Integrand size = 168, antiderivative size = 38 \[ \int \frac {e^{\frac {-2 e^{2 x}-8 x+e^x (8+2 x)+\left (4 x^2+3 x^3+e^x \left (-4 x-x^2\right )\right ) \log (x)}{2 e^x-2 x}} \left (-2 e^{3 x}-4 x^2-3 x^3+e^{2 x} (-4+3 x)+e^x \left (8 x+2 x^2\right )+\left (e^{2 x} (-4-2 x)-4 x^2-6 x^3+e^x \left (8 x+10 x^2-2 x^3\right )\right ) \log (x)\right )}{2 e^{2 x}-4 e^x x+2 x^2} \, dx=e^{4-e^x+x^2 \left (\frac {1}{2} \left (-1-\frac {4}{x}\right )+\frac {x}{e^x-x}\right ) \log (x)} \]
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\[ \int \frac {e^{\frac {-2 e^{2 x}-8 x+e^x (8+2 x)+\left (4 x^2+3 x^3+e^x \left (-4 x-x^2\right )\right ) \log (x)}{2 e^x-2 x}} \left (-2 e^{3 x}-4 x^2-3 x^3+e^{2 x} (-4+3 x)+e^x \left (8 x+2 x^2\right )+\left (e^{2 x} (-4-2 x)-4 x^2-6 x^3+e^x \left (8 x+10 x^2-2 x^3\right )\right ) \log (x)\right )}{2 e^{2 x}-4 e^x x+2 x^2} \, dx=\int \frac {\exp \left (\frac {-2 e^{2 x}-8 x+e^x (8+2 x)+\left (4 x^2+3 x^3+e^x \left (-4 x-x^2\right )\right ) \log (x)}{2 e^x-2 x}\right ) \left (-2 e^{3 x}-4 x^2-3 x^3+e^{2 x} (-4+3 x)+e^x \left (8 x+2 x^2\right )+\left (e^{2 x} (-4-2 x)-4 x^2-6 x^3+e^x \left (8 x+10 x^2-2 x^3\right )\right ) \log (x)\right )}{2 e^{2 x}-4 e^x x+2 x^2} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {\exp \left (\frac {-2 e^{2 x}-8 x+e^x (8+2 x)+\left (4 x^2+3 x^3+e^x \left (-4 x-x^2\right )\right ) \log (x)}{2 \left (e^x-x\right )}\right ) \left (-2 e^{3 x}-4 x^2-3 x^3+e^{2 x} (-4+3 x)+e^x \left (8 x+2 x^2\right )+\left (e^{2 x} (-4-2 x)-4 x^2-6 x^3+e^x \left (8 x+10 x^2-2 x^3\right )\right ) \log (x)\right )}{2 \left (e^x-x\right )^2} \, dx \\ & = \frac {1}{2} \int \frac {\exp \left (\frac {-2 e^{2 x}-8 x+e^x (8+2 x)+\left (4 x^2+3 x^3+e^x \left (-4 x-x^2\right )\right ) \log (x)}{2 \left (e^x-x\right )}\right ) \left (-2 e^{3 x}-4 x^2-3 x^3+e^{2 x} (-4+3 x)+e^x \left (8 x+2 x^2\right )+\left (e^{2 x} (-4-2 x)-4 x^2-6 x^3+e^x \left (8 x+10 x^2-2 x^3\right )\right ) \log (x)\right )}{\left (e^x-x\right )^2} \, dx \\ & = \frac {1}{2} \int \left (-4 \exp \left (\frac {-2 e^{2 x}-8 x+e^x (8+2 x)+\left (4 x^2+3 x^3+e^x \left (-4 x-x^2\right )\right ) \log (x)}{2 \left (e^x-x\right )}\right )-2 \exp \left (x+\frac {-2 e^{2 x}-8 x+e^x (8+2 x)+\left (4 x^2+3 x^3+e^x \left (-4 x-x^2\right )\right ) \log (x)}{2 \left (e^x-x\right )}\right )-\exp \left (\frac {-2 e^{2 x}-8 x+e^x (8+2 x)+\left (4 x^2+3 x^3+e^x \left (-4 x-x^2\right )\right ) \log (x)}{2 \left (e^x-x\right )}\right ) x-4 \exp \left (\frac {-2 e^{2 x}-8 x+e^x (8+2 x)+\left (4 x^2+3 x^3+e^x \left (-4 x-x^2\right )\right ) \log (x)}{2 \left (e^x-x\right )}\right ) \log (x)-2 \exp \left (\frac {-2 e^{2 x}-8 x+e^x (8+2 x)+\left (4 x^2+3 x^3+e^x \left (-4 x-x^2\right )\right ) \log (x)}{2 \left (e^x-x\right )}\right ) x \log (x)-\frac {2 \exp \left (\frac {-2 e^{2 x}-8 x+e^x (8+2 x)+\left (4 x^2+3 x^3+e^x \left (-4 x-x^2\right )\right ) \log (x)}{2 \left (e^x-x\right )}\right ) (-1+x) x^3 \log (x)}{\left (e^x-x\right )^2}-\frac {2 \exp \left (\frac {-2 e^{2 x}-8 x+e^x (8+2 x)+\left (4 x^2+3 x^3+e^x \left (-4 x-x^2\right )\right ) \log (x)}{2 \left (e^x-x\right )}\right ) x^2 (-1-3 \log (x)+x \log (x))}{e^x-x}\right ) \, dx \\ & = -\left (\frac {1}{2} \int \exp \left (\frac {-2 e^{2 x}-8 x+e^x (8+2 x)+\left (4 x^2+3 x^3+e^x \left (-4 x-x^2\right )\right ) \log (x)}{2 \left (e^x-x\right )}\right ) x \, dx\right )-2 \int \exp \left (\frac {-2 e^{2 x}-8 x+e^x (8+2 x)+\left (4 x^2+3 x^3+e^x \left (-4 x-x^2\right )\right ) \log (x)}{2 \left (e^x-x\right )}\right ) \, dx-2 \int \exp \left (\frac {-2 e^{2 x}-8 x+e^x (8+2 x)+\left (4 x^2+3 x^3+e^x \left (-4 x-x^2\right )\right ) \log (x)}{2 \left (e^x-x\right )}\right ) \log (x) \, dx-\int \exp \left (x+\frac {-2 e^{2 x}-8 x+e^x (8+2 x)+\left (4 x^2+3 x^3+e^x \left (-4 x-x^2\right )\right ) \log (x)}{2 \left (e^x-x\right )}\right ) \, dx-\int \exp \left (\frac {-2 e^{2 x}-8 x+e^x (8+2 x)+\left (4 x^2+3 x^3+e^x \left (-4 x-x^2\right )\right ) \log (x)}{2 \left (e^x-x\right )}\right ) x \log (x) \, dx-\int \frac {\exp \left (\frac {-2 e^{2 x}-8 x+e^x (8+2 x)+\left (4 x^2+3 x^3+e^x \left (-4 x-x^2\right )\right ) \log (x)}{2 \left (e^x-x\right )}\right ) (-1+x) x^3 \log (x)}{\left (e^x-x\right )^2} \, dx-\int \frac {\exp \left (\frac {-2 e^{2 x}-8 x+e^x (8+2 x)+\left (4 x^2+3 x^3+e^x \left (-4 x-x^2\right )\right ) \log (x)}{2 \left (e^x-x\right )}\right ) x^2 (-1-3 \log (x)+x \log (x))}{e^x-x} \, dx \\ & = -\left (\frac {1}{2} \int e^{4-e^x} x^{1+\frac {x \left (-e^x (4+x)+x (4+3 x)\right )}{2 \left (e^x-x\right )}} \, dx\right )-2 \int e^{4-e^x} x^{\frac {x \left (-e^x (4+x)+x (4+3 x)\right )}{2 \left (e^x-x\right )}} \, dx+2 \int \frac {\int e^{4-e^x} x^{\frac {x \left (-e^x (4+x)+x (4+3 x)\right )}{2 \left (e^x-x\right )}} \, dx}{x} \, dx-\log (x) \int e^{4-e^x} x^{1+\frac {x \left (-e^x (4+x)+x (4+3 x)\right )}{2 \left (e^x-x\right )}} \, dx+\log (x) \int \frac {e^{4-e^x} x^{3+\frac {x \left (-e^x (4+x)+x (4+3 x)\right )}{2 \left (e^x-x\right )}}}{\left (e^x-x\right )^2} \, dx-\log (x) \int \frac {e^{4-e^x} x^{4+\frac {x \left (-e^x (4+x)+x (4+3 x)\right )}{2 \left (e^x-x\right )}}}{\left (e^x-x\right )^2} \, dx-(2 \log (x)) \int e^{4-e^x} x^{\frac {x \left (-e^x (4+x)+x (4+3 x)\right )}{2 \left (e^x-x\right )}} \, dx-\int e^{4-e^x+x} x^{\frac {x \left (-e^x (4+x)+x (4+3 x)\right )}{2 \left (e^x-x\right )}} \, dx-\int \frac {e^{4-e^x} x^{2+\frac {x \left (-e^x (4+x)+x (4+3 x)\right )}{2 \left (e^x-x\right )}} (-1+(-3+x) \log (x))}{e^x-x} \, dx+\int \frac {\int e^{4-e^x} x^{1+\frac {x \left (-e^x (4+x)+x (4+3 x)\right )}{2 \left (e^x-x\right )}} \, dx}{x} \, dx+\int \frac {-\int \frac {e^{4-e^x} x^{3+\frac {x \left (-e^x (4+x)+x (4+3 x)\right )}{2 \left (e^x-x\right )}}}{\left (e^x-x\right )^2} \, dx+\int \frac {e^{4-e^x} x^{4+\frac {x \left (-e^x (4+x)+x (4+3 x)\right )}{2 \left (e^x-x\right )}}}{\left (e^x-x\right )^2} \, dx}{x} \, dx \\ & = -\left (\frac {1}{2} \int e^{4-e^x} x^{1+\frac {x \left (-e^x (4+x)+x (4+3 x)\right )}{2 \left (e^x-x\right )}} \, dx\right )-2 \int e^{4-e^x} x^{\frac {x \left (-e^x (4+x)+x (4+3 x)\right )}{2 \left (e^x-x\right )}} \, dx+2 \int \frac {\int e^{4-e^x} x^{\frac {x \left (-e^x (4+x)+x (4+3 x)\right )}{2 \left (e^x-x\right )}} \, dx}{x} \, dx-\log (x) \int e^{4-e^x} x^{1+\frac {x \left (-e^x (4+x)+x (4+3 x)\right )}{2 \left (e^x-x\right )}} \, dx+\log (x) \int \frac {e^{4-e^x} x^{3+\frac {x \left (-e^x (4+x)+x (4+3 x)\right )}{2 \left (e^x-x\right )}}}{\left (e^x-x\right )^2} \, dx-\log (x) \int \frac {e^{4-e^x} x^{4+\frac {x \left (-e^x (4+x)+x (4+3 x)\right )}{2 \left (e^x-x\right )}}}{\left (e^x-x\right )^2} \, dx-(2 \log (x)) \int e^{4-e^x} x^{\frac {x \left (-e^x (4+x)+x (4+3 x)\right )}{2 \left (e^x-x\right )}} \, dx-\int e^{4-e^x+x} x^{\frac {x \left (-e^x (4+x)+x (4+3 x)\right )}{2 \left (e^x-x\right )}} \, dx-\int \left (-\frac {e^{4-e^x} x^{2+\frac {x \left (-e^x (4+x)+x (4+3 x)\right )}{2 \left (e^x-x\right )}}}{e^x-x}-\frac {3 e^{4-e^x} x^{2+\frac {x \left (-e^x (4+x)+x (4+3 x)\right )}{2 \left (e^x-x\right )}} \log (x)}{e^x-x}+\frac {e^{4-e^x} x^{3+\frac {x \left (-e^x (4+x)+x (4+3 x)\right )}{2 \left (e^x-x\right )}} \log (x)}{e^x-x}\right ) \, dx+\int \frac {\int e^{4-e^x} x^{1+\frac {x \left (-e^x (4+x)+x (4+3 x)\right )}{2 \left (e^x-x\right )}} \, dx}{x} \, dx+\int \left (-\frac {\int \frac {e^{4-e^x} x^{3+\frac {x \left (-e^x (4+x)+x (4+3 x)\right )}{2 \left (e^x-x\right )}}}{\left (e^x-x\right )^2} \, dx}{x}+\frac {\int \frac {e^{4-e^x} x^{4+\frac {x \left (-e^x (4+x)+x (4+3 x)\right )}{2 \left (e^x-x\right )}}}{\left (e^x-x\right )^2} \, dx}{x}\right ) \, dx \\ & = -\left (\frac {1}{2} \int e^{4-e^x} x^{1+\frac {x \left (-e^x (4+x)+x (4+3 x)\right )}{2 \left (e^x-x\right )}} \, dx\right )-2 \int e^{4-e^x} x^{\frac {x \left (-e^x (4+x)+x (4+3 x)\right )}{2 \left (e^x-x\right )}} \, dx+2 \int \frac {\int e^{4-e^x} x^{\frac {x \left (-e^x (4+x)+x (4+3 x)\right )}{2 \left (e^x-x\right )}} \, dx}{x} \, dx+3 \int \frac {e^{4-e^x} x^{2+\frac {x \left (-e^x (4+x)+x (4+3 x)\right )}{2 \left (e^x-x\right )}} \log (x)}{e^x-x} \, dx-\log (x) \int e^{4-e^x} x^{1+\frac {x \left (-e^x (4+x)+x (4+3 x)\right )}{2 \left (e^x-x\right )}} \, dx+\log (x) \int \frac {e^{4-e^x} x^{3+\frac {x \left (-e^x (4+x)+x (4+3 x)\right )}{2 \left (e^x-x\right )}}}{\left (e^x-x\right )^2} \, dx-\log (x) \int \frac {e^{4-e^x} x^{4+\frac {x \left (-e^x (4+x)+x (4+3 x)\right )}{2 \left (e^x-x\right )}}}{\left (e^x-x\right )^2} \, dx-(2 \log (x)) \int e^{4-e^x} x^{\frac {x \left (-e^x (4+x)+x (4+3 x)\right )}{2 \left (e^x-x\right )}} \, dx-\int e^{4-e^x+x} x^{\frac {x \left (-e^x (4+x)+x (4+3 x)\right )}{2 \left (e^x-x\right )}} \, dx+\int \frac {e^{4-e^x} x^{2+\frac {x \left (-e^x (4+x)+x (4+3 x)\right )}{2 \left (e^x-x\right )}}}{e^x-x} \, dx-\int \frac {e^{4-e^x} x^{3+\frac {x \left (-e^x (4+x)+x (4+3 x)\right )}{2 \left (e^x-x\right )}} \log (x)}{e^x-x} \, dx+\int \frac {\int e^{4-e^x} x^{1+\frac {x \left (-e^x (4+x)+x (4+3 x)\right )}{2 \left (e^x-x\right )}} \, dx}{x} \, dx-\int \frac {\int \frac {e^{4-e^x} x^{3+\frac {x \left (-e^x (4+x)+x (4+3 x)\right )}{2 \left (e^x-x\right )}}}{\left (e^x-x\right )^2} \, dx}{x} \, dx+\int \frac {\int \frac {e^{4-e^x} x^{4+\frac {x \left (-e^x (4+x)+x (4+3 x)\right )}{2 \left (e^x-x\right )}}}{\left (e^x-x\right )^2} \, dx}{x} \, dx \\ & = -\left (\frac {1}{2} \int e^{4-e^x} x^{1+\frac {x \left (-e^x (4+x)+x (4+3 x)\right )}{2 \left (e^x-x\right )}} \, dx\right )-2 \int e^{4-e^x} x^{\frac {x \left (-e^x (4+x)+x (4+3 x)\right )}{2 \left (e^x-x\right )}} \, dx+2 \int \frac {\int e^{4-e^x} x^{\frac {x \left (-e^x (4+x)+x (4+3 x)\right )}{2 \left (e^x-x\right )}} \, dx}{x} \, dx-3 \int \frac {\int \frac {e^{4-e^x} x^{2+\frac {x \left (-e^x (4+x)+x (4+3 x)\right )}{2 \left (e^x-x\right )}}}{e^x-x} \, dx}{x} \, dx-\log (x) \int e^{4-e^x} x^{1+\frac {x \left (-e^x (4+x)+x (4+3 x)\right )}{2 \left (e^x-x\right )}} \, dx+\log (x) \int \frac {e^{4-e^x} x^{3+\frac {x \left (-e^x (4+x)+x (4+3 x)\right )}{2 \left (e^x-x\right )}}}{\left (e^x-x\right )^2} \, dx-\log (x) \int \frac {e^{4-e^x} x^{3+\frac {x \left (-e^x (4+x)+x (4+3 x)\right )}{2 \left (e^x-x\right )}}}{e^x-x} \, dx-\log (x) \int \frac {e^{4-e^x} x^{4+\frac {x \left (-e^x (4+x)+x (4+3 x)\right )}{2 \left (e^x-x\right )}}}{\left (e^x-x\right )^2} \, dx-(2 \log (x)) \int e^{4-e^x} x^{\frac {x \left (-e^x (4+x)+x (4+3 x)\right )}{2 \left (e^x-x\right )}} \, dx+(3 \log (x)) \int \frac {e^{4-e^x} x^{2+\frac {x \left (-e^x (4+x)+x (4+3 x)\right )}{2 \left (e^x-x\right )}}}{e^x-x} \, dx-\int e^{4-e^x+x} x^{\frac {x \left (-e^x (4+x)+x (4+3 x)\right )}{2 \left (e^x-x\right )}} \, dx+\int \frac {e^{4-e^x} x^{2+\frac {x \left (-e^x (4+x)+x (4+3 x)\right )}{2 \left (e^x-x\right )}}}{e^x-x} \, dx+\int \frac {\int e^{4-e^x} x^{1+\frac {x \left (-e^x (4+x)+x (4+3 x)\right )}{2 \left (e^x-x\right )}} \, dx}{x} \, dx-\int \frac {\int \frac {e^{4-e^x} x^{3+\frac {x \left (-e^x (4+x)+x (4+3 x)\right )}{2 \left (e^x-x\right )}}}{\left (e^x-x\right )^2} \, dx}{x} \, dx+\int \frac {\int \frac {e^{4-e^x} x^{3+\frac {x \left (-e^x (4+x)+x (4+3 x)\right )}{2 \left (e^x-x\right )}}}{e^x-x} \, dx}{x} \, dx+\int \frac {\int \frac {e^{4-e^x} x^{4+\frac {x \left (-e^x (4+x)+x (4+3 x)\right )}{2 \left (e^x-x\right )}}}{\left (e^x-x\right )^2} \, dx}{x} \, dx \\ \end{align*}
Time = 0.24 (sec) , antiderivative size = 42, normalized size of antiderivative = 1.11 \[ \int \frac {e^{\frac {-2 e^{2 x}-8 x+e^x (8+2 x)+\left (4 x^2+3 x^3+e^x \left (-4 x-x^2\right )\right ) \log (x)}{2 e^x-2 x}} \left (-2 e^{3 x}-4 x^2-3 x^3+e^{2 x} (-4+3 x)+e^x \left (8 x+2 x^2\right )+\left (e^{2 x} (-4-2 x)-4 x^2-6 x^3+e^x \left (8 x+10 x^2-2 x^3\right )\right ) \log (x)\right )}{2 e^{2 x}-4 e^x x+2 x^2} \, dx=e^{4-e^x} x^{\frac {x \left (-e^x (4+x)+x (4+3 x)\right )}{2 \left (e^x-x\right )}} \]
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Time = 10.95 (sec) , antiderivative size = 56, normalized size of antiderivative = 1.47
method | result | size |
parallelrisch | \({\mathrm e}^{\frac {\left (\left (-x^{2}-4 x \right ) {\mathrm e}^{x}+3 x^{3}+4 x^{2}\right ) \ln \left (x \right )-2 \,{\mathrm e}^{2 x}+\left (2 x +8\right ) {\mathrm e}^{x}-8 x}{2 \,{\mathrm e}^{x}-2 x}}\) | \(56\) |
risch | \({\mathrm e}^{-\frac {x^{2} {\mathrm e}^{x} \ln \left (x \right )-3 x^{3} \ln \left (x \right )+4 x \,{\mathrm e}^{x} \ln \left (x \right )-4 x^{2} \ln \left (x \right )-2 \,{\mathrm e}^{x} x -8 \,{\mathrm e}^{x}+2 \,{\mathrm e}^{2 x}+8 x}{2 \left ({\mathrm e}^{x}-x \right )}}\) | \(60\) |
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Time = 0.30 (sec) , antiderivative size = 53, normalized size of antiderivative = 1.39 \[ \int \frac {e^{\frac {-2 e^{2 x}-8 x+e^x (8+2 x)+\left (4 x^2+3 x^3+e^x \left (-4 x-x^2\right )\right ) \log (x)}{2 e^x-2 x}} \left (-2 e^{3 x}-4 x^2-3 x^3+e^{2 x} (-4+3 x)+e^x \left (8 x+2 x^2\right )+\left (e^{2 x} (-4-2 x)-4 x^2-6 x^3+e^x \left (8 x+10 x^2-2 x^3\right )\right ) \log (x)\right )}{2 e^{2 x}-4 e^x x+2 x^2} \, dx=e^{\left (-\frac {2 \, {\left (x + 4\right )} e^{x} + {\left (3 \, x^{3} + 4 \, x^{2} - {\left (x^{2} + 4 \, x\right )} e^{x}\right )} \log \left (x\right ) - 8 \, x - 2 \, e^{\left (2 \, x\right )}}{2 \, {\left (x - e^{x}\right )}}\right )} \]
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Leaf count of result is larger than twice the leaf count of optimal. 53 vs. \(2 (26) = 52\).
Time = 0.58 (sec) , antiderivative size = 53, normalized size of antiderivative = 1.39 \[ \int \frac {e^{\frac {-2 e^{2 x}-8 x+e^x (8+2 x)+\left (4 x^2+3 x^3+e^x \left (-4 x-x^2\right )\right ) \log (x)}{2 e^x-2 x}} \left (-2 e^{3 x}-4 x^2-3 x^3+e^{2 x} (-4+3 x)+e^x \left (8 x+2 x^2\right )+\left (e^{2 x} (-4-2 x)-4 x^2-6 x^3+e^x \left (8 x+10 x^2-2 x^3\right )\right ) \log (x)\right )}{2 e^{2 x}-4 e^x x+2 x^2} \, dx=e^{\frac {- 8 x + \left (2 x + 8\right ) e^{x} + \left (3 x^{3} + 4 x^{2} + \left (- x^{2} - 4 x\right ) e^{x}\right ) \log {\left (x \right )} - 2 e^{2 x}}{- 2 x + 2 e^{x}}} \]
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Time = 0.52 (sec) , antiderivative size = 50, normalized size of antiderivative = 1.32 \[ \int \frac {e^{\frac {-2 e^{2 x}-8 x+e^x (8+2 x)+\left (4 x^2+3 x^3+e^x \left (-4 x-x^2\right )\right ) \log (x)}{2 e^x-2 x}} \left (-2 e^{3 x}-4 x^2-3 x^3+e^{2 x} (-4+3 x)+e^x \left (8 x+2 x^2\right )+\left (e^{2 x} (-4-2 x)-4 x^2-6 x^3+e^x \left (8 x+10 x^2-2 x^3\right )\right ) \log (x)\right )}{2 e^{2 x}-4 e^x x+2 x^2} \, dx=e^{\left (-\frac {3}{2} \, x^{2} \log \left (x\right ) - x e^{x} \log \left (x\right ) - 2 \, x \log \left (x\right ) - e^{\left (2 \, x\right )} \log \left (x\right ) - \frac {e^{\left (3 \, x\right )} \log \left (x\right )}{x - e^{x}} - e^{x} + 4\right )} \]
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Time = 0.54 (sec) , antiderivative size = 60, normalized size of antiderivative = 1.58 \[ \int \frac {e^{\frac {-2 e^{2 x}-8 x+e^x (8+2 x)+\left (4 x^2+3 x^3+e^x \left (-4 x-x^2\right )\right ) \log (x)}{2 e^x-2 x}} \left (-2 e^{3 x}-4 x^2-3 x^3+e^{2 x} (-4+3 x)+e^x \left (8 x+2 x^2\right )+\left (e^{2 x} (-4-2 x)-4 x^2-6 x^3+e^x \left (8 x+10 x^2-2 x^3\right )\right ) \log (x)\right )}{2 e^{2 x}-4 e^x x+2 x^2} \, dx=e^{\left (-\frac {3 \, x^{3} \log \left (x\right ) - x^{2} e^{x} \log \left (x\right ) + 4 \, x^{2} \log \left (x\right ) - 4 \, x e^{x} \log \left (x\right ) + 2 \, x e^{x} - 8 \, x - 2 \, e^{\left (2 \, x\right )} + 8 \, e^{x}}{2 \, {\left (x - e^{x}\right )}}\right )} \]
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Time = 9.39 (sec) , antiderivative size = 98, normalized size of antiderivative = 2.58 \[ \int \frac {e^{\frac {-2 e^{2 x}-8 x+e^x (8+2 x)+\left (4 x^2+3 x^3+e^x \left (-4 x-x^2\right )\right ) \log (x)}{2 e^x-2 x}} \left (-2 e^{3 x}-4 x^2-3 x^3+e^{2 x} (-4+3 x)+e^x \left (8 x+2 x^2\right )+\left (e^{2 x} (-4-2 x)-4 x^2-6 x^3+e^x \left (8 x+10 x^2-2 x^3\right )\right ) \log (x)\right )}{2 e^{2 x}-4 e^x x+2 x^2} \, dx=x^{\frac {x^2\,{\mathrm {e}}^x+4\,x\,{\mathrm {e}}^x-4\,x^2-3\,x^3}{2\,\left (x-{\mathrm {e}}^x\right )}}\,{\mathrm {e}}^{\frac {8\,x}{2\,x-2\,{\mathrm {e}}^x}}\,{\mathrm {e}}^{-\frac {8\,{\mathrm {e}}^x}{2\,x-2\,{\mathrm {e}}^x}}\,{\mathrm {e}}^{\frac {2\,{\mathrm {e}}^{2\,x}}{2\,x-2\,{\mathrm {e}}^x}}\,{\mathrm {e}}^{-\frac {2\,x\,{\mathrm {e}}^x}{2\,x-2\,{\mathrm {e}}^x}} \]
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