3.86.61 \(\int \frac {e^{e^{e^x}-e^{2+x^2}+e^{e^{e^x}-e^{2+x^2}} (16+x-8 \log (x)+\log ^2(x))} (-8+x+e^{2+x^2} (-32 x^2-2 x^3)+(2+16 e^{2+x^2} x^2) \log (x)-2 e^{2+x^2} x^2 \log ^2(x)+e^{e^x} (e^x (16 x+x^2)-8 e^x x \log (x)+e^x x \log ^2(x)))}{x} \, dx\)

Optimal. Leaf size=30 \[ e^{e^{e^{e^x}-e^{2+x^2}} \left (x+(4-\log (x))^2\right )} \]

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Rubi [F]  time = 111.46, 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 {\exp \left (e^{e^x}-e^{2+x^2}+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) \left (-8+x+e^{2+x^2} \left (-32 x^2-2 x^3\right )+\left (2+16 e^{2+x^2} x^2\right ) \log (x)-2 e^{2+x^2} x^2 \log ^2(x)+e^{e^x} \left (e^x \left (16 x+x^2\right )-8 e^x x \log (x)+e^x x \log ^2(x)\right )\right )}{x} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(E^(E^E^x - E^(2 + x^2) + E^(E^E^x - E^(2 + x^2))*(16 + x - 8*Log[x] + Log[x]^2))*(-8 + x + E^(2 + x^2)*(-
32*x^2 - 2*x^3) + (2 + 16*E^(2 + x^2)*x^2)*Log[x] - 2*E^(2 + x^2)*x^2*Log[x]^2 + E^E^x*(E^x*(16*x + x^2) - 8*E
^x*x*Log[x] + E^x*x*Log[x]^2)))/x,x]

[Out]

Defer[Int][E^(E^E^x - E^(2 + x^2) + E^(E^E^x - E^(2 + x^2))*(16 + x - 8*Log[x] + Log[x]^2)), x] + 16*Defer[Int
][E^(E^E^x + E^x - E^(2 + x^2) + x + E^(E^E^x - E^(2 + x^2))*(16 + x - 8*Log[x] + Log[x]^2)), x] - 8*Defer[Int
][E^(E^E^x - E^(2 + x^2) + E^(E^E^x - E^(2 + x^2))*(16 + x - 8*Log[x] + Log[x]^2))/x, x] + Defer[Int][E^(E^E^x
+ E^x - E^(2 + x^2) + x + E^(E^E^x - E^(2 + x^2))*(16 + x - 8*Log[x] + Log[x]^2))*x, x] - 32*Defer[Int][E^(2
+ E^E^x - E^(2 + x^2) + x^2 + E^(E^E^x - E^(2 + x^2))*(16 + x - 8*Log[x] + Log[x]^2))*x, x] - 2*Defer[Int][E^(
2 + E^E^x - E^(2 + x^2) + x^2 + E^(E^E^x - E^(2 + x^2))*(16 + x - 8*Log[x] + Log[x]^2))*x^2, x] - 8*Defer[Int]
[E^(E^E^x + E^x - E^(2 + x^2) + x + E^(E^E^x - E^(2 + x^2))*(16 + x - 8*Log[x] + Log[x]^2))*Log[x], x] + 2*Def
er[Int][(E^(E^E^x - E^(2 + x^2) + E^(E^E^x - E^(2 + x^2))*(16 + x - 8*Log[x] + Log[x]^2))*Log[x])/x, x] + 16*D
efer[Int][E^(2 + E^E^x - E^(2 + x^2) + x^2 + E^(E^E^x - E^(2 + x^2))*(16 + x - 8*Log[x] + Log[x]^2))*x*Log[x],
x] + Defer[Int][E^(E^E^x + E^x - E^(2 + x^2) + x + E^(E^E^x - E^(2 + x^2))*(16 + x - 8*Log[x] + Log[x]^2))*Lo
g[x]^2, x] - 2*Defer[Int][E^(2 + E^E^x - E^(2 + x^2) + x^2 + E^(E^E^x - E^(2 + x^2))*(16 + x - 8*Log[x] + Log[
x]^2))*x*Log[x]^2, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-2 \exp \left (2+e^{e^x}-e^{2+x^2}+x^2+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) x \left (16+x-8 \log (x)+\log ^2(x)\right )+\frac {\exp \left (e^{e^x}-e^{2+x^2}+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) \left (-8+x+16 e^{e^x+x} x+e^{e^x+x} x^2+2 \log (x)-8 e^{e^x+x} x \log (x)+e^{e^x+x} x \log ^2(x)\right )}{x}\right ) \, dx\\ &=-\left (2 \int \exp \left (2+e^{e^x}-e^{2+x^2}+x^2+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) x \left (16+x-8 \log (x)+\log ^2(x)\right ) \, dx\right )+\int \frac {\exp \left (e^{e^x}-e^{2+x^2}+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) \left (-8+x+16 e^{e^x+x} x+e^{e^x+x} x^2+2 \log (x)-8 e^{e^x+x} x \log (x)+e^{e^x+x} x \log ^2(x)\right )}{x} \, dx\\ &=-\left (2 \int \left (\exp \left (2+e^{e^x}-e^{2+x^2}+x^2+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) x (16+x)-8 \exp \left (2+e^{e^x}-e^{2+x^2}+x^2+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) x \log (x)+\exp \left (2+e^{e^x}-e^{2+x^2}+x^2+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) x \log ^2(x)\right ) \, dx\right )+\int \left (\frac {\exp \left (e^{e^x}-e^{2+x^2}+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) (-8+x+2 \log (x))}{x}+\exp \left (e^{e^x}+e^x-e^{2+x^2}+x+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) \, dx\\ &=-\left (2 \int \exp \left (2+e^{e^x}-e^{2+x^2}+x^2+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) x (16+x) \, dx\right )-2 \int \exp \left (2+e^{e^x}-e^{2+x^2}+x^2+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) x \log ^2(x) \, dx+16 \int \exp \left (2+e^{e^x}-e^{2+x^2}+x^2+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) x \log (x) \, dx+\int \frac {\exp \left (e^{e^x}-e^{2+x^2}+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) (-8+x+2 \log (x))}{x} \, dx+\int \exp \left (e^{e^x}+e^x-e^{2+x^2}+x+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) \left (16+x-8 \log (x)+\log ^2(x)\right ) \, dx\\ &=-\left (2 \int \left (16 \exp \left (2+e^{e^x}-e^{2+x^2}+x^2+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) x+\exp \left (2+e^{e^x}-e^{2+x^2}+x^2+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) x^2\right ) \, dx\right )-2 \int \exp \left (2+e^{e^x}-e^{2+x^2}+x^2+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) x \log ^2(x) \, dx+16 \int \exp \left (2+e^{e^x}-e^{2+x^2}+x^2+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) x \log (x) \, dx+\int \left (\frac {\exp \left (e^{e^x}-e^{2+x^2}+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) (-8+x)}{x}+\frac {2 \exp \left (e^{e^x}-e^{2+x^2}+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) \log (x)}{x}\right ) \, dx+\int \left (16 \exp \left (e^{e^x}+e^x-e^{2+x^2}+x+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right )+\exp \left (e^{e^x}+e^x-e^{2+x^2}+x+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) x-8 \exp \left (e^{e^x}+e^x-e^{2+x^2}+x+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) \log (x)+\exp \left (e^{e^x}+e^x-e^{2+x^2}+x+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) \log ^2(x)\right ) \, dx\\ &=-\left (2 \int \exp \left (2+e^{e^x}-e^{2+x^2}+x^2+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) x^2 \, dx\right )+2 \int \frac {\exp \left (e^{e^x}-e^{2+x^2}+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) \log (x)}{x} \, dx-2 \int \exp \left (2+e^{e^x}-e^{2+x^2}+x^2+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) x \log ^2(x) \, dx-8 \int \exp \left (e^{e^x}+e^x-e^{2+x^2}+x+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) \log (x) \, dx+16 \int \exp \left (e^{e^x}+e^x-e^{2+x^2}+x+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) \, dx+16 \int \exp \left (2+e^{e^x}-e^{2+x^2}+x^2+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) x \log (x) \, dx-32 \int \exp \left (2+e^{e^x}-e^{2+x^2}+x^2+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) x \, dx+\int \frac {\exp \left (e^{e^x}-e^{2+x^2}+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) (-8+x)}{x} \, dx+\int \exp \left (e^{e^x}+e^x-e^{2+x^2}+x+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) x \, dx+\int \exp \left (e^{e^x}+e^x-e^{2+x^2}+x+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) \log ^2(x) \, dx\\ &=-\left (2 \int \exp \left (2+e^{e^x}-e^{2+x^2}+x^2+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) x^2 \, dx\right )+2 \int \frac {\exp \left (e^{e^x}-e^{2+x^2}+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) \log (x)}{x} \, dx-2 \int \exp \left (2+e^{e^x}-e^{2+x^2}+x^2+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) x \log ^2(x) \, dx-8 \int \exp \left (e^{e^x}+e^x-e^{2+x^2}+x+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) \log (x) \, dx+16 \int \exp \left (e^{e^x}+e^x-e^{2+x^2}+x+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) \, dx+16 \int \exp \left (2+e^{e^x}-e^{2+x^2}+x^2+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) x \log (x) \, dx-32 \int \exp \left (2+e^{e^x}-e^{2+x^2}+x^2+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) x \, dx+\int \left (\exp \left (e^{e^x}-e^{2+x^2}+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right )-\frac {8 \exp \left (e^{e^x}-e^{2+x^2}+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right )}{x}\right ) \, dx+\int \exp \left (e^{e^x}+e^x-e^{2+x^2}+x+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) x \, dx+\int \exp \left (e^{e^x}+e^x-e^{2+x^2}+x+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) \log ^2(x) \, dx\\ &=-\left (2 \int \exp \left (2+e^{e^x}-e^{2+x^2}+x^2+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) x^2 \, dx\right )+2 \int \frac {\exp \left (e^{e^x}-e^{2+x^2}+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) \log (x)}{x} \, dx-2 \int \exp \left (2+e^{e^x}-e^{2+x^2}+x^2+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) x \log ^2(x) \, dx-8 \int \frac {\exp \left (e^{e^x}-e^{2+x^2}+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right )}{x} \, dx-8 \int \exp \left (e^{e^x}+e^x-e^{2+x^2}+x+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) \log (x) \, dx+16 \int \exp \left (e^{e^x}+e^x-e^{2+x^2}+x+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) \, dx+16 \int \exp \left (2+e^{e^x}-e^{2+x^2}+x^2+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) x \log (x) \, dx-32 \int \exp \left (2+e^{e^x}-e^{2+x^2}+x^2+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) x \, dx+\int \exp \left (e^{e^x}-e^{2+x^2}+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) \, dx+\int \exp \left (e^{e^x}+e^x-e^{2+x^2}+x+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) x \, dx+\int \exp \left (e^{e^x}+e^x-e^{2+x^2}+x+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) \log ^2(x) \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.29, size = 31, normalized size = 1.03 \begin {gather*} e^{e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^(E^E^x - E^(2 + x^2) + E^(E^E^x - E^(2 + x^2))*(16 + x - 8*Log[x] + Log[x]^2))*(-8 + x + E^(2 + x
^2)*(-32*x^2 - 2*x^3) + (2 + 16*E^(2 + x^2)*x^2)*Log[x] - 2*E^(2 + x^2)*x^2*Log[x]^2 + E^E^x*(E^x*(16*x + x^2)
- 8*E^x*x*Log[x] + E^x*x*Log[x]^2)))/x,x]

[Out]

E^(E^(E^E^x - E^(2 + x^2))*(16 + x - 8*Log[x] + Log[x]^2))

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fricas [A]  time = 0.72, size = 26, normalized size = 0.87 \begin {gather*} e^{\left ({\left (\log \relax (x)^{2} + x - 8 \, \log \relax (x) + 16\right )} e^{\left (-e^{\left (x^{2} + 2\right )} + e^{\left (e^{x}\right )}\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((x*exp(x)*log(x)^2-8*x*exp(x)*log(x)+(x^2+16*x)*exp(x))*exp(exp(x))-2*x^2*exp(x^2+2)*log(x)^2+(16*x
^2*exp(x^2+2)+2)*log(x)+(-2*x^3-32*x^2)*exp(x^2+2)-8+x)*exp(exp(exp(x))-exp(x^2+2))*exp((log(x)^2-8*log(x)+x+1
6)*exp(exp(exp(x))-exp(x^2+2)))/x,x, algorithm="fricas")

[Out]

e^((log(x)^2 + x - 8*log(x) + 16)*e^(-e^(x^2 + 2) + e^(e^x)))

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int -\frac {{\left (2 \, x^{2} e^{\left (x^{2} + 2\right )} \log \relax (x)^{2} + 2 \, {\left (x^{3} + 16 \, x^{2}\right )} e^{\left (x^{2} + 2\right )} - {\left (x e^{x} \log \relax (x)^{2} - 8 \, x e^{x} \log \relax (x) + {\left (x^{2} + 16 \, x\right )} e^{x}\right )} e^{\left (e^{x}\right )} - 2 \, {\left (8 \, x^{2} e^{\left (x^{2} + 2\right )} + 1\right )} \log \relax (x) - x + 8\right )} e^{\left ({\left (\log \relax (x)^{2} + x - 8 \, \log \relax (x) + 16\right )} e^{\left (-e^{\left (x^{2} + 2\right )} + e^{\left (e^{x}\right )}\right )} - e^{\left (x^{2} + 2\right )} + e^{\left (e^{x}\right )}\right )}}{x}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((x*exp(x)*log(x)^2-8*x*exp(x)*log(x)+(x^2+16*x)*exp(x))*exp(exp(x))-2*x^2*exp(x^2+2)*log(x)^2+(16*x
^2*exp(x^2+2)+2)*log(x)+(-2*x^3-32*x^2)*exp(x^2+2)-8+x)*exp(exp(exp(x))-exp(x^2+2))*exp((log(x)^2-8*log(x)+x+1
6)*exp(exp(exp(x))-exp(x^2+2)))/x,x, algorithm="giac")

[Out]

integrate(-(2*x^2*e^(x^2 + 2)*log(x)^2 + 2*(x^3 + 16*x^2)*e^(x^2 + 2) - (x*e^x*log(x)^2 - 8*x*e^x*log(x) + (x^
2 + 16*x)*e^x)*e^(e^x) - 2*(8*x^2*e^(x^2 + 2) + 1)*log(x) - x + 8)*e^((log(x)^2 + x - 8*log(x) + 16)*e^(-e^(x^
2 + 2) + e^(e^x)) - e^(x^2 + 2) + e^(e^x))/x, x)

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maple [A]  time = 0.14, size = 27, normalized size = 0.90

method	result	size
risch	\({\mathrm e}^{\left (\ln \relax (x )^{2}-8 \ln \relax (x )+x +16\right ) {\mathrm e}^{{\mathrm e}^{{\mathrm e}^{x}}-{\mathrm e}^{x^{2}+2}}}\)	\(27\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((x*exp(x)*ln(x)^2-8*x*exp(x)*ln(x)+(x^2+16*x)*exp(x))*exp(exp(x))-2*x^2*exp(x^2+2)*ln(x)^2+(16*x^2*exp(x^
2+2)+2)*ln(x)+(-2*x^3-32*x^2)*exp(x^2+2)-8+x)*exp(exp(exp(x))-exp(x^2+2))*exp((ln(x)^2-8*ln(x)+x+16)*exp(exp(e
xp(x))-exp(x^2+2)))/x,x,method=_RETURNVERBOSE)

[Out]

exp((ln(x)^2-8*ln(x)+x+16)*exp(exp(exp(x))-exp(x^2+2)))

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maxima [B]  time = 1.47, size = 67, normalized size = 2.23 \begin {gather*} e^{\left (e^{\left (-e^{\left (x^{2} + 2\right )} + e^{\left (e^{x}\right )}\right )} \log \relax (x)^{2} + x e^{\left (-e^{\left (x^{2} + 2\right )} + e^{\left (e^{x}\right )}\right )} - 8 \, e^{\left (-e^{\left (x^{2} + 2\right )} + e^{\left (e^{x}\right )}\right )} \log \relax (x) + 16 \, e^{\left (-e^{\left (x^{2} + 2\right )} + e^{\left (e^{x}\right )}\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((x*exp(x)*log(x)^2-8*x*exp(x)*log(x)+(x^2+16*x)*exp(x))*exp(exp(x))-2*x^2*exp(x^2+2)*log(x)^2+(16*x
^2*exp(x^2+2)+2)*log(x)+(-2*x^3-32*x^2)*exp(x^2+2)-8+x)*exp(exp(exp(x))-exp(x^2+2))*exp((log(x)^2-8*log(x)+x+1
6)*exp(exp(exp(x))-exp(x^2+2)))/x,x, algorithm="maxima")

[Out]

e^(e^(-e^(x^2 + 2) + e^(e^x))*log(x)^2 + x*e^(-e^(x^2 + 2) + e^(e^x)) - 8*e^(-e^(x^2 + 2) + e^(e^x))*log(x) +
16*e^(-e^(x^2 + 2) + e^(e^x)))

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mupad [B]  time = 5.39, size = 71, normalized size = 2.37 \begin {gather*} \frac {{\mathrm {e}}^{{\mathrm {e}}^{-{\mathrm {e}}^{x^2}\,{\mathrm {e}}^2}\,{\mathrm {e}}^{{\mathrm {e}}^{{\mathrm {e}}^x}}\,{\ln \relax (x)}^2}\,{\mathrm {e}}^{x\,{\mathrm {e}}^{-{\mathrm {e}}^{x^2}\,{\mathrm {e}}^2}\,{\mathrm {e}}^{{\mathrm {e}}^{{\mathrm {e}}^x}}}\,{\mathrm {e}}^{16\,{\mathrm {e}}^{-{\mathrm {e}}^{x^2}\,{\mathrm {e}}^2}\,{\mathrm {e}}^{{\mathrm {e}}^{{\mathrm {e}}^x}}}}{x^{8\,{\mathrm {e}}^{-{\mathrm {e}}^{x^2}\,{\mathrm {e}}^2}\,{\mathrm {e}}^{{\mathrm {e}}^{{\mathrm {e}}^x}}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(exp(exp(x)) - exp(x^2 + 2))*exp(exp(exp(exp(x)) - exp(x^2 + 2))*(x - 8*log(x) + log(x)^2 + 16))*(x +
log(x)*(16*x^2*exp(x^2 + 2) + 2) - exp(x^2 + 2)*(32*x^2 + 2*x^3) + exp(exp(x))*(exp(x)*(16*x + x^2) - 8*x*exp(
x)*log(x) + x*exp(x)*log(x)^2) - 2*x^2*exp(x^2 + 2)*log(x)^2 - 8))/x,x)

[Out]

(exp(exp(-exp(x^2)*exp(2))*exp(exp(exp(x)))*log(x)^2)*exp(x*exp(-exp(x^2)*exp(2))*exp(exp(exp(x))))*exp(16*exp
(-exp(x^2)*exp(2))*exp(exp(exp(x)))))/x^(8*exp(-exp(x^2)*exp(2))*exp(exp(exp(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(((x*exp(x)*ln(x)**2-8*x*exp(x)*ln(x)+(x**2+16*x)*exp(x))*exp(exp(x))-2*x**2*exp(x**2+2)*ln(x)**2+(16
*x**2*exp(x**2+2)+2)*ln(x)+(-2*x**3-32*x**2)*exp(x**2+2)-8+x)*exp(exp(exp(x))-exp(x**2+2))*exp((ln(x)**2-8*ln(
x)+x+16)*exp(exp(exp(x))-exp(x**2+2)))/x,x)

[Out]

Timed out

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