Integrand size = 113, antiderivative size = 30 \[ \int \frac {-2 e^{2 e^{x^2} (-3+x)} x+e^{e^{\log ^2(2)}+e^{x^2} (-3+x)} \left (2+\left (2+e^{x^2} \left (2 x-12 x^2+4 x^3\right )\right ) \log (x)\right )}{e^{2 e^{\log ^2(2)}}-2 e^{e^{\log ^2(2)}+e^{x^2} (-3+x)} x+e^{2 e^{x^2} (-3+x)} x^2} \, dx=\frac {2 x \log (x)}{e^{e^{\log ^2(2)}-e^{x^2} (-3+x)}-x} \]
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\[ \int \frac {-2 e^{2 e^{x^2} (-3+x)} x+e^{e^{\log ^2(2)}+e^{x^2} (-3+x)} \left (2+\left (2+e^{x^2} \left (2 x-12 x^2+4 x^3\right )\right ) \log (x)\right )}{e^{2 e^{\log ^2(2)}}-2 e^{e^{\log ^2(2)}+e^{x^2} (-3+x)} x+e^{2 e^{x^2} (-3+x)} x^2} \, dx=\int \frac {-2 e^{2 e^{x^2} (-3+x)} x+e^{e^{\log ^2(2)}+e^{x^2} (-3+x)} \left (2+\left (2+e^{x^2} \left (2 x-12 x^2+4 x^3\right )\right ) \log (x)\right )}{e^{2 e^{\log ^2(2)}}-2 e^{e^{\log ^2(2)}+e^{x^2} (-3+x)} x+e^{2 e^{x^2} (-3+x)} x^2} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {-2 e^{2 e^{x^2} (-3+x)} x+e^{e^{\log ^2(2)}+e^{x^2} (-3+x)} \left (2+\left (2+e^{x^2} \left (2 x-12 x^2+4 x^3\right )\right ) \log (x)\right )}{\left (e^{e^{\log ^2(2)}}-e^{e^{x^2} (-3+x)} x\right )^2} \, dx \\ & = \int \left (\frac {2 e^{e^{\log ^2(2)}+e^{x^2} (-3+x)+x^2} x \left (1-6 x+2 x^2\right ) \log (x)}{\left (-e^{e^{\log ^2(2)}}+e^{e^{x^2} (-3+x)} x\right )^2}-\frac {2 e^{e^{x^2} (-3+x)} \left (-e^{e^{\log ^2(2)}}+e^{e^{x^2} (-3+x)} x-e^{e^{\log ^2(2)}} \log (x)\right )}{\left (-e^{e^{\log ^2(2)}}+e^{e^{x^2} (-3+x)} x\right )^2}\right ) \, dx \\ & = 2 \int \frac {e^{e^{\log ^2(2)}+e^{x^2} (-3+x)+x^2} x \left (1-6 x+2 x^2\right ) \log (x)}{\left (-e^{e^{\log ^2(2)}}+e^{e^{x^2} (-3+x)} x\right )^2} \, dx-2 \int \frac {e^{e^{x^2} (-3+x)} \left (-e^{e^{\log ^2(2)}}+e^{e^{x^2} (-3+x)} x-e^{e^{\log ^2(2)}} \log (x)\right )}{\left (-e^{e^{\log ^2(2)}}+e^{e^{x^2} (-3+x)} x\right )^2} \, dx \\ & = -\left (2 \int \left (-\frac {e^{e^{x^2} (-3+x)}}{e^{e^{\log ^2(2)}}-e^{e^{x^2} (-3+x)} x}-\frac {e^{e^{\log ^2(2)}+e^{x^2} (-3+x)} \log (x)}{\left (e^{e^{\log ^2(2)}}-e^{e^{x^2} (-3+x)} x\right )^2}\right ) \, dx\right )-2 \int \frac {\int \frac {e^{e^{\log ^2(2)}+e^{x^2} (-3+x)+x^2} x}{\left (e^{e^{\log ^2(2)}}-e^{e^{x^2} (-3+x)} x\right )^2} \, dx-6 \int \frac {e^{e^{\log ^2(2)}+e^{x^2} (-3+x)+x^2} x^2}{\left (e^{e^{\log ^2(2)}}-e^{e^{x^2} (-3+x)} x\right )^2} \, dx+2 \int \frac {e^{e^{\log ^2(2)}+e^{x^2} (-3+x)+x^2} x^3}{\left (e^{e^{\log ^2(2)}}-e^{e^{x^2} (-3+x)} x\right )^2} \, dx}{x} \, dx+(2 \log (x)) \int \frac {e^{e^{\log ^2(2)}+e^{x^2} (-3+x)+x^2} x}{\left (-e^{e^{\log ^2(2)}}+e^{e^{x^2} (-3+x)} x\right )^2} \, dx+(4 \log (x)) \int \frac {e^{e^{\log ^2(2)}+e^{x^2} (-3+x)+x^2} x^3}{\left (-e^{e^{\log ^2(2)}}+e^{e^{x^2} (-3+x)} x\right )^2} \, dx-(12 \log (x)) \int \frac {e^{e^{\log ^2(2)}+e^{x^2} (-3+x)+x^2} x^2}{\left (-e^{e^{\log ^2(2)}}+e^{e^{x^2} (-3+x)} x\right )^2} \, dx \\ & = 2 \int \frac {e^{e^{x^2} (-3+x)}}{e^{e^{\log ^2(2)}}-e^{e^{x^2} (-3+x)} x} \, dx+2 \int \frac {e^{e^{\log ^2(2)}+e^{x^2} (-3+x)} \log (x)}{\left (e^{e^{\log ^2(2)}}-e^{e^{x^2} (-3+x)} x\right )^2} \, dx-2 \int \left (\frac {\int \frac {e^{e^{\log ^2(2)}+e^{x^2} (-3+x)+x^2} x}{\left (e^{e^{\log ^2(2)}}-e^{e^{x^2} (-3+x)} x\right )^2} \, dx-6 \int \frac {e^{e^{\log ^2(2)}+e^{x^2} (-3+x)+x^2} x^2}{\left (e^{e^{\log ^2(2)}}-e^{e^{x^2} (-3+x)} x\right )^2} \, dx}{x}+\frac {2 \int \frac {e^{e^{\log ^2(2)}+e^{x^2} (-3+x)+x^2} x^3}{\left (e^{e^{\log ^2(2)}}-e^{e^{x^2} (-3+x)} x\right )^2} \, dx}{x}\right ) \, dx+(2 \log (x)) \int \frac {e^{e^{\log ^2(2)}+e^{x^2} (-3+x)+x^2} x}{\left (-e^{e^{\log ^2(2)}}+e^{e^{x^2} (-3+x)} x\right )^2} \, dx+(4 \log (x)) \int \frac {e^{e^{\log ^2(2)}+e^{x^2} (-3+x)+x^2} x^3}{\left (-e^{e^{\log ^2(2)}}+e^{e^{x^2} (-3+x)} x\right )^2} \, dx-(12 \log (x)) \int \frac {e^{e^{\log ^2(2)}+e^{x^2} (-3+x)+x^2} x^2}{\left (-e^{e^{\log ^2(2)}}+e^{e^{x^2} (-3+x)} x\right )^2} \, dx \\ & = 2 \int \frac {e^{e^{x^2} (-3+x)}}{e^{e^{\log ^2(2)}}-e^{e^{x^2} (-3+x)} x} \, dx-2 \int \frac {\int \frac {e^{e^{\log ^2(2)}+e^{x^2} (-3+x)}}{\left (e^{e^{\log ^2(2)}}-e^{e^{x^2} (-3+x)} x\right )^2} \, dx}{x} \, dx-2 \int \frac {\int \frac {e^{e^{\log ^2(2)}+e^{x^2} (-3+x)+x^2} x}{\left (e^{e^{\log ^2(2)}}-e^{e^{x^2} (-3+x)} x\right )^2} \, dx-6 \int \frac {e^{e^{\log ^2(2)}+e^{x^2} (-3+x)+x^2} x^2}{\left (e^{e^{\log ^2(2)}}-e^{e^{x^2} (-3+x)} x\right )^2} \, dx}{x} \, dx-4 \int \frac {\int \frac {e^{e^{\log ^2(2)}+e^{x^2} (-3+x)+x^2} x^3}{\left (e^{e^{\log ^2(2)}}-e^{e^{x^2} (-3+x)} x\right )^2} \, dx}{x} \, dx+(2 \log (x)) \int \frac {e^{e^{\log ^2(2)}+e^{x^2} (-3+x)}}{\left (e^{e^{\log ^2(2)}}-e^{e^{x^2} (-3+x)} x\right )^2} \, dx+(2 \log (x)) \int \frac {e^{e^{\log ^2(2)}+e^{x^2} (-3+x)+x^2} x}{\left (-e^{e^{\log ^2(2)}}+e^{e^{x^2} (-3+x)} x\right )^2} \, dx+(4 \log (x)) \int \frac {e^{e^{\log ^2(2)}+e^{x^2} (-3+x)+x^2} x^3}{\left (-e^{e^{\log ^2(2)}}+e^{e^{x^2} (-3+x)} x\right )^2} \, dx-(12 \log (x)) \int \frac {e^{e^{\log ^2(2)}+e^{x^2} (-3+x)+x^2} x^2}{\left (-e^{e^{\log ^2(2)}}+e^{e^{x^2} (-3+x)} x\right )^2} \, dx \\ & = 2 \int \frac {e^{e^{x^2} (-3+x)}}{e^{e^{\log ^2(2)}}-e^{e^{x^2} (-3+x)} x} \, dx-2 \int \frac {\int \frac {e^{e^{\log ^2(2)}+e^{x^2} (-3+x)}}{\left (e^{e^{\log ^2(2)}}-e^{e^{x^2} (-3+x)} x\right )^2} \, dx}{x} \, dx-2 \int \left (\frac {\int \frac {e^{e^{\log ^2(2)}+e^{x^2} (-3+x)+x^2} x}{\left (e^{e^{\log ^2(2)}}-e^{e^{x^2} (-3+x)} x\right )^2} \, dx}{x}-\frac {6 \int \frac {e^{e^{\log ^2(2)}+e^{x^2} (-3+x)+x^2} x^2}{\left (e^{e^{\log ^2(2)}}-e^{e^{x^2} (-3+x)} x\right )^2} \, dx}{x}\right ) \, dx-4 \int \frac {\int \frac {e^{e^{\log ^2(2)}+e^{x^2} (-3+x)+x^2} x^3}{\left (e^{e^{\log ^2(2)}}-e^{e^{x^2} (-3+x)} x\right )^2} \, dx}{x} \, dx+(2 \log (x)) \int \frac {e^{e^{\log ^2(2)}+e^{x^2} (-3+x)}}{\left (e^{e^{\log ^2(2)}}-e^{e^{x^2} (-3+x)} x\right )^2} \, dx+(2 \log (x)) \int \frac {e^{e^{\log ^2(2)}+e^{x^2} (-3+x)+x^2} x}{\left (-e^{e^{\log ^2(2)}}+e^{e^{x^2} (-3+x)} x\right )^2} \, dx+(4 \log (x)) \int \frac {e^{e^{\log ^2(2)}+e^{x^2} (-3+x)+x^2} x^3}{\left (-e^{e^{\log ^2(2)}}+e^{e^{x^2} (-3+x)} x\right )^2} \, dx-(12 \log (x)) \int \frac {e^{e^{\log ^2(2)}+e^{x^2} (-3+x)+x^2} x^2}{\left (-e^{e^{\log ^2(2)}}+e^{e^{x^2} (-3+x)} x\right )^2} \, dx \\ & = 2 \int \frac {e^{e^{x^2} (-3+x)}}{e^{e^{\log ^2(2)}}-e^{e^{x^2} (-3+x)} x} \, dx-2 \int \frac {\int \frac {e^{e^{\log ^2(2)}+e^{x^2} (-3+x)}}{\left (e^{e^{\log ^2(2)}}-e^{e^{x^2} (-3+x)} x\right )^2} \, dx}{x} \, dx-2 \int \frac {\int \frac {e^{e^{\log ^2(2)}+e^{x^2} (-3+x)+x^2} x}{\left (e^{e^{\log ^2(2)}}-e^{e^{x^2} (-3+x)} x\right )^2} \, dx}{x} \, dx-4 \int \frac {\int \frac {e^{e^{\log ^2(2)}+e^{x^2} (-3+x)+x^2} x^3}{\left (e^{e^{\log ^2(2)}}-e^{e^{x^2} (-3+x)} x\right )^2} \, dx}{x} \, dx+12 \int \frac {\int \frac {e^{e^{\log ^2(2)}+e^{x^2} (-3+x)+x^2} x^2}{\left (e^{e^{\log ^2(2)}}-e^{e^{x^2} (-3+x)} x\right )^2} \, dx}{x} \, dx+(2 \log (x)) \int \frac {e^{e^{\log ^2(2)}+e^{x^2} (-3+x)}}{\left (e^{e^{\log ^2(2)}}-e^{e^{x^2} (-3+x)} x\right )^2} \, dx+(2 \log (x)) \int \frac {e^{e^{\log ^2(2)}+e^{x^2} (-3+x)+x^2} x}{\left (-e^{e^{\log ^2(2)}}+e^{e^{x^2} (-3+x)} x\right )^2} \, dx+(4 \log (x)) \int \frac {e^{e^{\log ^2(2)}+e^{x^2} (-3+x)+x^2} x^3}{\left (-e^{e^{\log ^2(2)}}+e^{e^{x^2} (-3+x)} x\right )^2} \, dx-(12 \log (x)) \int \frac {e^{e^{\log ^2(2)}+e^{x^2} (-3+x)+x^2} x^2}{\left (-e^{e^{\log ^2(2)}}+e^{e^{x^2} (-3+x)} x\right )^2} \, dx \\ \end{align*}
Time = 0.29 (sec) , antiderivative size = 45, normalized size of antiderivative = 1.50 \[ \int \frac {-2 e^{2 e^{x^2} (-3+x)} x+e^{e^{\log ^2(2)}+e^{x^2} (-3+x)} \left (2+\left (2+e^{x^2} \left (2 x-12 x^2+4 x^3\right )\right ) \log (x)\right )}{e^{2 e^{\log ^2(2)}}-2 e^{e^{\log ^2(2)}+e^{x^2} (-3+x)} x+e^{2 e^{x^2} (-3+x)} x^2} \, dx=2 \left (-\log (x)-\frac {e^{e^{\log ^2(2)}} \log (x)}{-e^{e^{\log ^2(2)}}+e^{e^{x^2} (-3+x)} x}\right ) \]
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Time = 6.15 (sec) , antiderivative size = 36, normalized size of antiderivative = 1.20
method | result | size |
parallelrisch | \(\frac {2 x \ln \left (x \right ) {\mathrm e}^{\left (-3+x \right ) {\mathrm e}^{x^{2}}}}{-x \,{\mathrm e}^{\left (-3+x \right ) {\mathrm e}^{x^{2}}}+{\mathrm e}^{{\mathrm e}^{\ln \left (2\right )^{2}}}}\) | \(36\) |
risch | \(-2 \ln \left (x \right )+\frac {2 \,{\mathrm e}^{{\mathrm e}^{\ln \left (2\right )^{2}}} \ln \left (x \right )}{-x \,{\mathrm e}^{\left (-3+x \right ) {\mathrm e}^{x^{2}}}+{\mathrm e}^{{\mathrm e}^{\ln \left (2\right )^{2}}}}\) | \(37\) |
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Time = 0.24 (sec) , antiderivative size = 50, normalized size of antiderivative = 1.67 \[ \int \frac {-2 e^{2 e^{x^2} (-3+x)} x+e^{e^{\log ^2(2)}+e^{x^2} (-3+x)} \left (2+\left (2+e^{x^2} \left (2 x-12 x^2+4 x^3\right )\right ) \log (x)\right )}{e^{2 e^{\log ^2(2)}}-2 e^{e^{\log ^2(2)}+e^{x^2} (-3+x)} x+e^{2 e^{x^2} (-3+x)} x^2} \, dx=-\frac {2 \, x e^{\left ({\left (x - 3\right )} e^{\left (x^{2}\right )} + e^{\left (\log \left (2\right )^{2}\right )}\right )} \log \left (x\right )}{x e^{\left ({\left (x - 3\right )} e^{\left (x^{2}\right )} + e^{\left (\log \left (2\right )^{2}\right )}\right )} - e^{\left (2 \, e^{\left (\log \left (2\right )^{2}\right )}\right )}} \]
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Time = 0.19 (sec) , antiderivative size = 39, normalized size of antiderivative = 1.30 \[ \int \frac {-2 e^{2 e^{x^2} (-3+x)} x+e^{e^{\log ^2(2)}+e^{x^2} (-3+x)} \left (2+\left (2+e^{x^2} \left (2 x-12 x^2+4 x^3\right )\right ) \log (x)\right )}{e^{2 e^{\log ^2(2)}}-2 e^{e^{\log ^2(2)}+e^{x^2} (-3+x)} x+e^{2 e^{x^2} (-3+x)} x^2} \, dx=- 2 \log {\left (x \right )} - \frac {2 e^{e^{\log {\left (2 \right )}^{2}}} \log {\left (x \right )}}{x e^{\left (x - 3\right ) e^{x^{2}}} - e^{e^{\log {\left (2 \right )}^{2}}}} \]
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Time = 0.41 (sec) , antiderivative size = 49, normalized size of antiderivative = 1.63 \[ \int \frac {-2 e^{2 e^{x^2} (-3+x)} x+e^{e^{\log ^2(2)}+e^{x^2} (-3+x)} \left (2+\left (2+e^{x^2} \left (2 x-12 x^2+4 x^3\right )\right ) \log (x)\right )}{e^{2 e^{\log ^2(2)}}-2 e^{e^{\log ^2(2)}+e^{x^2} (-3+x)} x+e^{2 e^{x^2} (-3+x)} x^2} \, dx=-\frac {2 \, e^{\left (3 \, e^{\left (x^{2}\right )} + e^{\left (\log \left (2\right )^{2}\right )}\right )} \log \left (x\right )}{x e^{\left (x e^{\left (x^{2}\right )}\right )} - e^{\left (3 \, e^{\left (x^{2}\right )} + e^{\left (\log \left (2\right )^{2}\right )}\right )}} - 2 \, \log \left (x\right ) \]
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Time = 0.38 (sec) , antiderivative size = 46, normalized size of antiderivative = 1.53 \[ \int \frac {-2 e^{2 e^{x^2} (-3+x)} x+e^{e^{\log ^2(2)}+e^{x^2} (-3+x)} \left (2+\left (2+e^{x^2} \left (2 x-12 x^2+4 x^3\right )\right ) \log (x)\right )}{e^{2 e^{\log ^2(2)}}-2 e^{e^{\log ^2(2)}+e^{x^2} (-3+x)} x+e^{2 e^{x^2} (-3+x)} x^2} \, dx=-\frac {2 \, x e^{\left (x e^{\left (x^{2}\right )} - 3 \, e^{\left (x^{2}\right )}\right )} \log \left (x\right )}{x e^{\left (x e^{\left (x^{2}\right )} - 3 \, e^{\left (x^{2}\right )}\right )} - e^{\left (e^{\left (\log \left (2\right )^{2}\right )}\right )}} \]
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Time = 9.54 (sec) , antiderivative size = 161, normalized size of antiderivative = 5.37 \[ \int \frac {-2 e^{2 e^{x^2} (-3+x)} x+e^{e^{\log ^2(2)}+e^{x^2} (-3+x)} \left (2+\left (2+e^{x^2} \left (2 x-12 x^2+4 x^3\right )\right ) \log (x)\right )}{e^{2 e^{\log ^2(2)}}-2 e^{e^{\log ^2(2)}+e^{x^2} (-3+x)} x+e^{2 e^{x^2} (-3+x)} x^2} \, dx=-2\,\ln \left (x\right )-\frac {2\,\left (x^2\,{\mathrm {e}}^{x^2+2\,{\mathrm {e}}^{{\ln \left (2\right )}^2}}\,\ln \left (x\right )-6\,x^3\,{\mathrm {e}}^{x^2+2\,{\mathrm {e}}^{{\ln \left (2\right )}^2}}\,\ln \left (x\right )+2\,x^4\,{\mathrm {e}}^{x^2+2\,{\mathrm {e}}^{{\ln \left (2\right )}^2}}\,\ln \left (x\right )+x\,{\mathrm {e}}^{2\,{\mathrm {e}}^{{\ln \left (2\right )}^2}}\,\ln \left (x\right )\right )}{\left ({\mathrm {e}}^{x\,{\mathrm {e}}^{x^2}-3\,{\mathrm {e}}^{x^2}}-\frac {{\mathrm {e}}^{{\mathrm {e}}^{{\ln \left (2\right )}^2}}}{x}\right )\,\left (x^3\,{\mathrm {e}}^{x^2+{\mathrm {e}}^{{\ln \left (2\right )}^2}}-6\,x^4\,{\mathrm {e}}^{x^2+{\mathrm {e}}^{{\ln \left (2\right )}^2}}+2\,x^5\,{\mathrm {e}}^{x^2+{\mathrm {e}}^{{\ln \left (2\right )}^2}}+x^2\,{\mathrm {e}}^{{\mathrm {e}}^{{\ln \left (2\right )}^2}}\right )} \]
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