Integrand size = 97, antiderivative size = 30 \[ \int \frac {e^{-x+\frac {e^{-x} \left (-3 x^3+3 e^x x^4+e^x \left (x-x^2\right ) \log (x)\right )}{\log (x)}} \left (3 x^2-3 e^x x^3+\left (-9 x^2+3 x^3+12 e^x x^3\right ) \log (x)+e^x (1-2 x) \log ^2(x)\right )}{\log ^2(x)} \, dx=e^{x-x^2+\frac {3 x^2 \left (-e^{-x} x+x^2\right )}{\log (x)}} \]
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\[ \int \frac {e^{-x+\frac {e^{-x} \left (-3 x^3+3 e^x x^4+e^x \left (x-x^2\right ) \log (x)\right )}{\log (x)}} \left (3 x^2-3 e^x x^3+\left (-9 x^2+3 x^3+12 e^x x^3\right ) \log (x)+e^x (1-2 x) \log ^2(x)\right )}{\log ^2(x)} \, dx=\int \frac {\exp \left (-x+\frac {e^{-x} \left (-3 x^3+3 e^x x^4+e^x \left (x-x^2\right ) \log (x)\right )}{\log (x)}\right ) \left (3 x^2-3 e^x x^3+\left (-9 x^2+3 x^3+12 e^x x^3\right ) \log (x)+e^x (1-2 x) \log ^2(x)\right )}{\log ^2(x)} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {\exp \left (\frac {e^{-x} x^2 \left (-3 x+3 e^x x^2-e^x \log (x)\right )}{\log (x)}\right ) \left (3 x^2-3 e^x x^3+\left (-9 x^2+3 x^3+12 e^x x^3\right ) \log (x)+e^x (1-2 x) \log ^2(x)\right )}{\log ^2(x)} \, dx \\ & = \int \left (\frac {3 \exp \left (\frac {e^{-x} x^2 \left (-3 x+3 e^x x^2-e^x \log (x)\right )}{\log (x)}\right ) x^2 (1-3 \log (x)+x \log (x))}{\log ^2(x)}-\frac {\exp \left (x+\frac {e^{-x} x^2 \left (-3 x+3 e^x x^2-e^x \log (x)\right )}{\log (x)}\right ) \left (3 x^3-12 x^3 \log (x)-\log ^2(x)+2 x \log ^2(x)\right )}{\log ^2(x)}\right ) \, dx \\ & = 3 \int \frac {\exp \left (\frac {e^{-x} x^2 \left (-3 x+3 e^x x^2-e^x \log (x)\right )}{\log (x)}\right ) x^2 (1-3 \log (x)+x \log (x))}{\log ^2(x)} \, dx-\int \frac {\exp \left (x+\frac {e^{-x} x^2 \left (-3 x+3 e^x x^2-e^x \log (x)\right )}{\log (x)}\right ) \left (3 x^3-12 x^3 \log (x)-\log ^2(x)+2 x \log ^2(x)\right )}{\log ^2(x)} \, dx \\ & = 3 \int \left (\frac {\exp \left (\frac {e^{-x} x^2 \left (-3 x+3 e^x x^2-e^x \log (x)\right )}{\log (x)}\right ) x^2}{\log ^2(x)}+\frac {\exp \left (\frac {e^{-x} x^2 \left (-3 x+3 e^x x^2-e^x \log (x)\right )}{\log (x)}\right ) (-3+x) x^2}{\log (x)}\right ) \, dx-\int \left (-\exp \left (x+\frac {e^{-x} x^2 \left (-3 x+3 e^x x^2-e^x \log (x)\right )}{\log (x)}\right )+2 \exp \left (x+\frac {e^{-x} x^2 \left (-3 x+3 e^x x^2-e^x \log (x)\right )}{\log (x)}\right ) x+\frac {3 \exp \left (x+\frac {e^{-x} x^2 \left (-3 x+3 e^x x^2-e^x \log (x)\right )}{\log (x)}\right ) x^3}{\log ^2(x)}-\frac {12 \exp \left (x+\frac {e^{-x} x^2 \left (-3 x+3 e^x x^2-e^x \log (x)\right )}{\log (x)}\right ) x^3}{\log (x)}\right ) \, dx \\ & = -\left (2 \int \exp \left (x+\frac {e^{-x} x^2 \left (-3 x+3 e^x x^2-e^x \log (x)\right )}{\log (x)}\right ) x \, dx\right )+3 \int \frac {\exp \left (\frac {e^{-x} x^2 \left (-3 x+3 e^x x^2-e^x \log (x)\right )}{\log (x)}\right ) x^2}{\log ^2(x)} \, dx-3 \int \frac {\exp \left (x+\frac {e^{-x} x^2 \left (-3 x+3 e^x x^2-e^x \log (x)\right )}{\log (x)}\right ) x^3}{\log ^2(x)} \, dx+3 \int \frac {\exp \left (\frac {e^{-x} x^2 \left (-3 x+3 e^x x^2-e^x \log (x)\right )}{\log (x)}\right ) (-3+x) x^2}{\log (x)} \, dx+12 \int \frac {\exp \left (x+\frac {e^{-x} x^2 \left (-3 x+3 e^x x^2-e^x \log (x)\right )}{\log (x)}\right ) x^3}{\log (x)} \, dx+\int \exp \left (x+\frac {e^{-x} x^2 \left (-3 x+3 e^x x^2-e^x \log (x)\right )}{\log (x)}\right ) \, dx \\ & = -\left (2 \int \exp \left (x+\frac {e^{-x} x^2 \left (-3 x+3 e^x x^2-e^x \log (x)\right )}{\log (x)}\right ) x \, dx\right )+3 \int \left (-\frac {3 \exp \left (\frac {e^{-x} x^2 \left (-3 x+3 e^x x^2-e^x \log (x)\right )}{\log (x)}\right ) x^2}{\log (x)}+\frac {\exp \left (\frac {e^{-x} x^2 \left (-3 x+3 e^x x^2-e^x \log (x)\right )}{\log (x)}\right ) x^3}{\log (x)}\right ) \, dx+3 \int \frac {\exp \left (\frac {e^{-x} x^2 \left (-3 x+3 e^x x^2-e^x \log (x)\right )}{\log (x)}\right ) x^2}{\log ^2(x)} \, dx-3 \int \frac {\exp \left (x+\frac {e^{-x} x^2 \left (-3 x+3 e^x x^2-e^x \log (x)\right )}{\log (x)}\right ) x^3}{\log ^2(x)} \, dx+12 \int \frac {\exp \left (x+\frac {e^{-x} x^2 \left (-3 x+3 e^x x^2-e^x \log (x)\right )}{\log (x)}\right ) x^3}{\log (x)} \, dx+\int \exp \left (x+\frac {e^{-x} x^2 \left (-3 x+3 e^x x^2-e^x \log (x)\right )}{\log (x)}\right ) \, dx \\ & = -\left (2 \int \exp \left (x+\frac {e^{-x} x^2 \left (-3 x+3 e^x x^2-e^x \log (x)\right )}{\log (x)}\right ) x \, dx\right )+3 \int \frac {\exp \left (\frac {e^{-x} x^2 \left (-3 x+3 e^x x^2-e^x \log (x)\right )}{\log (x)}\right ) x^2}{\log ^2(x)} \, dx-3 \int \frac {\exp \left (x+\frac {e^{-x} x^2 \left (-3 x+3 e^x x^2-e^x \log (x)\right )}{\log (x)}\right ) x^3}{\log ^2(x)} \, dx+3 \int \frac {\exp \left (\frac {e^{-x} x^2 \left (-3 x+3 e^x x^2-e^x \log (x)\right )}{\log (x)}\right ) x^3}{\log (x)} \, dx-9 \int \frac {\exp \left (\frac {e^{-x} x^2 \left (-3 x+3 e^x x^2-e^x \log (x)\right )}{\log (x)}\right ) x^2}{\log (x)} \, dx+12 \int \frac {\exp \left (x+\frac {e^{-x} x^2 \left (-3 x+3 e^x x^2-e^x \log (x)\right )}{\log (x)}\right ) x^3}{\log (x)} \, dx+\int \exp \left (x+\frac {e^{-x} x^2 \left (-3 x+3 e^x x^2-e^x \log (x)\right )}{\log (x)}\right ) \, dx \\ \end{align*}
Time = 5.16 (sec) , antiderivative size = 27, normalized size of antiderivative = 0.90 \[ \int \frac {e^{-x+\frac {e^{-x} \left (-3 x^3+3 e^x x^4+e^x \left (x-x^2\right ) \log (x)\right )}{\log (x)}} \left (3 x^2-3 e^x x^3+\left (-9 x^2+3 x^3+12 e^x x^3\right ) \log (x)+e^x (1-2 x) \log ^2(x)\right )}{\log ^2(x)} \, dx=e^{x-x^2-\frac {3 \left (e^{-x}-x\right ) x^3}{\log (x)}} \]
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Time = 0.83 (sec) , antiderivative size = 36, normalized size of antiderivative = 1.20
method | result | size |
parallelrisch | \({\mathrm e}^{\frac {\left (\left (-x^{2}+x \right ) {\mathrm e}^{x} \ln \left (x \right )+3 \,{\mathrm e}^{x} x^{4}-3 x^{3}\right ) {\mathrm e}^{-x}}{\ln \left (x \right )}}\) | \(36\) |
risch | \({\mathrm e}^{-\frac {x \left (-3 \,{\mathrm e}^{x} x^{3}+x \,{\mathrm e}^{x} \ln \left (x \right )-{\mathrm e}^{x} \ln \left (x \right )+3 x^{2}\right ) {\mathrm e}^{-x}}{\ln \left (x \right )}}\) | \(38\) |
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Time = 0.25 (sec) , antiderivative size = 34, normalized size of antiderivative = 1.13 \[ \int \frac {e^{-x+\frac {e^{-x} \left (-3 x^3+3 e^x x^4+e^x \left (x-x^2\right ) \log (x)\right )}{\log (x)}} \left (3 x^2-3 e^x x^3+\left (-9 x^2+3 x^3+12 e^x x^3\right ) \log (x)+e^x (1-2 x) \log ^2(x)\right )}{\log ^2(x)} \, dx=e^{\left (x + \frac {{\left (3 \, x^{4} e^{x} - x^{2} e^{x} \log \left (x\right ) - 3 \, x^{3}\right )} e^{\left (-x\right )}}{\log \left (x\right )}\right )} \]
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Time = 0.38 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.07 \[ \int \frac {e^{-x+\frac {e^{-x} \left (-3 x^3+3 e^x x^4+e^x \left (x-x^2\right ) \log (x)\right )}{\log (x)}} \left (3 x^2-3 e^x x^3+\left (-9 x^2+3 x^3+12 e^x x^3\right ) \log (x)+e^x (1-2 x) \log ^2(x)\right )}{\log ^2(x)} \, dx=e^{\frac {\left (3 x^{4} e^{x} - 3 x^{3} + \left (- x^{2} + x\right ) e^{x} \log {\left (x \right )}\right ) e^{- x}}{\log {\left (x \right )}}} \]
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Time = 0.35 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.00 \[ \int \frac {e^{-x+\frac {e^{-x} \left (-3 x^3+3 e^x x^4+e^x \left (x-x^2\right ) \log (x)\right )}{\log (x)}} \left (3 x^2-3 e^x x^3+\left (-9 x^2+3 x^3+12 e^x x^3\right ) \log (x)+e^x (1-2 x) \log ^2(x)\right )}{\log ^2(x)} \, dx=e^{\left (\frac {3 \, x^{4}}{\log \left (x\right )} - \frac {3 \, x^{3} e^{\left (-x\right )}}{\log \left (x\right )} - x^{2} + x\right )} \]
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\[ \int \frac {e^{-x+\frac {e^{-x} \left (-3 x^3+3 e^x x^4+e^x \left (x-x^2\right ) \log (x)\right )}{\log (x)}} \left (3 x^2-3 e^x x^3+\left (-9 x^2+3 x^3+12 e^x x^3\right ) \log (x)+e^x (1-2 x) \log ^2(x)\right )}{\log ^2(x)} \, dx=\int { -\frac {{\left (3 \, x^{3} e^{x} + {\left (2 \, x - 1\right )} e^{x} \log \left (x\right )^{2} - 3 \, x^{2} - 3 \, {\left (4 \, x^{3} e^{x} + x^{3} - 3 \, x^{2}\right )} \log \left (x\right )\right )} e^{\left (-x + \frac {{\left (3 \, x^{4} e^{x} - 3 \, x^{3} - {\left (x^{2} - x\right )} e^{x} \log \left (x\right )\right )} e^{\left (-x\right )}}{\log \left (x\right )}\right )}}{\log \left (x\right )^{2}} \,d x } \]
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Time = 7.14 (sec) , antiderivative size = 33, normalized size of antiderivative = 1.10 \[ \int \frac {e^{-x+\frac {e^{-x} \left (-3 x^3+3 e^x x^4+e^x \left (x-x^2\right ) \log (x)\right )}{\log (x)}} \left (3 x^2-3 e^x x^3+\left (-9 x^2+3 x^3+12 e^x x^3\right ) \log (x)+e^x (1-2 x) \log ^2(x)\right )}{\log ^2(x)} \, dx={\mathrm {e}}^{-\frac {3\,x^3\,{\mathrm {e}}^{-x}}{\ln \left (x\right )}}\,{\mathrm {e}}^{-x^2}\,{\mathrm {e}}^x\,{\mathrm {e}}^{\frac {3\,x^4}{\ln \left (x\right )}} \]
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