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

Optimal. Leaf size=22 \[ e^{e^{5-x}} \left (-4+\log ^2\left (e^x-x\right )\right ) \]

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Rubi [F]  time = 4.74, 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 {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 \end {gather*}

Verification is not applicable to the result.

[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 {gather*} \begin {aligned} \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 \text {Ei}\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 ) \text {Ei}\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 \operatorname {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 \text {Ei}\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 (\text {Ei}\left (e^{5-x}\right )+\frac {(-1+x) \text {Ei}\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 \text {Ei}\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 \text {Ei}\left (e^{5-x}\right ) \, dx+2 \int \frac {(-1+x) \text {Ei}\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 \text {Ei}\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 {\text {Ei}\left (e^{5-x}\right )}{e^x-x}+\frac {x \text {Ei}\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 \operatorname {Subst}\left (\int \frac {e^{-5+x}}{x} \, dx,x,e^{5-x}\right )-2 \operatorname {Subst}\left (\int \frac {\text {Ei}(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 \text {Ei}\left (e^{5-x}\right )}{e^5}-2 \left (E_1\left (-e^{5-x}\right )+\text {Ei}\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 \text {Ei}\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 {\text {Ei}\left (e^{5-x}\right )}{e^x-x} \, dx+2 \int \frac {x \text {Ei}\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 \operatorname {Subst}\left (\int \frac {E_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 \text {Ei}\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 (E_1\left (-e^{5-x}\right )+\text {Ei}\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 \text {Ei}\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 {\text {Ei}\left (e^{5-x}\right )}{e^x-x} \, dx+2 \int \frac {x \text {Ei}\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 \text {Ei}\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 (E_1\left (-e^{5-x}\right )+\text {Ei}\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 \text {Ei}\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 {\text {Ei}\left (e^{5-x}\right )}{e^x-x} \, dx+2 \int \frac {x \text {Ei}\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 {aligned} \end {gather*}

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Mathematica [A]  time = 0.63, size = 22, normalized size = 1.00 \begin {gather*} e^{e^{5-x}} \left (-4+\log ^2\left (e^x-x\right )\right ) \end {gather*}

Antiderivative was successfully verified.

[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)

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fricas [A]  time = 1.00, size = 27, normalized size = 1.23 \begin {gather*} e^{\left (e^{\left (-x + 5\right )}\right )} \log \left (-x + e^{x}\right )^{2} - 4 \, e^{\left (e^{\left (-x + 5\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[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))

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \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} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[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)

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maple [A]  time = 0.04, size = 28, normalized size = 1.27

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

Verification of antiderivative is not currently implemented for this CAS.

[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))

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maxima [A]  time = 0.41, size = 19, normalized size = 0.86 \begin {gather*} {\left (\log \left (-x + e^{x}\right )^{2} - 4\right )} e^{\left (e^{\left (-x + 5\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[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))

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mupad [F]  time = 0.00, size = -1, normalized size = -0.05 \begin {gather*} -\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 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[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)

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sympy [F(-1)]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[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

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