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