Integrand size = 201, antiderivative size = 33 \[ \int \frac {3 x^2+e^5 \left (-x^2-x^3\right )+\left (-6 x+2 e^5 x^2\right ) \log \left (\frac {e^x x}{6}\right )+\left (-6 x+2 e^5 x^2\right ) \log \left (\frac {3-e^5 x}{x}\right )}{-3 x^4+e^5 x^5+\left (-3+e^5 x\right ) \log ^2\left (\frac {e^x x}{6}\right )+\left (6 x^2-2 e^5 x^3\right ) \log \left (\frac {3-e^5 x}{x}\right )+\left (-3+e^5 x\right ) \log ^2\left (\frac {3-e^5 x}{x}\right )+\log \left (\frac {e^x x}{6}\right ) \left (6 x^2-2 e^5 x^3+\left (-6+2 e^5 x\right ) \log \left (\frac {3-e^5 x}{x}\right )\right )} \, dx=\frac {x^2}{-x^2+\log \left (-e^5+\frac {3}{x}\right )+\log \left (\frac {e^x x}{6}\right )} \]
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\[ \int \frac {3 x^2+e^5 \left (-x^2-x^3\right )+\left (-6 x+2 e^5 x^2\right ) \log \left (\frac {e^x x}{6}\right )+\left (-6 x+2 e^5 x^2\right ) \log \left (\frac {3-e^5 x}{x}\right )}{-3 x^4+e^5 x^5+\left (-3+e^5 x\right ) \log ^2\left (\frac {e^x x}{6}\right )+\left (6 x^2-2 e^5 x^3\right ) \log \left (\frac {3-e^5 x}{x}\right )+\left (-3+e^5 x\right ) \log ^2\left (\frac {3-e^5 x}{x}\right )+\log \left (\frac {e^x x}{6}\right ) \left (6 x^2-2 e^5 x^3+\left (-6+2 e^5 x\right ) \log \left (\frac {3-e^5 x}{x}\right )\right )} \, dx=\int \frac {3 x^2+e^5 \left (-x^2-x^3\right )+\left (-6 x+2 e^5 x^2\right ) \log \left (\frac {e^x x}{6}\right )+\left (-6 x+2 e^5 x^2\right ) \log \left (\frac {3-e^5 x}{x}\right )}{-3 x^4+e^5 x^5+\left (-3+e^5 x\right ) \log ^2\left (\frac {e^x x}{6}\right )+\left (6 x^2-2 e^5 x^3\right ) \log \left (\frac {3-e^5 x}{x}\right )+\left (-3+e^5 x\right ) \log ^2\left (\frac {3-e^5 x}{x}\right )+\log \left (\frac {e^x x}{6}\right ) \left (6 x^2-2 e^5 x^3+\left (-6+2 e^5 x\right ) \log \left (\frac {3-e^5 x}{x}\right )\right )} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {x \left (x \left (-3+e^5 (1+x)\right )+\left (6-2 e^5 x\right ) \log \left (-e^5+\frac {3}{x}\right )+\left (6-2 e^5 x\right ) \log \left (\frac {e^x x}{6}\right )\right )}{\left (3-e^5 x\right ) \left (x^2-\log \left (-e^5+\frac {3}{x}\right )-\log \left (\frac {e^x x}{6}\right )\right )^2} \, dx \\ & = \int \left (\frac {x^2 \left (-3+e^5+\left (6+e^5\right ) x-2 e^5 x^2\right )}{\left (3-e^5 x\right ) \left (x^2-\log \left (-e^5+\frac {3}{x}\right )-\log \left (\frac {e^x x}{6}\right )\right )^2}-\frac {2 x}{x^2-\log \left (-e^5+\frac {3}{x}\right )-\log \left (\frac {e^x x}{6}\right )}\right ) \, dx \\ & = -\left (2 \int \frac {x}{x^2-\log \left (-e^5+\frac {3}{x}\right )-\log \left (\frac {e^x x}{6}\right )} \, dx\right )+\int \frac {x^2 \left (-3+e^5+\left (6+e^5\right ) x-2 e^5 x^2\right )}{\left (3-e^5 x\right ) \left (x^2-\log \left (-e^5+\frac {3}{x}\right )-\log \left (\frac {e^x x}{6}\right )\right )^2} \, dx \\ & = -\left (2 \int \frac {x}{x^2-\log \left (-e^5+\frac {3}{x}\right )-\log \left (\frac {e^x x}{6}\right )} \, dx\right )+\int \left (-\frac {3}{e^5 \left (x^2-\log \left (-e^5+\frac {3}{x}\right )-\log \left (\frac {e^x x}{6}\right )\right )^2}-\frac {x}{\left (x^2-\log \left (-e^5+\frac {3}{x}\right )-\log \left (\frac {e^x x}{6}\right )\right )^2}-\frac {x^2}{\left (x^2-\log \left (-e^5+\frac {3}{x}\right )-\log \left (\frac {e^x x}{6}\right )\right )^2}+\frac {2 x^3}{\left (x^2-\log \left (-e^5+\frac {3}{x}\right )-\log \left (\frac {e^x x}{6}\right )\right )^2}-\frac {9}{e^5 \left (-3+e^5 x\right ) \left (x^2-\log \left (-e^5+\frac {3}{x}\right )-\log \left (\frac {e^x x}{6}\right )\right )^2}\right ) \, dx \\ & = 2 \int \frac {x^3}{\left (x^2-\log \left (-e^5+\frac {3}{x}\right )-\log \left (\frac {e^x x}{6}\right )\right )^2} \, dx-2 \int \frac {x}{x^2-\log \left (-e^5+\frac {3}{x}\right )-\log \left (\frac {e^x x}{6}\right )} \, dx-\frac {3 \int \frac {1}{\left (x^2-\log \left (-e^5+\frac {3}{x}\right )-\log \left (\frac {e^x x}{6}\right )\right )^2} \, dx}{e^5}-\frac {9 \int \frac {1}{\left (-3+e^5 x\right ) \left (x^2-\log \left (-e^5+\frac {3}{x}\right )-\log \left (\frac {e^x x}{6}\right )\right )^2} \, dx}{e^5}-\int \frac {x}{\left (x^2-\log \left (-e^5+\frac {3}{x}\right )-\log \left (\frac {e^x x}{6}\right )\right )^2} \, dx-\int \frac {x^2}{\left (x^2-\log \left (-e^5+\frac {3}{x}\right )-\log \left (\frac {e^x x}{6}\right )\right )^2} \, dx \\ \end{align*}
Time = 0.07 (sec) , antiderivative size = 33, normalized size of antiderivative = 1.00 \[ \int \frac {3 x^2+e^5 \left (-x^2-x^3\right )+\left (-6 x+2 e^5 x^2\right ) \log \left (\frac {e^x x}{6}\right )+\left (-6 x+2 e^5 x^2\right ) \log \left (\frac {3-e^5 x}{x}\right )}{-3 x^4+e^5 x^5+\left (-3+e^5 x\right ) \log ^2\left (\frac {e^x x}{6}\right )+\left (6 x^2-2 e^5 x^3\right ) \log \left (\frac {3-e^5 x}{x}\right )+\left (-3+e^5 x\right ) \log ^2\left (\frac {3-e^5 x}{x}\right )+\log \left (\frac {e^x x}{6}\right ) \left (6 x^2-2 e^5 x^3+\left (-6+2 e^5 x\right ) \log \left (\frac {3-e^5 x}{x}\right )\right )} \, dx=\frac {x^2}{-x^2+\log \left (-e^5+\frac {3}{x}\right )+\log \left (\frac {e^x x}{6}\right )} \]
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Time = 18.61 (sec) , antiderivative size = 34, normalized size of antiderivative = 1.03
method | result | size |
parallelrisch | \(-\frac {x^{2}}{x^{2}-\ln \left (\frac {{\mathrm e}^{x} x}{6}\right )-\ln \left (-\frac {x \,{\mathrm e}^{5}-3}{x}\right )}\) | \(34\) |
risch | \(-\frac {2 x^{2}}{-i \pi \operatorname {csgn}\left (i {\mathrm e}^{x} x \right )^{2} \operatorname {csgn}\left (i {\mathrm e}^{x}\right )+i \pi \,\operatorname {csgn}\left (i \left (x \,{\mathrm e}^{5}-3\right )\right ) \operatorname {csgn}\left (\frac {i \left (x \,{\mathrm e}^{5}-3\right )}{x}\right ) \operatorname {csgn}\left (\frac {i}{x}\right )+i \pi \,\operatorname {csgn}\left (i {\mathrm e}^{x} x \right ) \operatorname {csgn}\left (i {\mathrm e}^{x}\right ) \operatorname {csgn}\left (i x \right )+2 i \pi {\operatorname {csgn}\left (\frac {i \left (x \,{\mathrm e}^{5}-3\right )}{x}\right )}^{2}-i \pi {\operatorname {csgn}\left (\frac {i \left (x \,{\mathrm e}^{5}-3\right )}{x}\right )}^{2} \operatorname {csgn}\left (\frac {i}{x}\right )-i \pi \,\operatorname {csgn}\left (i \left (x \,{\mathrm e}^{5}-3\right )\right ) {\operatorname {csgn}\left (\frac {i \left (x \,{\mathrm e}^{5}-3\right )}{x}\right )}^{2}+i \pi \operatorname {csgn}\left (i {\mathrm e}^{x} x \right )^{3}-i \pi \operatorname {csgn}\left (i {\mathrm e}^{x} x \right )^{2} \operatorname {csgn}\left (i x \right )-2 i \pi -i \pi {\operatorname {csgn}\left (\frac {i \left (x \,{\mathrm e}^{5}-3\right )}{x}\right )}^{3}+2 x^{2}+2 \ln \left (3\right )+2 \ln \left (2\right )-2 \ln \left (x \,{\mathrm e}^{5}-3\right )-2 \ln \left ({\mathrm e}^{x}\right )}\) | \(239\) |
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Time = 0.26 (sec) , antiderivative size = 33, normalized size of antiderivative = 1.00 \[ \int \frac {3 x^2+e^5 \left (-x^2-x^3\right )+\left (-6 x+2 e^5 x^2\right ) \log \left (\frac {e^x x}{6}\right )+\left (-6 x+2 e^5 x^2\right ) \log \left (\frac {3-e^5 x}{x}\right )}{-3 x^4+e^5 x^5+\left (-3+e^5 x\right ) \log ^2\left (\frac {e^x x}{6}\right )+\left (6 x^2-2 e^5 x^3\right ) \log \left (\frac {3-e^5 x}{x}\right )+\left (-3+e^5 x\right ) \log ^2\left (\frac {3-e^5 x}{x}\right )+\log \left (\frac {e^x x}{6}\right ) \left (6 x^2-2 e^5 x^3+\left (-6+2 e^5 x\right ) \log \left (\frac {3-e^5 x}{x}\right )\right )} \, dx=-\frac {x^{2}}{x^{2} - \log \left (\frac {1}{6} \, x e^{x}\right ) - \log \left (-\frac {x e^{5} - 3}{x}\right )} \]
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Time = 0.20 (sec) , antiderivative size = 24, normalized size of antiderivative = 0.73 \[ \int \frac {3 x^2+e^5 \left (-x^2-x^3\right )+\left (-6 x+2 e^5 x^2\right ) \log \left (\frac {e^x x}{6}\right )+\left (-6 x+2 e^5 x^2\right ) \log \left (\frac {3-e^5 x}{x}\right )}{-3 x^4+e^5 x^5+\left (-3+e^5 x\right ) \log ^2\left (\frac {e^x x}{6}\right )+\left (6 x^2-2 e^5 x^3\right ) \log \left (\frac {3-e^5 x}{x}\right )+\left (-3+e^5 x\right ) \log ^2\left (\frac {3-e^5 x}{x}\right )+\log \left (\frac {e^x x}{6}\right ) \left (6 x^2-2 e^5 x^3+\left (-6+2 e^5 x\right ) \log \left (\frac {3-e^5 x}{x}\right )\right )} \, dx=\frac {x^{2}}{- x^{2} + \log {\left (\frac {- x e^{5} + 3}{x} \right )} + \log {\left (\frac {x e^{x}}{6} \right )}} \]
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Time = 0.38 (sec) , antiderivative size = 28, normalized size of antiderivative = 0.85 \[ \int \frac {3 x^2+e^5 \left (-x^2-x^3\right )+\left (-6 x+2 e^5 x^2\right ) \log \left (\frac {e^x x}{6}\right )+\left (-6 x+2 e^5 x^2\right ) \log \left (\frac {3-e^5 x}{x}\right )}{-3 x^4+e^5 x^5+\left (-3+e^5 x\right ) \log ^2\left (\frac {e^x x}{6}\right )+\left (6 x^2-2 e^5 x^3\right ) \log \left (\frac {3-e^5 x}{x}\right )+\left (-3+e^5 x\right ) \log ^2\left (\frac {3-e^5 x}{x}\right )+\log \left (\frac {e^x x}{6}\right ) \left (6 x^2-2 e^5 x^3+\left (-6+2 e^5 x\right ) \log \left (\frac {3-e^5 x}{x}\right )\right )} \, dx=-\frac {x^{2}}{x^{2} - x + \log \left (3\right ) + \log \left (2\right ) - \log \left (-x e^{5} + 3\right )} \]
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Time = 0.30 (sec) , antiderivative size = 26, normalized size of antiderivative = 0.79 \[ \int \frac {3 x^2+e^5 \left (-x^2-x^3\right )+\left (-6 x+2 e^5 x^2\right ) \log \left (\frac {e^x x}{6}\right )+\left (-6 x+2 e^5 x^2\right ) \log \left (\frac {3-e^5 x}{x}\right )}{-3 x^4+e^5 x^5+\left (-3+e^5 x\right ) \log ^2\left (\frac {e^x x}{6}\right )+\left (6 x^2-2 e^5 x^3\right ) \log \left (\frac {3-e^5 x}{x}\right )+\left (-3+e^5 x\right ) \log ^2\left (\frac {3-e^5 x}{x}\right )+\log \left (\frac {e^x x}{6}\right ) \left (6 x^2-2 e^5 x^3+\left (-6+2 e^5 x\right ) \log \left (\frac {3-e^5 x}{x}\right )\right )} \, dx=-\frac {x^{2}}{x^{2} - x + \log \left (6\right ) - \log \left (-x e^{5} + 3\right )} \]
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Time = 13.71 (sec) , antiderivative size = 30, normalized size of antiderivative = 0.91 \[ \int \frac {3 x^2+e^5 \left (-x^2-x^3\right )+\left (-6 x+2 e^5 x^2\right ) \log \left (\frac {e^x x}{6}\right )+\left (-6 x+2 e^5 x^2\right ) \log \left (\frac {3-e^5 x}{x}\right )}{-3 x^4+e^5 x^5+\left (-3+e^5 x\right ) \log ^2\left (\frac {e^x x}{6}\right )+\left (6 x^2-2 e^5 x^3\right ) \log \left (\frac {3-e^5 x}{x}\right )+\left (-3+e^5 x\right ) \log ^2\left (\frac {3-e^5 x}{x}\right )+\log \left (\frac {e^x x}{6}\right ) \left (6 x^2-2 e^5 x^3+\left (-6+2 e^5 x\right ) \log \left (\frac {3-e^5 x}{x}\right )\right )} \, dx=\frac {x^2}{\ln \left (\frac {x\,{\mathrm {e}}^x}{6}\right )+\ln \left (-\frac {x\,{\mathrm {e}}^5-3}{x}\right )-x^2} \]
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