Integrand size = 155, antiderivative size = 26 \[ \int \frac {e^{\frac {-7 x+e^{36+e^4+12 x^2+x^4+e^2 \left (-12-2 x^2\right )} x}{16+\log (x)}} \left (-105+e^{36+e^4+12 x^2+x^4+e^2 \left (-12-2 x^2\right )} \left (15+384 x^2-64 e^2 x^2+64 x^4\right )+\left (-7+e^{36+e^4+12 x^2+x^4+e^2 \left (-12-2 x^2\right )} \left (1+24 x^2-4 e^2 x^2+4 x^4\right )\right ) \log (x)\right )}{256+32 \log (x)+\log ^2(x)} \, dx=e^{\frac {\left (-7+e^{\left (-6+e^2-x^2\right )^2}\right ) x}{16+\log (x)}} \]
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\[ \int \frac {e^{\frac {-7 x+e^{36+e^4+12 x^2+x^4+e^2 \left (-12-2 x^2\right )} x}{16+\log (x)}} \left (-105+e^{36+e^4+12 x^2+x^4+e^2 \left (-12-2 x^2\right )} \left (15+384 x^2-64 e^2 x^2+64 x^4\right )+\left (-7+e^{36+e^4+12 x^2+x^4+e^2 \left (-12-2 x^2\right )} \left (1+24 x^2-4 e^2 x^2+4 x^4\right )\right ) \log (x)\right )}{256+32 \log (x)+\log ^2(x)} \, dx=\int \frac {\exp \left (\frac {-7 x+e^{36+e^4+12 x^2+x^4+e^2 \left (-12-2 x^2\right )} x}{16+\log (x)}\right ) \left (-105+e^{36+e^4+12 x^2+x^4+e^2 \left (-12-2 x^2\right )} \left (15+384 x^2-64 e^2 x^2+64 x^4\right )+\left (-7+e^{36+e^4+12 x^2+x^4+e^2 \left (-12-2 x^2\right )} \left (1+24 x^2-4 e^2 x^2+4 x^4\right )\right ) \log (x)\right )}{256+32 \log (x)+\log ^2(x)} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {\exp \left (\frac {-7 x+e^{36+e^4+12 x^2+x^4+e^2 \left (-12-2 x^2\right )} x}{16+\log (x)}\right ) \left (-105+e^{36+e^4+12 x^2+x^4+e^2 \left (-12-2 x^2\right )} \left (15+384 x^2-64 e^2 x^2+64 x^4\right )+\left (-7+e^{36+e^4+12 x^2+x^4+e^2 \left (-12-2 x^2\right )} \left (1+24 x^2-4 e^2 x^2+4 x^4\right )\right ) \log (x)\right )}{(16+\log (x))^2} \, dx \\ & = \int \frac {e^{\frac {\left (-7+e^{\left (6-e^2+x^2\right )^2}\right ) x}{16+\log (x)}} \left (-105+e^{\left (6-e^2+x^2\right )^2} \left (15-64 \left (-6+e^2\right ) x^2+64 x^4\right )+\left (-7+e^{\left (6-e^2+x^2\right )^2} \left (1-4 \left (-6+e^2\right ) x^2+4 x^4\right )\right ) \log (x)\right )}{(16+\log (x))^2} \, dx \\ & = \int \left (-\frac {7 e^{\frac {\left (-7+e^{\left (6-e^2+x^2\right )^2}\right ) x}{16+\log (x)}} (15+\log (x))}{(16+\log (x))^2}+\frac {\exp \left (\left (-6+e^2\right )^2+2 \left (6-e^2\right ) x^2+x^4+\frac {\left (-7+e^{\left (6-e^2+x^2\right )^2}\right ) x}{16+\log (x)}\right ) \left (15+384 \left (1-\frac {e^2}{6}\right ) x^2+64 x^4+\log (x)+24 \left (1-\frac {e^2}{6}\right ) x^2 \log (x)+4 x^4 \log (x)\right )}{(16+\log (x))^2}\right ) \, dx \\ & = -\left (7 \int \frac {e^{\frac {\left (-7+e^{\left (6-e^2+x^2\right )^2}\right ) x}{16+\log (x)}} (15+\log (x))}{(16+\log (x))^2} \, dx\right )+\int \frac {\exp \left (\left (-6+e^2\right )^2+2 \left (6-e^2\right ) x^2+x^4+\frac {\left (-7+e^{\left (6-e^2+x^2\right )^2}\right ) x}{16+\log (x)}\right ) \left (15+384 \left (1-\frac {e^2}{6}\right ) x^2+64 x^4+\log (x)+24 \left (1-\frac {e^2}{6}\right ) x^2 \log (x)+4 x^4 \log (x)\right )}{(16+\log (x))^2} \, dx \\ & = -\left (7 \int \left (-\frac {e^{\frac {\left (-7+e^{\left (6-e^2+x^2\right )^2}\right ) x}{16+\log (x)}}}{(16+\log (x))^2}+\frac {e^{\frac {\left (-7+e^{\left (6-e^2+x^2\right )^2}\right ) x}{16+\log (x)}}}{16+\log (x)}\right ) \, dx\right )+\int \left (-\frac {\exp \left (\left (-6+e^2\right )^2+2 \left (6-e^2\right ) x^2+x^4+\frac {\left (-7+e^{\left (6-e^2+x^2\right )^2}\right ) x}{16+\log (x)}\right )}{(16+\log (x))^2}+\frac {\exp \left (\left (-6+e^2\right )^2+2 \left (6-e^2\right ) x^2+x^4+\frac {\left (-7+e^{\left (6-e^2+x^2\right )^2}\right ) x}{16+\log (x)}\right ) \left (1+4 \left (6-e^2\right ) x^2+4 x^4\right )}{16+\log (x)}\right ) \, dx \\ & = 7 \int \frac {e^{\frac {\left (-7+e^{\left (6-e^2+x^2\right )^2}\right ) x}{16+\log (x)}}}{(16+\log (x))^2} \, dx-7 \int \frac {e^{\frac {\left (-7+e^{\left (6-e^2+x^2\right )^2}\right ) x}{16+\log (x)}}}{16+\log (x)} \, dx-\int \frac {\exp \left (\left (-6+e^2\right )^2+2 \left (6-e^2\right ) x^2+x^4+\frac {\left (-7+e^{\left (6-e^2+x^2\right )^2}\right ) x}{16+\log (x)}\right )}{(16+\log (x))^2} \, dx+\int \frac {\exp \left (\left (-6+e^2\right )^2+2 \left (6-e^2\right ) x^2+x^4+\frac {\left (-7+e^{\left (6-e^2+x^2\right )^2}\right ) x}{16+\log (x)}\right ) \left (1+4 \left (6-e^2\right ) x^2+4 x^4\right )}{16+\log (x)} \, dx \\ & = 7 \int \frac {e^{\frac {\left (-7+e^{\left (6-e^2+x^2\right )^2}\right ) x}{16+\log (x)}}}{(16+\log (x))^2} \, dx-7 \int \frac {e^{\frac {\left (-7+e^{\left (6-e^2+x^2\right )^2}\right ) x}{16+\log (x)}}}{16+\log (x)} \, dx-\int \frac {\exp \left (\left (-6+e^2\right )^2+2 \left (6-e^2\right ) x^2+x^4+\frac {\left (-7+e^{\left (6-e^2+x^2\right )^2}\right ) x}{16+\log (x)}\right )}{(16+\log (x))^2} \, dx+\int \left (\frac {\exp \left (\left (-6+e^2\right )^2+2 \left (6-e^2\right ) x^2+x^4+\frac {\left (-7+e^{\left (6-e^2+x^2\right )^2}\right ) x}{16+\log (x)}\right )}{16+\log (x)}-\frac {4 \exp \left (\left (-6+e^2\right )^2+2 \left (6-e^2\right ) x^2+x^4+\frac {\left (-7+e^{\left (6-e^2+x^2\right )^2}\right ) x}{16+\log (x)}\right ) \left (-6+e^2\right ) x^2}{16+\log (x)}+\frac {4 \exp \left (\left (-6+e^2\right )^2+2 \left (6-e^2\right ) x^2+x^4+\frac {\left (-7+e^{\left (6-e^2+x^2\right )^2}\right ) x}{16+\log (x)}\right ) x^4}{16+\log (x)}\right ) \, dx \\ & = 4 \int \frac {\exp \left (\left (-6+e^2\right )^2+2 \left (6-e^2\right ) x^2+x^4+\frac {\left (-7+e^{\left (6-e^2+x^2\right )^2}\right ) x}{16+\log (x)}\right ) x^4}{16+\log (x)} \, dx+7 \int \frac {e^{\frac {\left (-7+e^{\left (6-e^2+x^2\right )^2}\right ) x}{16+\log (x)}}}{(16+\log (x))^2} \, dx-7 \int \frac {e^{\frac {\left (-7+e^{\left (6-e^2+x^2\right )^2}\right ) x}{16+\log (x)}}}{16+\log (x)} \, dx+\left (4 \left (6-e^2\right )\right ) \int \frac {\exp \left (\left (-6+e^2\right )^2+2 \left (6-e^2\right ) x^2+x^4+\frac {\left (-7+e^{\left (6-e^2+x^2\right )^2}\right ) x}{16+\log (x)}\right ) x^2}{16+\log (x)} \, dx-\int \frac {\exp \left (\left (-6+e^2\right )^2+2 \left (6-e^2\right ) x^2+x^4+\frac {\left (-7+e^{\left (6-e^2+x^2\right )^2}\right ) x}{16+\log (x)}\right )}{(16+\log (x))^2} \, dx+\int \frac {\exp \left (\left (-6+e^2\right )^2+2 \left (6-e^2\right ) x^2+x^4+\frac {\left (-7+e^{\left (6-e^2+x^2\right )^2}\right ) x}{16+\log (x)}\right )}{16+\log (x)} \, dx \\ \end{align*}
\[ \int \frac {e^{\frac {-7 x+e^{36+e^4+12 x^2+x^4+e^2 \left (-12-2 x^2\right )} x}{16+\log (x)}} \left (-105+e^{36+e^4+12 x^2+x^4+e^2 \left (-12-2 x^2\right )} \left (15+384 x^2-64 e^2 x^2+64 x^4\right )+\left (-7+e^{36+e^4+12 x^2+x^4+e^2 \left (-12-2 x^2\right )} \left (1+24 x^2-4 e^2 x^2+4 x^4\right )\right ) \log (x)\right )}{256+32 \log (x)+\log ^2(x)} \, dx=\int \frac {e^{\frac {-7 x+e^{36+e^4+12 x^2+x^4+e^2 \left (-12-2 x^2\right )} x}{16+\log (x)}} \left (-105+e^{36+e^4+12 x^2+x^4+e^2 \left (-12-2 x^2\right )} \left (15+384 x^2-64 e^2 x^2+64 x^4\right )+\left (-7+e^{36+e^4+12 x^2+x^4+e^2 \left (-12-2 x^2\right )} \left (1+24 x^2-4 e^2 x^2+4 x^4\right )\right ) \log (x)\right )}{256+32 \log (x)+\log ^2(x)} \, dx \]
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Time = 57.95 (sec) , antiderivative size = 36, normalized size of antiderivative = 1.38
method | result | size |
risch | \({\mathrm e}^{\frac {x \left ({\mathrm e}^{x^{4}-2 x^{2} {\mathrm e}^{2}+12 x^{2}-12 \,{\mathrm e}^{2}+{\mathrm e}^{4}+36}-7\right )}{16+\ln \left (x \right )}}\) | \(36\) |
parallelrisch | \({\mathrm e}^{\frac {x \left ({\mathrm e}^{x^{4}-2 x^{2} {\mathrm e}^{2}+12 x^{2}-12 \,{\mathrm e}^{2}+{\mathrm e}^{4}+36}-7\right )}{16+\ln \left (x \right )}}\) | \(38\) |
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Time = 0.25 (sec) , antiderivative size = 36, normalized size of antiderivative = 1.38 \[ \int \frac {e^{\frac {-7 x+e^{36+e^4+12 x^2+x^4+e^2 \left (-12-2 x^2\right )} x}{16+\log (x)}} \left (-105+e^{36+e^4+12 x^2+x^4+e^2 \left (-12-2 x^2\right )} \left (15+384 x^2-64 e^2 x^2+64 x^4\right )+\left (-7+e^{36+e^4+12 x^2+x^4+e^2 \left (-12-2 x^2\right )} \left (1+24 x^2-4 e^2 x^2+4 x^4\right )\right ) \log (x)\right )}{256+32 \log (x)+\log ^2(x)} \, dx=e^{\left (\frac {x e^{\left (x^{4} + 12 \, x^{2} - 2 \, {\left (x^{2} + 6\right )} e^{2} + e^{4} + 36\right )} - 7 \, x}{\log \left (x\right ) + 16}\right )} \]
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Time = 1.61 (sec) , antiderivative size = 37, normalized size of antiderivative = 1.42 \[ \int \frac {e^{\frac {-7 x+e^{36+e^4+12 x^2+x^4+e^2 \left (-12-2 x^2\right )} x}{16+\log (x)}} \left (-105+e^{36+e^4+12 x^2+x^4+e^2 \left (-12-2 x^2\right )} \left (15+384 x^2-64 e^2 x^2+64 x^4\right )+\left (-7+e^{36+e^4+12 x^2+x^4+e^2 \left (-12-2 x^2\right )} \left (1+24 x^2-4 e^2 x^2+4 x^4\right )\right ) \log (x)\right )}{256+32 \log (x)+\log ^2(x)} \, dx=e^{\frac {x e^{x^{4} + 12 x^{2} + \left (- 2 x^{2} - 12\right ) e^{2} + 36 + e^{4}} - 7 x}{\log {\left (x \right )} + 16}} \]
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Exception generated. \[ \int \frac {e^{\frac {-7 x+e^{36+e^4+12 x^2+x^4+e^2 \left (-12-2 x^2\right )} x}{16+\log (x)}} \left (-105+e^{36+e^4+12 x^2+x^4+e^2 \left (-12-2 x^2\right )} \left (15+384 x^2-64 e^2 x^2+64 x^4\right )+\left (-7+e^{36+e^4+12 x^2+x^4+e^2 \left (-12-2 x^2\right )} \left (1+24 x^2-4 e^2 x^2+4 x^4\right )\right ) \log (x)\right )}{256+32 \log (x)+\log ^2(x)} \, dx=\text {Exception raised: RuntimeError} \]
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\[ \int \frac {e^{\frac {-7 x+e^{36+e^4+12 x^2+x^4+e^2 \left (-12-2 x^2\right )} x}{16+\log (x)}} \left (-105+e^{36+e^4+12 x^2+x^4+e^2 \left (-12-2 x^2\right )} \left (15+384 x^2-64 e^2 x^2+64 x^4\right )+\left (-7+e^{36+e^4+12 x^2+x^4+e^2 \left (-12-2 x^2\right )} \left (1+24 x^2-4 e^2 x^2+4 x^4\right )\right ) \log (x)\right )}{256+32 \log (x)+\log ^2(x)} \, dx=\int { \frac {{\left ({\left (64 \, x^{4} - 64 \, x^{2} e^{2} + 384 \, x^{2} + 15\right )} e^{\left (x^{4} + 12 \, x^{2} - 2 \, {\left (x^{2} + 6\right )} e^{2} + e^{4} + 36\right )} + {\left ({\left (4 \, x^{4} - 4 \, x^{2} e^{2} + 24 \, x^{2} + 1\right )} e^{\left (x^{4} + 12 \, x^{2} - 2 \, {\left (x^{2} + 6\right )} e^{2} + e^{4} + 36\right )} - 7\right )} \log \left (x\right ) - 105\right )} e^{\left (\frac {x e^{\left (x^{4} + 12 \, x^{2} - 2 \, {\left (x^{2} + 6\right )} e^{2} + e^{4} + 36\right )} - 7 \, x}{\log \left (x\right ) + 16}\right )}}{\log \left (x\right )^{2} + 32 \, \log \left (x\right ) + 256} \,d x } \]
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Time = 11.71 (sec) , antiderivative size = 48, normalized size of antiderivative = 1.85 \[ \int \frac {e^{\frac {-7 x+e^{36+e^4+12 x^2+x^4+e^2 \left (-12-2 x^2\right )} x}{16+\log (x)}} \left (-105+e^{36+e^4+12 x^2+x^4+e^2 \left (-12-2 x^2\right )} \left (15+384 x^2-64 e^2 x^2+64 x^4\right )+\left (-7+e^{36+e^4+12 x^2+x^4+e^2 \left (-12-2 x^2\right )} \left (1+24 x^2-4 e^2 x^2+4 x^4\right )\right ) \log (x)\right )}{256+32 \log (x)+\log ^2(x)} \, dx={\mathrm {e}}^{\frac {x\,{\mathrm {e}}^{-2\,x^2\,{\mathrm {e}}^2}\,{\mathrm {e}}^{-12\,{\mathrm {e}}^2}\,{\mathrm {e}}^{x^4}\,{\mathrm {e}}^{36}\,{\mathrm {e}}^{12\,x^2}\,{\mathrm {e}}^{{\mathrm {e}}^4}}{\ln \left (x\right )+16}}\,{\mathrm {e}}^{-\frac {7\,x}{\ln \left (x\right )+16}} \]
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