\(\int e^{\frac {4-12 \log (3)+e^{2 e^{3+x}} \log ^2(3)+e^{e^{3+x}} (-4+2 x-2 x^2) \log ^2(3)+(13-4 x+5 x^2-2 x^3+x^4) \log ^2(3)}{\log ^2(3)}} (-4+2 e^{3+2 e^{3+x}+x}+10 x-6 x^2+4 x^3+e^{e^{3+x}} (2-4 x+e^{3+x} (-4+2 x-2 x^2))) \, dx\) [3548]

Optimal result

Integrand size = 131, antiderivative size = 32 \[ \int e^{\frac {4-12 \log (3)+e^{2 e^{3+x}} \log ^2(3)+e^{e^{3+x}} \left (-4+2 x-2 x^2\right ) \log ^2(3)+\left (13-4 x+5 x^2-2 x^3+x^4\right ) \log ^2(3)}{\log ^2(3)}} \left (-4+2 e^{3+2 e^{3+x}+x}+10 x-6 x^2+4 x^3+e^{e^{3+x}} \left (2-4 x+e^{3+x} \left (-4+2 x-2 x^2\right )\right )\right ) \, dx=e^{\left (2-e^{e^{3+x}}-x+x^2\right )^2+\left (3-\frac {2}{\log (3)}\right )^2} \]

[Out]

exp((3-2/ln(3))^2+(2-x+x^2-exp(exp(3+x)))^2)

Rubi [F]

\[ \int e^{\frac {4-12 \log (3)+e^{2 e^{3+x}} \log ^2(3)+e^{e^{3+x}} \left (-4+2 x-2 x^2\right ) \log ^2(3)+\left (13-4 x+5 x^2-2 x^3+x^4\right ) \log ^2(3)}{\log ^2(3)}} \left (-4+2 e^{3+2 e^{3+x}+x}+10 x-6 x^2+4 x^3+e^{e^{3+x}} \left (2-4 x+e^{3+x} \left (-4+2 x-2 x^2\right )\right )\right ) \, dx=\int \exp \left (\frac {4-12 \log (3)+e^{2 e^{3+x}} \log ^2(3)+e^{e^{3+x}} \left (-4+2 x-2 x^2\right ) \log ^2(3)+\left (13-4 x+5 x^2-2 x^3+x^4\right ) \log ^2(3)}{\log ^2(3)}\right ) \left (-4+2 e^{3+2 e^{3+x}+x}+10 x-6 x^2+4 x^3+e^{e^{3+x}} \left (2-4 x+e^{3+x} \left (-4+2 x-2 x^2\right )\right )\right ) \, dx \]

[In]

Int[E^((4 - 12*Log[3] + E^(2*E^(3 + x))*Log[3]^2 + E^E^(3 + x)*(-4 + 2*x - 2*x^2)*Log[3]^2 + (13 - 4*x + 5*x^2
- 2*x^3 + x^4)*Log[3]^2)/Log[3]^2)*(-4 + 2*E^(3 + 2*E^(3 + x) + x) + 10*x - 6*x^2 + 4*x^3 + E^E^(3 + x)*(2 -
4*x + E^(3 + x)*(-4 + 2*x - 2*x^2))),x]

[Out]

(-4*Defer[Int][E^(E^(2*E^(3 + x)) - 4*x + 5*x^2 - 2*x^3 + x^4 - 2*E^E^(3 + x)*(2 - x + x^2) + 13*(1 + 4/(13*Lo
g[3]^2))), x])/E^(12/Log[3]) + (2*Defer[Int][E^(E^(2*E^(3 + x)) + E^(3 + x) - 4*x + 5*x^2 - 2*x^3 + x^4 - 2*E^
E^(3 + x)*(2 - x + x^2) + 13*(1 + 4/(13*Log[3]^2))), x])/E^(12/Log[3]) - (4*Defer[Int][E^(E^(2*E^(3 + x)) + E^
(3 + x) - 3*x + 5*x^2 - 2*x^3 + x^4 - 2*E^E^(3 + x)*(2 - x + x^2) + 3*(16/3 + 4/(3*Log[3]^2))), x])/E^(12/Log[
3]) + (2*Defer[Int][E^(E^(2*E^(3 + x)) + 2*E^(3 + x) - 3*x + 5*x^2 - 2*x^3 + x^4 - 2*E^E^(3 + x)*(2 - x + x^2)
+ 3*(16/3 + 4/(3*Log[3]^2))), x])/E^(12/Log[3]) + (10*Defer[Int][E^(E^(2*E^(3 + x)) - 4*x + 5*x^2 - 2*x^3 + x
^4 - 2*E^E^(3 + x)*(2 - x + x^2) + 13*(1 + 4/(13*Log[3]^2)))*x, x])/E^(12/Log[3]) - (4*Defer[Int][E^(E^(2*E^(3
+ x)) + E^(3 + x) - 4*x + 5*x^2 - 2*x^3 + x^4 - 2*E^E^(3 + x)*(2 - x + x^2) + 13*(1 + 4/(13*Log[3]^2)))*x, x]
)/E^(12/Log[3]) + (2*Defer[Int][E^(E^(2*E^(3 + x)) + E^(3 + x) - 3*x + 5*x^2 - 2*x^3 + x^4 - 2*E^E^(3 + x)*(2
- x + x^2) + 3*(16/3 + 4/(3*Log[3]^2)))*x, x])/E^(12/Log[3]) - (6*Defer[Int][E^(E^(2*E^(3 + x)) - 4*x + 5*x^2
- 2*x^3 + x^4 - 2*E^E^(3 + x)*(2 - x + x^2) + 13*(1 + 4/(13*Log[3]^2)))*x^2, x])/E^(12/Log[3]) - (2*Defer[Int]
[E^(E^(2*E^(3 + x)) + E^(3 + x) - 3*x + 5*x^2 - 2*x^3 + x^4 - 2*E^E^(3 + x)*(2 - x + x^2) + 3*(16/3 + 4/(3*Log
[3]^2)))*x^2, x])/E^(12/Log[3]) + (4*Defer[Int][E^(E^(2*E^(3 + x)) - 4*x + 5*x^2 - 2*x^3 + x^4 - 2*E^E^(3 + x)
*(2 - x + x^2) + 13*(1 + 4/(13*Log[3]^2)))*x^3, x])/E^(12/Log[3])

Rubi steps \begin{align*} \text {integral}& = \int 3^{-\frac {12}{\log ^2(3)}} \exp \left (\frac {4+e^{2 e^{3+x}} \log ^2(3)+e^{e^{3+x}} \left (-4+2 x-2 x^2\right ) \log ^2(3)+\left (13-4 x+5 x^2-2 x^3+x^4\right ) \log ^2(3)}{\log ^2(3)}\right ) \left (-4+2 e^{3+2 e^{3+x}+x}+10 x-6 x^2+4 x^3+e^{e^{3+x}} \left (2-4 x+e^{3+x} \left (-4+2 x-2 x^2\right )\right )\right ) \, dx \\ & = e^{-\frac {12}{\log (3)}} \int \exp \left (\frac {4+e^{2 e^{3+x}} \log ^2(3)+e^{e^{3+x}} \left (-4+2 x-2 x^2\right ) \log ^2(3)+\left (13-4 x+5 x^2-2 x^3+x^4\right ) \log ^2(3)}{\log ^2(3)}\right ) \left (-4+2 e^{3+2 e^{3+x}+x}+10 x-6 x^2+4 x^3+e^{e^{3+x}} \left (2-4 x+e^{3+x} \left (-4+2 x-2 x^2\right )\right )\right ) \, dx \\ & = e^{-\frac {12}{\log (3)}} \int 2 \exp \left (e^{2 e^{3+x}}-4 x+5 x^2-2 x^3+x^4-2 e^{e^{3+x}} \left (2-x+x^2\right )+13 \left (1+\frac {4}{13 \log ^2(3)}\right )\right ) \left (1+e^{3+e^{3+x}+x}-2 x\right ) \left (-2+e^{e^{3+x}}+x-x^2\right ) \, dx \\ & = \left (2 e^{-\frac {12}{\log (3)}}\right ) \int \exp \left (e^{2 e^{3+x}}-4 x+5 x^2-2 x^3+x^4-2 e^{e^{3+x}} \left (2-x+x^2\right )+13 \left (1+\frac {4}{13 \log ^2(3)}\right )\right ) \left (1+e^{3+e^{3+x}+x}-2 x\right ) \left (-2+e^{e^{3+x}}+x-x^2\right ) \, dx \\ & = \left (2 e^{-\frac {12}{\log (3)}}\right ) \int \left (\exp \left (3+e^{2 e^{3+x}}+e^{3+x}-3 x+5 x^2-2 x^3+x^4-2 e^{e^{3+x}} \left (2-x+x^2\right )+13 \left (1+\frac {4}{13 \log ^2(3)}\right )\right ) \left (-2+e^{e^{3+x}}+x-x^2\right )+\exp \left (e^{2 e^{3+x}}-4 x+5 x^2-2 x^3+x^4-2 e^{e^{3+x}} \left (2-x+x^2\right )+13 \left (1+\frac {4}{13 \log ^2(3)}\right )\right ) (-1+2 x) \left (2-e^{e^{3+x}}-x+x^2\right )\right ) \, dx \\ & = \left (2 e^{-\frac {12}{\log (3)}}\right ) \int \exp \left (3+e^{2 e^{3+x}}+e^{3+x}-3 x+5 x^2-2 x^3+x^4-2 e^{e^{3+x}} \left (2-x+x^2\right )+13 \left (1+\frac {4}{13 \log ^2(3)}\right )\right ) \left (-2+e^{e^{3+x}}+x-x^2\right ) \, dx+\left (2 e^{-\frac {12}{\log (3)}}\right ) \int \exp \left (e^{2 e^{3+x}}-4 x+5 x^2-2 x^3+x^4-2 e^{e^{3+x}} \left (2-x+x^2\right )+13 \left (1+\frac {4}{13 \log ^2(3)}\right )\right ) (-1+2 x) \left (2-e^{e^{3+x}}-x+x^2\right ) \, dx \\ & = \left (2 e^{-\frac {12}{\log (3)}}\right ) \int \exp \left (e^{2 e^{3+x}}+e^{3+x}-3 x+5 x^2-2 x^3+x^4-2 e^{e^{3+x}} \left (2-x+x^2\right )+3 \left (\frac {16}{3}+\frac {4}{3 \log ^2(3)}\right )\right ) \left (-2+e^{e^{3+x}}+x-x^2\right ) \, dx+\left (2 e^{-\frac {12}{\log (3)}}\right ) \int \left (-2 \exp \left (e^{2 e^{3+x}}-4 x+5 x^2-2 x^3+x^4-2 e^{e^{3+x}} \left (2-x+x^2\right )+13 \left (1+\frac {4}{13 \log ^2(3)}\right )\right )+5 \exp \left (e^{2 e^{3+x}}-4 x+5 x^2-2 x^3+x^4-2 e^{e^{3+x}} \left (2-x+x^2\right )+13 \left (1+\frac {4}{13 \log ^2(3)}\right )\right ) x-3 \exp \left (e^{2 e^{3+x}}-4 x+5 x^2-2 x^3+x^4-2 e^{e^{3+x}} \left (2-x+x^2\right )+13 \left (1+\frac {4}{13 \log ^2(3)}\right )\right ) x^2+2 \exp \left (e^{2 e^{3+x}}-4 x+5 x^2-2 x^3+x^4-2 e^{e^{3+x}} \left (2-x+x^2\right )+13 \left (1+\frac {4}{13 \log ^2(3)}\right )\right ) x^3-\exp \left (e^{2 e^{3+x}}+e^{3+x}-4 x+5 x^2-2 x^3+x^4-2 e^{e^{3+x}} \left (2-x+x^2\right )+13 \left (1+\frac {4}{13 \log ^2(3)}\right )\right ) (-1+2 x)\right ) \, dx \\ & = -\left (\left (2 e^{-\frac {12}{\log (3)}}\right ) \int \exp \left (e^{2 e^{3+x}}+e^{3+x}-4 x+5 x^2-2 x^3+x^4-2 e^{e^{3+x}} \left (2-x+x^2\right )+13 \left (1+\frac {4}{13 \log ^2(3)}\right )\right ) (-1+2 x) \, dx\right )+\left (2 e^{-\frac {12}{\log (3)}}\right ) \int \left (-2 \exp \left (e^{2 e^{3+x}}+e^{3+x}-3 x+5 x^2-2 x^3+x^4-2 e^{e^{3+x}} \left (2-x+x^2\right )+3 \left (\frac {16}{3}+\frac {4}{3 \log ^2(3)}\right )\right )+\exp \left (e^{2 e^{3+x}}+2 e^{3+x}-3 x+5 x^2-2 x^3+x^4-2 e^{e^{3+x}} \left (2-x+x^2\right )+3 \left (\frac {16}{3}+\frac {4}{3 \log ^2(3)}\right )\right )+\exp \left (e^{2 e^{3+x}}+e^{3+x}-3 x+5 x^2-2 x^3+x^4-2 e^{e^{3+x}} \left (2-x+x^2\right )+3 \left (\frac {16}{3}+\frac {4}{3 \log ^2(3)}\right )\right ) x-\exp \left (e^{2 e^{3+x}}+e^{3+x}-3 x+5 x^2-2 x^3+x^4-2 e^{e^{3+x}} \left (2-x+x^2\right )+3 \left (\frac {16}{3}+\frac {4}{3 \log ^2(3)}\right )\right ) x^2\right ) \, dx-\left (4 e^{-\frac {12}{\log (3)}}\right ) \int \exp \left (e^{2 e^{3+x}}-4 x+5 x^2-2 x^3+x^4-2 e^{e^{3+x}} \left (2-x+x^2\right )+13 \left (1+\frac {4}{13 \log ^2(3)}\right )\right ) \, dx+\left (4 e^{-\frac {12}{\log (3)}}\right ) \int \exp \left (e^{2 e^{3+x}}-4 x+5 x^2-2 x^3+x^4-2 e^{e^{3+x}} \left (2-x+x^2\right )+13 \left (1+\frac {4}{13 \log ^2(3)}\right )\right ) x^3 \, dx-\left (6 e^{-\frac {12}{\log (3)}}\right ) \int \exp \left (e^{2 e^{3+x}}-4 x+5 x^2-2 x^3+x^4-2 e^{e^{3+x}} \left (2-x+x^2\right )+13 \left (1+\frac {4}{13 \log ^2(3)}\right )\right ) x^2 \, dx+\left (10 e^{-\frac {12}{\log (3)}}\right ) \int \exp \left (e^{2 e^{3+x}}-4 x+5 x^2-2 x^3+x^4-2 e^{e^{3+x}} \left (2-x+x^2\right )+13 \left (1+\frac {4}{13 \log ^2(3)}\right )\right ) x \, dx \\ & = \left (2 e^{-\frac {12}{\log (3)}}\right ) \int \exp \left (e^{2 e^{3+x}}+2 e^{3+x}-3 x+5 x^2-2 x^3+x^4-2 e^{e^{3+x}} \left (2-x+x^2\right )+3 \left (\frac {16}{3}+\frac {4}{3 \log ^2(3)}\right )\right ) \, dx+\left (2 e^{-\frac {12}{\log (3)}}\right ) \int \exp \left (e^{2 e^{3+x}}+e^{3+x}-3 x+5 x^2-2 x^3+x^4-2 e^{e^{3+x}} \left (2-x+x^2\right )+3 \left (\frac {16}{3}+\frac {4}{3 \log ^2(3)}\right )\right ) x \, dx-\left (2 e^{-\frac {12}{\log (3)}}\right ) \int \exp \left (e^{2 e^{3+x}}+e^{3+x}-3 x+5 x^2-2 x^3+x^4-2 e^{e^{3+x}} \left (2-x+x^2\right )+3 \left (\frac {16}{3}+\frac {4}{3 \log ^2(3)}\right )\right ) x^2 \, dx-\left (2 e^{-\frac {12}{\log (3)}}\right ) \int \left (-\exp \left (e^{2 e^{3+x}}+e^{3+x}-4 x+5 x^2-2 x^3+x^4-2 e^{e^{3+x}} \left (2-x+x^2\right )+13 \left (1+\frac {4}{13 \log ^2(3)}\right )\right )+2 \exp \left (e^{2 e^{3+x}}+e^{3+x}-4 x+5 x^2-2 x^3+x^4-2 e^{e^{3+x}} \left (2-x+x^2\right )+13 \left (1+\frac {4}{13 \log ^2(3)}\right )\right ) x\right ) \, dx-\left (4 e^{-\frac {12}{\log (3)}}\right ) \int \exp \left (e^{2 e^{3+x}}-4 x+5 x^2-2 x^3+x^4-2 e^{e^{3+x}} \left (2-x+x^2\right )+13 \left (1+\frac {4}{13 \log ^2(3)}\right )\right ) \, dx-\left (4 e^{-\frac {12}{\log (3)}}\right ) \int \exp \left (e^{2 e^{3+x}}+e^{3+x}-3 x+5 x^2-2 x^3+x^4-2 e^{e^{3+x}} \left (2-x+x^2\right )+3 \left (\frac {16}{3}+\frac {4}{3 \log ^2(3)}\right )\right ) \, dx+\left (4 e^{-\frac {12}{\log (3)}}\right ) \int \exp \left (e^{2 e^{3+x}}-4 x+5 x^2-2 x^3+x^4-2 e^{e^{3+x}} \left (2-x+x^2\right )+13 \left (1+\frac {4}{13 \log ^2(3)}\right )\right ) x^3 \, dx-\left (6 e^{-\frac {12}{\log (3)}}\right ) \int \exp \left (e^{2 e^{3+x}}-4 x+5 x^2-2 x^3+x^4-2 e^{e^{3+x}} \left (2-x+x^2\right )+13 \left (1+\frac {4}{13 \log ^2(3)}\right )\right ) x^2 \, dx+\left (10 e^{-\frac {12}{\log (3)}}\right ) \int \exp \left (e^{2 e^{3+x}}-4 x+5 x^2-2 x^3+x^4-2 e^{e^{3+x}} \left (2-x+x^2\right )+13 \left (1+\frac {4}{13 \log ^2(3)}\right )\right ) x \, dx \\ & = \left (2 e^{-\frac {12}{\log (3)}}\right ) \int \exp \left (e^{2 e^{3+x}}+e^{3+x}-4 x+5 x^2-2 x^3+x^4-2 e^{e^{3+x}} \left (2-x+x^2\right )+13 \left (1+\frac {4}{13 \log ^2(3)}\right )\right ) \, dx+\left (2 e^{-\frac {12}{\log (3)}}\right ) \int \exp \left (e^{2 e^{3+x}}+2 e^{3+x}-3 x+5 x^2-2 x^3+x^4-2 e^{e^{3+x}} \left (2-x+x^2\right )+3 \left (\frac {16}{3}+\frac {4}{3 \log ^2(3)}\right )\right ) \, dx+\left (2 e^{-\frac {12}{\log (3)}}\right ) \int \exp \left (e^{2 e^{3+x}}+e^{3+x}-3 x+5 x^2-2 x^3+x^4-2 e^{e^{3+x}} \left (2-x+x^2\right )+3 \left (\frac {16}{3}+\frac {4}{3 \log ^2(3)}\right )\right ) x \, dx-\left (2 e^{-\frac {12}{\log (3)}}\right ) \int \exp \left (e^{2 e^{3+x}}+e^{3+x}-3 x+5 x^2-2 x^3+x^4-2 e^{e^{3+x}} \left (2-x+x^2\right )+3 \left (\frac {16}{3}+\frac {4}{3 \log ^2(3)}\right )\right ) x^2 \, dx-\left (4 e^{-\frac {12}{\log (3)}}\right ) \int \exp \left (e^{2 e^{3+x}}-4 x+5 x^2-2 x^3+x^4-2 e^{e^{3+x}} \left (2-x+x^2\right )+13 \left (1+\frac {4}{13 \log ^2(3)}\right )\right ) \, dx-\left (4 e^{-\frac {12}{\log (3)}}\right ) \int \exp \left (e^{2 e^{3+x}}+e^{3+x}-3 x+5 x^2-2 x^3+x^4-2 e^{e^{3+x}} \left (2-x+x^2\right )+3 \left (\frac {16}{3}+\frac {4}{3 \log ^2(3)}\right )\right ) \, dx-\left (4 e^{-\frac {12}{\log (3)}}\right ) \int \exp \left (e^{2 e^{3+x}}+e^{3+x}-4 x+5 x^2-2 x^3+x^4-2 e^{e^{3+x}} \left (2-x+x^2\right )+13 \left (1+\frac {4}{13 \log ^2(3)}\right )\right ) x \, dx+\left (4 e^{-\frac {12}{\log (3)}}\right ) \int \exp \left (e^{2 e^{3+x}}-4 x+5 x^2-2 x^3+x^4-2 e^{e^{3+x}} \left (2-x+x^2\right )+13 \left (1+\frac {4}{13 \log ^2(3)}\right )\right ) x^3 \, dx-\left (6 e^{-\frac {12}{\log (3)}}\right ) \int \exp \left (e^{2 e^{3+x}}-4 x+5 x^2-2 x^3+x^4-2 e^{e^{3+x}} \left (2-x+x^2\right )+13 \left (1+\frac {4}{13 \log ^2(3)}\right )\right ) x^2 \, dx+\left (10 e^{-\frac {12}{\log (3)}}\right ) \int \exp \left (e^{2 e^{3+x}}-4 x+5 x^2-2 x^3+x^4-2 e^{e^{3+x}} \left (2-x+x^2\right )+13 \left (1+\frac {4}{13 \log ^2(3)}\right )\right ) x \, dx \\ \end{align*}

Mathematica [A] (verified)

Time = 0.20 (sec) , antiderivative size = 58, normalized size of antiderivative = 1.81 \[ \int e^{\frac {4-12 \log (3)+e^{2 e^{3+x}} \log ^2(3)+e^{e^{3+x}} \left (-4+2 x-2 x^2\right ) \log ^2(3)+\left (13-4 x+5 x^2-2 x^3+x^4\right ) \log ^2(3)}{\log ^2(3)}} \left (-4+2 e^{3+2 e^{3+x}+x}+10 x-6 x^2+4 x^3+e^{e^{3+x}} \left (2-4 x+e^{3+x} \left (-4+2 x-2 x^2\right )\right )\right ) \, dx=e^{13+e^{2 e^{3+x}}-4 x+5 x^2-2 x^3+x^4-2 e^{e^{3+x}} \left (2-x+x^2\right )-\frac {4 (-1+3 \log (3))}{\log ^2(3)}} \]

[In]

Integrate[E^((4 - 12*Log[3] + E^(2*E^(3 + x))*Log[3]^2 + E^E^(3 + x)*(-4 + 2*x - 2*x^2)*Log[3]^2 + (13 - 4*x +
5*x^2 - 2*x^3 + x^4)*Log[3]^2)/Log[3]^2)*(-4 + 2*E^(3 + 2*E^(3 + x) + x) + 10*x - 6*x^2 + 4*x^3 + E^E^(3 + x)
*(2 - 4*x + E^(3 + x)*(-4 + 2*x - 2*x^2))),x]

[Out]

E^(13 + E^(2*E^(3 + x)) - 4*x + 5*x^2 - 2*x^3 + x^4 - 2*E^E^(3 + x)*(2 - x + x^2) - (4*(-1 + 3*Log[3]))/Log[3]
^2)

Maple [B] (verified)

Leaf count of result is larger than twice the leaf count of optimal. \(67\) vs. \(2(29)=58\).

Time = 1.43 (sec) , antiderivative size = 68, normalized size of antiderivative = 2.12

method	result	size
parallelrisch	\({\mathrm e}^{\frac {\ln \left (3\right )^{2} {\mathrm e}^{2 \,{\mathrm e}^{3+x}}+\left (-2 x^{2}+2 x -4\right ) \ln \left (3\right )^{2} {\mathrm e}^{{\mathrm e}^{3+x}}+\left (x^{4}-2 x^{3}+5 x^{2}-4 x +13\right ) \ln \left (3\right )^{2}-12 \ln \left (3\right )+4}{\ln \left (3\right )^{2}}}\)	\(68\)
risch	\({\mathrm e}^{\frac {x^{4} \ln \left (3\right )^{2}-2 \ln \left (3\right )^{2} {\mathrm e}^{{\mathrm e}^{3+x}} x^{2}-2 x^{3} \ln \left (3\right )^{2}+2 \ln \left (3\right )^{2} {\mathrm e}^{{\mathrm e}^{3+x}} x +5 x^{2} \ln \left (3\right )^{2}-4 \ln \left (3\right )^{2} {\mathrm e}^{{\mathrm e}^{3+x}}+\ln \left (3\right )^{2} {\mathrm e}^{2 \,{\mathrm e}^{3+x}}-4 x \ln \left (3\right )^{2}+13 \ln \left (3\right )^{2}-12 \ln \left (3\right )+4}{\ln \left (3\right )^{2}}}\)	\(101\)

[In]

int((2*exp(3+x)*exp(exp(3+x))^2+((-2*x^2+2*x-4)*exp(3+x)-4*x+2)*exp(exp(3+x))+4*x^3-6*x^2+10*x-4)*exp((ln(3)^2
*exp(exp(3+x))^2+(-2*x^2+2*x-4)*ln(3)^2*exp(exp(3+x))+(x^4-2*x^3+5*x^2-4*x+13)*ln(3)^2-12*ln(3)+4)/ln(3)^2),x,
method=_RETURNVERBOSE)

[Out]

exp((ln(3)^2*exp(exp(3+x))^2+(-2*x^2+2*x-4)*ln(3)^2*exp(exp(3+x))+(x^4-2*x^3+5*x^2-4*x+13)*ln(3)^2-12*ln(3)+4)
/ln(3)^2)

Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 69 vs. \(2 (29) = 58\).

Time = 0.25 (sec) , antiderivative size = 69, normalized size of antiderivative = 2.16 \[ \int e^{\frac {4-12 \log (3)+e^{2 e^{3+x}} \log ^2(3)+e^{e^{3+x}} \left (-4+2 x-2 x^2\right ) \log ^2(3)+\left (13-4 x+5 x^2-2 x^3+x^4\right ) \log ^2(3)}{\log ^2(3)}} \left (-4+2 e^{3+2 e^{3+x}+x}+10 x-6 x^2+4 x^3+e^{e^{3+x}} \left (2-4 x+e^{3+x} \left (-4+2 x-2 x^2\right )\right )\right ) \, dx=e^{\left (-\frac {2 \, {\left (x^{2} - x + 2\right )} e^{\left (e^{\left (x + 3\right )}\right )} \log \left (3\right )^{2} - {\left (x^{4} - 2 \, x^{3} + 5 \, x^{2} - 4 \, x + 13\right )} \log \left (3\right )^{2} - e^{\left (2 \, e^{\left (x + 3\right )}\right )} \log \left (3\right )^{2} + 12 \, \log \left (3\right ) - 4}{\log \left (3\right )^{2}}\right )} \]

[In]

integrate((2*exp(3+x)*exp(exp(3+x))^2+((-2*x^2+2*x-4)*exp(3+x)-4*x+2)*exp(exp(3+x))+4*x^3-6*x^2+10*x-4)*exp((l
og(3)^2*exp(exp(3+x))^2+(-2*x^2+2*x-4)*log(3)^2*exp(exp(3+x))+(x^4-2*x^3+5*x^2-4*x+13)*log(3)^2-12*log(3)+4)/l
og(3)^2),x, algorithm="fricas")

[Out]

e^(-(2*(x^2 - x + 2)*e^(e^(x + 3))*log(3)^2 - (x^4 - 2*x^3 + 5*x^2 - 4*x + 13)*log(3)^2 - e^(2*e^(x + 3))*log(
3)^2 + 12*log(3) - 4)/log(3)^2)

Sympy [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 71 vs. \(2 (24) = 48\).

Time = 0.34 (sec) , antiderivative size = 71, normalized size of antiderivative = 2.22 \[ \int e^{\frac {4-12 \log (3)+e^{2 e^{3+x}} \log ^2(3)+e^{e^{3+x}} \left (-4+2 x-2 x^2\right ) \log ^2(3)+\left (13-4 x+5 x^2-2 x^3+x^4\right ) \log ^2(3)}{\log ^2(3)}} \left (-4+2 e^{3+2 e^{3+x}+x}+10 x-6 x^2+4 x^3+e^{e^{3+x}} \left (2-4 x+e^{3+x} \left (-4+2 x-2 x^2\right )\right )\right ) \, dx=e^{\frac {\left (- 2 x^{2} + 2 x - 4\right ) e^{e^{x + 3}} \log {\left (3 \right )}^{2} + \left (x^{4} - 2 x^{3} + 5 x^{2} - 4 x + 13\right ) \log {\left (3 \right )}^{2} + e^{2 e^{x + 3}} \log {\left (3 \right )}^{2} - 12 \log {\left (3 \right )} + 4}{\log {\left (3 \right )}^{2}}} \]

[In]

integrate((2*exp(3+x)*exp(exp(3+x))**2+((-2*x**2+2*x-4)*exp(3+x)-4*x+2)*exp(exp(3+x))+4*x**3-6*x**2+10*x-4)*ex
p((ln(3)**2*exp(exp(3+x))**2+(-2*x**2+2*x-4)*ln(3)**2*exp(exp(3+x))+(x**4-2*x**3+5*x**2-4*x+13)*ln(3)**2-12*ln
(3)+4)/ln(3)**2),x)

[Out]

exp(((-2*x**2 + 2*x - 4)*exp(exp(x + 3))*log(3)**2 + (x**4 - 2*x**3 + 5*x**2 - 4*x + 13)*log(3)**2 + exp(2*exp
(x + 3))*log(3)**2 - 12*log(3) + 4)/log(3)**2)

Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 63 vs. \(2 (29) = 58\).

Time = 0.62 (sec) , antiderivative size = 63, normalized size of antiderivative = 1.97 \[ \int e^{\frac {4-12 \log (3)+e^{2 e^{3+x}} \log ^2(3)+e^{e^{3+x}} \left (-4+2 x-2 x^2\right ) \log ^2(3)+\left (13-4 x+5 x^2-2 x^3+x^4\right ) \log ^2(3)}{\log ^2(3)}} \left (-4+2 e^{3+2 e^{3+x}+x}+10 x-6 x^2+4 x^3+e^{e^{3+x}} \left (2-4 x+e^{3+x} \left (-4+2 x-2 x^2\right )\right )\right ) \, dx=e^{\left (x^{4} - 2 \, x^{3} - 2 \, x^{2} e^{\left (e^{\left (x + 3\right )}\right )} + 5 \, x^{2} + 2 \, x e^{\left (e^{\left (x + 3\right )}\right )} - 4 \, x - \frac {12}{\log \left (3\right )} + \frac {4}{\log \left (3\right )^{2}} + e^{\left (2 \, e^{\left (x + 3\right )}\right )} - 4 \, e^{\left (e^{\left (x + 3\right )}\right )} + 13\right )} \]

[In]

integrate((2*exp(3+x)*exp(exp(3+x))^2+((-2*x^2+2*x-4)*exp(3+x)-4*x+2)*exp(exp(3+x))+4*x^3-6*x^2+10*x-4)*exp((l
og(3)^2*exp(exp(3+x))^2+(-2*x^2+2*x-4)*log(3)^2*exp(exp(3+x))+(x^4-2*x^3+5*x^2-4*x+13)*log(3)^2-12*log(3)+4)/l
og(3)^2),x, algorithm="maxima")

[Out]

e^(x^4 - 2*x^3 - 2*x^2*e^(e^(x + 3)) + 5*x^2 + 2*x*e^(e^(x + 3)) - 4*x - 12/log(3) + 4/log(3)^2 + e^(2*e^(x +
3)) - 4*e^(e^(x + 3)) + 13)

Giac [F]

\[ \int e^{\frac {4-12 \log (3)+e^{2 e^{3+x}} \log ^2(3)+e^{e^{3+x}} \left (-4+2 x-2 x^2\right ) \log ^2(3)+\left (13-4 x+5 x^2-2 x^3+x^4\right ) \log ^2(3)}{\log ^2(3)}} \left (-4+2 e^{3+2 e^{3+x}+x}+10 x-6 x^2+4 x^3+e^{e^{3+x}} \left (2-4 x+e^{3+x} \left (-4+2 x-2 x^2\right )\right )\right ) \, dx=\int { 2 \, {\left (2 \, x^{3} - 3 \, x^{2} - {\left ({\left (x^{2} - x + 2\right )} e^{\left (x + 3\right )} + 2 \, x - 1\right )} e^{\left (e^{\left (x + 3\right )}\right )} + 5 \, x + e^{\left (x + 2 \, e^{\left (x + 3\right )} + 3\right )} - 2\right )} e^{\left (-\frac {2 \, {\left (x^{2} - x + 2\right )} e^{\left (e^{\left (x + 3\right )}\right )} \log \left (3\right )^{2} - {\left (x^{4} - 2 \, x^{3} + 5 \, x^{2} - 4 \, x + 13\right )} \log \left (3\right )^{2} - e^{\left (2 \, e^{\left (x + 3\right )}\right )} \log \left (3\right )^{2} + 12 \, \log \left (3\right ) - 4}{\log \left (3\right )^{2}}\right )} \,d x } \]

[In]

integrate((2*exp(3+x)*exp(exp(3+x))^2+((-2*x^2+2*x-4)*exp(3+x)-4*x+2)*exp(exp(3+x))+4*x^3-6*x^2+10*x-4)*exp((l
og(3)^2*exp(exp(3+x))^2+(-2*x^2+2*x-4)*log(3)^2*exp(exp(3+x))+(x^4-2*x^3+5*x^2-4*x+13)*log(3)^2-12*log(3)+4)/l
og(3)^2),x, algorithm="giac")

[Out]

integrate(2*(2*x^3 - 3*x^2 - ((x^2 - x + 2)*e^(x + 3) + 2*x - 1)*e^(e^(x + 3)) + 5*x + e^(x + 2*e^(x + 3) + 3)
- 2)*e^(-(2*(x^2 - x + 2)*e^(e^(x + 3))*log(3)^2 - (x^4 - 2*x^3 + 5*x^2 - 4*x + 13)*log(3)^2 - e^(2*e^(x + 3)
)*log(3)^2 + 12*log(3) - 4)/log(3)^2), x)

Mupad [B] (verification not implemented)

Time = 9.37 (sec) , antiderivative size = 76, normalized size of antiderivative = 2.38 \[ \int e^{\frac {4-12 \log (3)+e^{2 e^{3+x}} \log ^2(3)+e^{e^{3+x}} \left (-4+2 x-2 x^2\right ) \log ^2(3)+\left (13-4 x+5 x^2-2 x^3+x^4\right ) \log ^2(3)}{\log ^2(3)}} \left (-4+2 e^{3+2 e^{3+x}+x}+10 x-6 x^2+4 x^3+e^{e^{3+x}} \left (2-4 x+e^{3+x} \left (-4+2 x-2 x^2\right )\right )\right ) \, dx={\mathrm {e}}^{-4\,x}\,{\mathrm {e}}^{x^4}\,{\mathrm {e}}^{2\,x\,{\mathrm {e}}^{{\mathrm {e}}^3\,{\mathrm {e}}^x}}\,{\mathrm {e}}^{13}\,{\mathrm {e}}^{{\mathrm {e}}^{2\,{\mathrm {e}}^3\,{\mathrm {e}}^x}}\,{\mathrm {e}}^{\frac {4}{{\ln \left (3\right )}^2}}\,{\mathrm {e}}^{-\frac {12}{\ln \left (3\right )}}\,{\mathrm {e}}^{-2\,x^3}\,{\mathrm {e}}^{5\,x^2}\,{\mathrm {e}}^{-2\,x^2\,{\mathrm {e}}^{{\mathrm {e}}^3\,{\mathrm {e}}^x}}\,{\mathrm {e}}^{-4\,{\mathrm {e}}^{{\mathrm {e}}^3\,{\mathrm {e}}^x}} \]

[In]

int(exp((exp(2*exp(x + 3))*log(3)^2 - 12*log(3) + log(3)^2*(5*x^2 - 4*x - 2*x^3 + x^4 + 13) - exp(exp(x + 3))*
log(3)^2*(2*x^2 - 2*x + 4) + 4)/log(3)^2)*(10*x - exp(exp(x + 3))*(4*x + exp(x + 3)*(2*x^2 - 2*x + 4) - 2) + 2
*exp(2*exp(x + 3))*exp(x + 3) - 6*x^2 + 4*x^3 - 4),x)

[Out]

exp(-4*x)*exp(x^4)*exp(2*x*exp(exp(3)*exp(x)))*exp(13)*exp(exp(2*exp(3)*exp(x)))*exp(4/log(3)^2)*exp(-12/log(3
))*exp(-2*x^3)*exp(5*x^2)*exp(-2*x^2*exp(exp(3)*exp(x)))*exp(-4*exp(exp(3)*exp(x)))