Integrand size = 64, antiderivative size = 24 \[ \int \frac {1}{5} e^{\frac {1}{5} \left (-60+15 e x+15 x^2-(3 e+3 x) \log (x)\right )} \left (20 x-6 x^2+60 x^3+e \left (-6 x+30 x^2\right )-6 x^2 \log (x)\right ) \, dx=2 e^{-3 \left (4-(e+x) \left (x-\frac {\log (x)}{5}\right )\right )} x^2 \]
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Leaf count is larger than twice the leaf count of optimal. \(71\) vs. \(2(24)=48\).
Time = 0.06 (sec) , antiderivative size = 71, normalized size of antiderivative = 2.96, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.031, Rules used = {12, 2326} \[ \int \frac {1}{5} e^{\frac {1}{5} \left (-60+15 e x+15 x^2-(3 e+3 x) \log (x)\right )} \left (20 x-6 x^2+60 x^3+e \left (-6 x+30 x^2\right )-6 x^2 \log (x)\right ) \, dx=-\frac {2 e^{-3 \left (-x^2-e x+4\right )} x^{-\frac {3}{5} (x+e)} \left (-10 x^3+x^2+e \left (x-5 x^2\right )+x^2 \log (x)\right )}{10 x-\frac {x+e}{x}-\log (x)+5 e} \]
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Rule 12
Rule 2326
Rubi steps \begin{align*} \text {integral}& = \frac {1}{5} \int \exp \left (\frac {1}{5} \left (-60+15 e x+15 x^2-(3 e+3 x) \log (x)\right )\right ) \left (20 x-6 x^2+60 x^3+e \left (-6 x+30 x^2\right )-6 x^2 \log (x)\right ) \, dx \\ & = -\frac {2 e^{-3 \left (4-e x-x^2\right )} x^{-\frac {3}{5} (e+x)} \left (x^2-10 x^3+e \left (x-5 x^2\right )+x^2 \log (x)\right )}{5 e+10 x-\frac {e+x}{x}-\log (x)} \\ \end{align*}
Time = 0.98 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.17 \[ \int \frac {1}{5} e^{\frac {1}{5} \left (-60+15 e x+15 x^2-(3 e+3 x) \log (x)\right )} \left (20 x-6 x^2+60 x^3+e \left (-6 x+30 x^2\right )-6 x^2 \log (x)\right ) \, dx=2 e^{3 \left (-4+e x+x^2\right )} x^{2-\frac {3 e}{5}-\frac {3 x}{5}} \]
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Time = 0.63 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.29
method | result | size |
risch | \(2 x^{2} x^{-\frac {3 x}{5}-\frac {3 \,{\mathrm e}}{5}} {\mathrm e}^{-12+3 x \,{\mathrm e}+3 x^{2}}\) | \(31\) |
norman | \(2 x^{2} {\mathrm e}^{\left (-\frac {3 x}{5}-\frac {3 \,{\mathrm e}}{5}\right ) \ln \left (x \right )+3 x \,{\mathrm e}+3 x^{2}-12}\) | \(33\) |
parallelrisch | \(2 x^{2} {\mathrm e}^{\left (-\frac {3 x}{5}-\frac {3 \,{\mathrm e}}{5}\right ) \ln \left (x \right )+3 x \,{\mathrm e}+3 x^{2}-12}\) | \(33\) |
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Time = 0.25 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.08 \[ \int \frac {1}{5} e^{\frac {1}{5} \left (-60+15 e x+15 x^2-(3 e+3 x) \log (x)\right )} \left (20 x-6 x^2+60 x^3+e \left (-6 x+30 x^2\right )-6 x^2 \log (x)\right ) \, dx=2 \, x^{2} e^{\left (3 \, x^{2} + 3 \, x e - \frac {3}{5} \, {\left (x + e\right )} \log \left (x\right ) - 12\right )} \]
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Time = 0.14 (sec) , antiderivative size = 34, normalized size of antiderivative = 1.42 \[ \int \frac {1}{5} e^{\frac {1}{5} \left (-60+15 e x+15 x^2-(3 e+3 x) \log (x)\right )} \left (20 x-6 x^2+60 x^3+e \left (-6 x+30 x^2\right )-6 x^2 \log (x)\right ) \, dx=2 x^{2} e^{3 x^{2} + 3 e x - \left (\frac {3 x}{5} + \frac {3 e}{5}\right ) \log {\left (x \right )} - 12} \]
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Time = 0.27 (sec) , antiderivative size = 29, normalized size of antiderivative = 1.21 \[ \int \frac {1}{5} e^{\frac {1}{5} \left (-60+15 e x+15 x^2-(3 e+3 x) \log (x)\right )} \left (20 x-6 x^2+60 x^3+e \left (-6 x+30 x^2\right )-6 x^2 \log (x)\right ) \, dx=2 \, x^{2} e^{\left (3 \, x^{2} + 3 \, x e - \frac {3}{5} \, x \log \left (x\right ) - \frac {3}{5} \, e \log \left (x\right ) - 12\right )} \]
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Time = 0.30 (sec) , antiderivative size = 29, normalized size of antiderivative = 1.21 \[ \int \frac {1}{5} e^{\frac {1}{5} \left (-60+15 e x+15 x^2-(3 e+3 x) \log (x)\right )} \left (20 x-6 x^2+60 x^3+e \left (-6 x+30 x^2\right )-6 x^2 \log (x)\right ) \, dx=2 \, x^{2} e^{\left (3 \, x^{2} + 3 \, x e - \frac {3}{5} \, x \log \left (x\right ) - \frac {3}{5} \, e \log \left (x\right ) - 12\right )} \]
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Time = 10.42 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.12 \[ \int \frac {1}{5} e^{\frac {1}{5} \left (-60+15 e x+15 x^2-(3 e+3 x) \log (x)\right )} \left (20 x-6 x^2+60 x^3+e \left (-6 x+30 x^2\right )-6 x^2 \log (x)\right ) \, dx=2\,x^{2-\frac {3\,\mathrm {e}}{5}-\frac {3\,x}{5}}\,{\mathrm {e}}^{-12}\,{\mathrm {e}}^{3\,x^2}\,{\mathrm {e}}^{3\,x\,\mathrm {e}} \]
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