Integrand size = 54, antiderivative size = 21 \[ \int \frac {1}{12} e^{\frac {1}{12} \left (-3 x+6 e^x x+2 e^x x \log \left (x^2\right )\right )} \left (-3+e^x (10+6 x)+e^x (2+2 x) \log \left (x^2\right )\right ) \, dx=e^{x \left (-\frac {1}{4}+\frac {1}{6} e^x \left (3+\log \left (x^2\right )\right )\right )} \]
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\[ \int \frac {1}{12} e^{\frac {1}{12} \left (-3 x+6 e^x x+2 e^x x \log \left (x^2\right )\right )} \left (-3+e^x (10+6 x)+e^x (2+2 x) \log \left (x^2\right )\right ) \, dx=\int \frac {1}{12} e^{\frac {1}{12} \left (-3 x+6 e^x x+2 e^x x \log \left (x^2\right )\right )} \left (-3+e^x (10+6 x)+e^x (2+2 x) \log \left (x^2\right )\right ) \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \frac {1}{12} \int e^{\frac {1}{12} \left (-3 x+6 e^x x+2 e^x x \log \left (x^2\right )\right )} \left (-3+e^x (10+6 x)+e^x (2+2 x) \log \left (x^2\right )\right ) \, dx \\ & = \frac {1}{12} \int \left (-3 e^{\frac {1}{12} \left (-3 x+6 e^x x+2 e^x x \log \left (x^2\right )\right )}+2 \exp \left (x+\frac {1}{12} \left (-3 x+6 e^x x+2 e^x x \log \left (x^2\right )\right )\right ) (5+3 x)+2 \exp \left (x+\frac {1}{12} \left (-3 x+6 e^x x+2 e^x x \log \left (x^2\right )\right )\right ) (1+x) \log \left (x^2\right )\right ) \, dx \\ & = \frac {1}{6} \int \exp \left (x+\frac {1}{12} \left (-3 x+6 e^x x+2 e^x x \log \left (x^2\right )\right )\right ) (5+3 x) \, dx+\frac {1}{6} \int \exp \left (x+\frac {1}{12} \left (-3 x+6 e^x x+2 e^x x \log \left (x^2\right )\right )\right ) (1+x) \log \left (x^2\right ) \, dx-\frac {1}{4} \int e^{\frac {1}{12} \left (-3 x+6 e^x x+2 e^x x \log \left (x^2\right )\right )} \, dx \\ & = \frac {1}{6} \int e^{\frac {1}{12} x \left (9+6 e^x+2 e^x \log \left (x^2\right )\right )} (5+3 x) \, dx+\frac {1}{6} \int e^{\frac {1}{12} x \left (9+6 e^x+2 e^x \log \left (x^2\right )\right )} (1+x) \log \left (x^2\right ) \, dx-\frac {1}{4} \int e^{\frac {1}{12} \left (-3 x+6 e^x x+2 e^x x \log \left (x^2\right )\right )} \, dx \\ & = \frac {1}{6} \int \left (5 e^{\frac {1}{12} x \left (9+6 e^x+2 e^x \log \left (x^2\right )\right )}+3 e^{\frac {1}{12} x \left (9+6 e^x+2 e^x \log \left (x^2\right )\right )} x\right ) \, dx+\frac {1}{6} \int \left (e^{\frac {1}{12} x \left (9+6 e^x+2 e^x \log \left (x^2\right )\right )} \log \left (x^2\right )+e^{\frac {1}{12} x \left (9+6 e^x+2 e^x \log \left (x^2\right )\right )} x \log \left (x^2\right )\right ) \, dx-\frac {1}{4} \int e^{\frac {1}{12} \left (-3 x+6 e^x x+2 e^x x \log \left (x^2\right )\right )} \, dx \\ & = \frac {1}{6} \int e^{\frac {1}{12} x \left (9+6 e^x+2 e^x \log \left (x^2\right )\right )} \log \left (x^2\right ) \, dx+\frac {1}{6} \int e^{\frac {1}{12} x \left (9+6 e^x+2 e^x \log \left (x^2\right )\right )} x \log \left (x^2\right ) \, dx-\frac {1}{4} \int e^{\frac {1}{12} \left (-3 x+6 e^x x+2 e^x x \log \left (x^2\right )\right )} \, dx+\frac {1}{2} \int e^{\frac {1}{12} x \left (9+6 e^x+2 e^x \log \left (x^2\right )\right )} x \, dx+\frac {5}{6} \int e^{\frac {1}{12} x \left (9+6 e^x+2 e^x \log \left (x^2\right )\right )} \, dx \\ \end{align*}
Time = 1.42 (sec) , antiderivative size = 29, normalized size of antiderivative = 1.38 \[ \int \frac {1}{12} e^{\frac {1}{12} \left (-3 x+6 e^x x+2 e^x x \log \left (x^2\right )\right )} \left (-3+e^x (10+6 x)+e^x (2+2 x) \log \left (x^2\right )\right ) \, dx=e^{-\frac {x}{4}+\frac {e^x x}{2}} \left (x^2\right )^{\frac {e^x x}{6}} \]
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Time = 0.38 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.90
method | result | size |
parallelrisch | \({\mathrm e}^{\frac {x \left (2 \,{\mathrm e}^{x} \ln \left (x^{2}\right )+6 \,{\mathrm e}^{x}-3\right )}{12}}\) | \(19\) |
default | \({\mathrm e}^{\frac {x \,{\mathrm e}^{x} \ln \left (x^{2}\right )}{6}+\frac {{\mathrm e}^{x} x}{2}-\frac {x}{4}}\) | \(20\) |
norman | \({\mathrm e}^{\frac {x \,{\mathrm e}^{x} \ln \left (x^{2}\right )}{6}+\frac {{\mathrm e}^{x} x}{2}-\frac {x}{4}}\) | \(20\) |
risch | \({\mathrm e}^{\frac {x \left (-i {\mathrm e}^{x} \pi \operatorname {csgn}\left (i x^{2}\right )^{3}+2 i {\mathrm e}^{x} \pi \operatorname {csgn}\left (i x^{2}\right )^{2} \operatorname {csgn}\left (i x \right )-i {\mathrm e}^{x} \pi \,\operatorname {csgn}\left (i x^{2}\right ) \operatorname {csgn}\left (i x \right )^{2}+4 \,{\mathrm e}^{x} \ln \left (x \right )+6 \,{\mathrm e}^{x}-3\right )}{12}}\) | \(72\) |
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Time = 0.24 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.90 \[ \int \frac {1}{12} e^{\frac {1}{12} \left (-3 x+6 e^x x+2 e^x x \log \left (x^2\right )\right )} \left (-3+e^x (10+6 x)+e^x (2+2 x) \log \left (x^2\right )\right ) \, dx=e^{\left (\frac {1}{6} \, x e^{x} \log \left (x^{2}\right ) + \frac {1}{2} \, x e^{x} - \frac {1}{4} \, x\right )} \]
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Time = 0.20 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.05 \[ \int \frac {1}{12} e^{\frac {1}{12} \left (-3 x+6 e^x x+2 e^x x \log \left (x^2\right )\right )} \left (-3+e^x (10+6 x)+e^x (2+2 x) \log \left (x^2\right )\right ) \, dx=e^{\frac {x e^{x} \log {\left (x^{2} \right )}}{6} + \frac {x e^{x}}{2} - \frac {x}{4}} \]
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\[ \int \frac {1}{12} e^{\frac {1}{12} \left (-3 x+6 e^x x+2 e^x x \log \left (x^2\right )\right )} \left (-3+e^x (10+6 x)+e^x (2+2 x) \log \left (x^2\right )\right ) \, dx=\int { \frac {1}{12} \, {\left (2 \, {\left (x + 1\right )} e^{x} \log \left (x^{2}\right ) + 2 \, {\left (3 \, x + 5\right )} e^{x} - 3\right )} e^{\left (\frac {1}{6} \, x e^{x} \log \left (x^{2}\right ) + \frac {1}{2} \, x e^{x} - \frac {1}{4} \, x\right )} \,d x } \]
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Time = 0.27 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.90 \[ \int \frac {1}{12} e^{\frac {1}{12} \left (-3 x+6 e^x x+2 e^x x \log \left (x^2\right )\right )} \left (-3+e^x (10+6 x)+e^x (2+2 x) \log \left (x^2\right )\right ) \, dx=e^{\left (\frac {1}{6} \, x e^{x} \log \left (x^{2}\right ) + \frac {1}{2} \, x e^{x} - \frac {1}{4} \, x\right )} \]
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Time = 9.04 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.95 \[ \int \frac {1}{12} e^{\frac {1}{12} \left (-3 x+6 e^x x+2 e^x x \log \left (x^2\right )\right )} \left (-3+e^x (10+6 x)+e^x (2+2 x) \log \left (x^2\right )\right ) \, dx={\mathrm {e}}^{\frac {x\,{\mathrm {e}}^x}{2}-\frac {x}{4}}\,{\left (x^2\right )}^{\frac {x\,{\mathrm {e}}^x}{6}} \]
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