5))*log(-x + e^x)^2 + 2*(e^x - 1)*e^(e^(-x + 5))*log(-x + e^x) - 4
*(x*e^(-x + 5) - e^5)*e^(e^(-x + 5)))/(x - e^x), x)

Mupad [F(-1)]

Timed out. \[ \int \frac {e^{e^{5-x}} \left (4 e^5-4 e^{5-x} x\right )+e^{e^{5-x}} \left (-2+2 e^x\right ) \log \left (e^x-x\right )+e^{e^{5-x}} \left (-e^5+e^{5-x} x\right ) \log ^2\left (e^x-x\right )}{e^x-x} \, dx=-\int \frac {-{\mathrm {e}}^{{\mathrm {e}}^{5-x}}\,\left ({\mathrm {e}}^5-x\,{\mathrm {e}}^{5-x}\right )\,{\ln \left ({\mathrm {e}}^x-x\right )}^2+{\mathrm {e}}^{{\mathrm {e}}^{5-x}}\,\left (2\,{\mathrm {e}}^x-2\right )\,\ln \left ({\mathrm {e}}^x-x\right )+{\mathrm {e}}^{{\mathrm {e}}^{5-x}}\,\left (4\,{\mathrm {e}}^5-4\,x\,{\mathrm {e}}^{5-x}\right )}{x-{\mathrm {e}}^x} \,d x \]

[In]

int(-(exp(exp(5 - x))*log(exp(x) - x)*(2*exp(x) - 2) - exp(exp(5 - x))*(4*x*exp(5 - x) - 4*exp(5 - x)*exp(x))
+ exp(exp(5 - x))*log(exp(x) - x)^2*(x*exp(5 - x) - exp(5 - x)*exp(x)))/(x - exp(x)),x)

[Out]

-int((exp(exp(5 - x))*(4*exp(5) - 4*x*exp(5 - x)) - exp(exp(5 - x))*log(exp(x) - x)^2*(exp(5) - x*exp(5 - x))
+ exp(exp(5 - x))*log(exp(x) - x)*(2*exp(x) - 2))/(x - exp(x)), x)