Integrand size = 183, antiderivative size = 31 \[ \int \frac {e^{\frac {e^{2/x} x-x \log \left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )}{\log \left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )}} \left (4 e^{2/x} x^3+e^{2/x} \left (2 x^2-x^3+(-2+x) \log (6)\right ) \log \left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )+\left (x^3-x \log (6)\right ) \log ^2\left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )\right )}{\left (-x^3+x \log (6)\right ) \log ^2\left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )} \, dx=-5+e^{x \left (-1+\frac {e^{2/x}}{\log \left (3 \left (x^2-\log (6)\right )^2\right )}\right )} \]
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\[ \int \frac {e^{\frac {e^{2/x} x-x \log \left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )}{\log \left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )}} \left (4 e^{2/x} x^3+e^{2/x} \left (2 x^2-x^3+(-2+x) \log (6)\right ) \log \left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )+\left (x^3-x \log (6)\right ) \log ^2\left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )\right )}{\left (-x^3+x \log (6)\right ) \log ^2\left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )} \, dx=\int \frac {\exp \left (\frac {e^{2/x} x-x \log \left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )}{\log \left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )}\right ) \left (4 e^{2/x} x^3+e^{2/x} \left (2 x^2-x^3+(-2+x) \log (6)\right ) \log \left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )+\left (x^3-x \log (6)\right ) \log ^2\left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )\right )}{\left (-x^3+x \log (6)\right ) \log ^2\left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {\exp \left (\frac {e^{2/x} x-x \log \left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )}{\log \left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )}\right ) \left (4 e^{2/x} x^3+e^{2/x} \left (2 x^2-x^3+(-2+x) \log (6)\right ) \log \left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )+\left (x^3-x \log (6)\right ) \log ^2\left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )\right )}{x \left (-x^2+\log (6)\right ) \log ^2\left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )} \, dx \\ & = \int \frac {e^{-x+\frac {e^{2/x} x}{\log \left (3 \left (x^2-\log (6)\right )^2\right )}} \left (-4 e^{2/x} x^3+e^{2/x} (-2+x) \left (x^2-\log (6)\right ) \log \left (3 \left (x^2-\log (6)\right )^2\right )+\left (-x^3+x \log (6)\right ) \log ^2\left (3 \left (x^2-\log (6)\right )^2\right )\right )}{x \left (x^2-\log (6)\right ) \log ^2\left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )} \, dx \\ & = \int \left (-e^{-x+\frac {e^{2/x} x}{\log \left (3 \left (x^2-\log (6)\right )^2\right )}}+\frac {e^{\frac {2}{x}-x+\frac {e^{2/x} x}{\log \left (3 \left (x^2-\log (6)\right )^2\right )}} \left (-4 x^3-2 x^2 \log \left (3 \left (x^2-\log (6)\right )^2\right )+x^3 \log \left (3 \left (x^2-\log (6)\right )^2\right )+2 \log (6) \log \left (3 \left (x^2-\log (6)\right )^2\right )-x \log (6) \log \left (3 \left (x^2-\log (6)\right )^2\right )\right )}{x \left (x^2-\log (6)\right ) \log ^2\left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )}\right ) \, dx \\ & = -\int e^{-x+\frac {e^{2/x} x}{\log \left (3 \left (x^2-\log (6)\right )^2\right )}} \, dx+\int \frac {e^{\frac {2}{x}-x+\frac {e^{2/x} x}{\log \left (3 \left (x^2-\log (6)\right )^2\right )}} \left (-4 x^3-2 x^2 \log \left (3 \left (x^2-\log (6)\right )^2\right )+x^3 \log \left (3 \left (x^2-\log (6)\right )^2\right )+2 \log (6) \log \left (3 \left (x^2-\log (6)\right )^2\right )-x \log (6) \log \left (3 \left (x^2-\log (6)\right )^2\right )\right )}{x \left (x^2-\log (6)\right ) \log ^2\left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )} \, dx \\ & = -\int e^{-x+\frac {e^{2/x} x}{\log \left (3 \left (x^2-\log (6)\right )^2\right )}} \, dx+\int \frac {e^{\frac {2}{x}-x+\frac {e^{2/x} x}{\log \left (3 \left (x^2-\log (6)\right )^2\right )}} \left (-4 x^3+(-2+x) \left (x^2-\log (6)\right ) \log \left (3 \left (x^2-\log (6)\right )^2\right )\right )}{x \left (x^2-\log (6)\right ) \log ^2\left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )} \, dx \\ & = -\int e^{-x+\frac {e^{2/x} x}{\log \left (3 \left (x^2-\log (6)\right )^2\right )}} \, dx+\int \left (\frac {e^{\frac {2}{x}-x+\frac {e^{2/x} x}{\log \left (3 \left (x^2-\log (6)\right )^2\right )}} x \left (-4 x^3-2 x^2 \log \left (3 \left (x^2-\log (6)\right )^2\right )+x^3 \log \left (3 \left (x^2-\log (6)\right )^2\right )+2 \log (6) \log \left (3 \left (x^2-\log (6)\right )^2\right )-x \log (6) \log \left (3 \left (x^2-\log (6)\right )^2\right )\right )}{\left (x^2-\log (6)\right ) \log (6) \log ^2\left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )}+\frac {e^{\frac {2}{x}-x+\frac {e^{2/x} x}{\log \left (3 \left (x^2-\log (6)\right )^2\right )}} \left (4 x^3+2 x^2 \log \left (3 \left (x^2-\log (6)\right )^2\right )-x^3 \log \left (3 \left (x^2-\log (6)\right )^2\right )-2 \log (6) \log \left (3 \left (x^2-\log (6)\right )^2\right )+x \log (6) \log \left (3 \left (x^2-\log (6)\right )^2\right )\right )}{x \log (6) \log ^2\left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )}\right ) \, dx \\ & = \frac {\int \frac {e^{\frac {2}{x}-x+\frac {e^{2/x} x}{\log \left (3 \left (x^2-\log (6)\right )^2\right )}} x \left (-4 x^3-2 x^2 \log \left (3 \left (x^2-\log (6)\right )^2\right )+x^3 \log \left (3 \left (x^2-\log (6)\right )^2\right )+2 \log (6) \log \left (3 \left (x^2-\log (6)\right )^2\right )-x \log (6) \log \left (3 \left (x^2-\log (6)\right )^2\right )\right )}{\left (x^2-\log (6)\right ) \log ^2\left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )} \, dx}{\log (6)}+\frac {\int \frac {e^{\frac {2}{x}-x+\frac {e^{2/x} x}{\log \left (3 \left (x^2-\log (6)\right )^2\right )}} \left (4 x^3+2 x^2 \log \left (3 \left (x^2-\log (6)\right )^2\right )-x^3 \log \left (3 \left (x^2-\log (6)\right )^2\right )-2 \log (6) \log \left (3 \left (x^2-\log (6)\right )^2\right )+x \log (6) \log \left (3 \left (x^2-\log (6)\right )^2\right )\right )}{x \log ^2\left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )} \, dx}{\log (6)}-\int e^{-x+\frac {e^{2/x} x}{\log \left (3 \left (x^2-\log (6)\right )^2\right )}} \, dx \\ & = \frac {\int \frac {e^{\frac {2}{x}-x+\frac {e^{2/x} x}{\log \left (3 \left (x^2-\log (6)\right )^2\right )}} \left (4 x^3-(-2+x) \left (x^2-\log (6)\right ) \log \left (3 \left (x^2-\log (6)\right )^2\right )\right )}{x \log ^2\left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )} \, dx}{\log (6)}+\frac {\int \frac {e^{\frac {2}{x}-x+\frac {e^{2/x} x}{\log \left (3 \left (x^2-\log (6)\right )^2\right )}} x \left (-4 x^3+(-2+x) \left (x^2-\log (6)\right ) \log \left (3 \left (x^2-\log (6)\right )^2\right )\right )}{\left (x^2-\log (6)\right ) \log ^2\left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )} \, dx}{\log (6)}-\int e^{-x+\frac {e^{2/x} x}{\log \left (3 \left (x^2-\log (6)\right )^2\right )}} \, dx \\ & = \frac {\int \left (\frac {4 e^{\frac {2}{x}-x+\frac {e^{2/x} x}{\log \left (3 \left (x^2-\log (6)\right )^2\right )}} x^2}{\log ^2\left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )}+\frac {2 e^{\frac {2}{x}-x+\frac {e^{2/x} x}{\log \left (3 \left (x^2-\log (6)\right )^2\right )}} x}{\log \left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )}-\frac {e^{\frac {2}{x}-x+\frac {e^{2/x} x}{\log \left (3 \left (x^2-\log (6)\right )^2\right )}} x^2}{\log \left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )}+\frac {e^{\frac {2}{x}-x+\frac {e^{2/x} x}{\log \left (3 \left (x^2-\log (6)\right )^2\right )}} \log (6)}{\log \left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )}-\frac {2 e^{\frac {2}{x}-x+\frac {e^{2/x} x}{\log \left (3 \left (x^2-\log (6)\right )^2\right )}} \log (6)}{x \log \left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )}\right ) \, dx}{\log (6)}+\frac {\int \left (\frac {4 e^{\frac {2}{x}-x+\frac {e^{2/x} x}{\log \left (3 \left (x^2-\log (6)\right )^2\right )}} x^4}{\left (-x^2+\log (6)\right ) \log ^2\left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )}+\frac {e^{\frac {2}{x}-x+\frac {e^{2/x} x}{\log \left (3 \left (x^2-\log (6)\right )^2\right )}} x^4}{\left (x^2-\log (6)\right ) \log \left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )}+\frac {2 e^{\frac {2}{x}-x+\frac {e^{2/x} x}{\log \left (3 \left (x^2-\log (6)\right )^2\right )}} x \log (6)}{\left (x^2-\log (6)\right ) \log \left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )}+\frac {2 e^{\frac {2}{x}-x+\frac {e^{2/x} x}{\log \left (3 \left (x^2-\log (6)\right )^2\right )}} x^3}{\left (-x^2+\log (6)\right ) \log \left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )}+\frac {e^{\frac {2}{x}-x+\frac {e^{2/x} x}{\log \left (3 \left (x^2-\log (6)\right )^2\right )}} x^2 \log (6)}{\left (-x^2+\log (6)\right ) \log \left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )}\right ) \, dx}{\log (6)}-\int e^{-x+\frac {e^{2/x} x}{\log \left (3 \left (x^2-\log (6)\right )^2\right )}} \, dx \\ & = -\left (2 \int \frac {e^{\frac {2}{x}-x+\frac {e^{2/x} x}{\log \left (3 \left (x^2-\log (6)\right )^2\right )}}}{x \log \left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )} \, dx\right )+2 \int \frac {e^{\frac {2}{x}-x+\frac {e^{2/x} x}{\log \left (3 \left (x^2-\log (6)\right )^2\right )}} x}{\left (x^2-\log (6)\right ) \log \left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )} \, dx-\frac {\int \frac {e^{\frac {2}{x}-x+\frac {e^{2/x} x}{\log \left (3 \left (x^2-\log (6)\right )^2\right )}} x^2}{\log \left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )} \, dx}{\log (6)}+\frac {\int \frac {e^{\frac {2}{x}-x+\frac {e^{2/x} x}{\log \left (3 \left (x^2-\log (6)\right )^2\right )}} x^4}{\left (x^2-\log (6)\right ) \log \left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )} \, dx}{\log (6)}+\frac {2 \int \frac {e^{\frac {2}{x}-x+\frac {e^{2/x} x}{\log \left (3 \left (x^2-\log (6)\right )^2\right )}} x}{\log \left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )} \, dx}{\log (6)}+\frac {2 \int \frac {e^{\frac {2}{x}-x+\frac {e^{2/x} x}{\log \left (3 \left (x^2-\log (6)\right )^2\right )}} x^3}{\left (-x^2+\log (6)\right ) \log \left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )} \, dx}{\log (6)}+\frac {4 \int \frac {e^{\frac {2}{x}-x+\frac {e^{2/x} x}{\log \left (3 \left (x^2-\log (6)\right )^2\right )}} x^2}{\log ^2\left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )} \, dx}{\log (6)}+\frac {4 \int \frac {e^{\frac {2}{x}-x+\frac {e^{2/x} x}{\log \left (3 \left (x^2-\log (6)\right )^2\right )}} x^4}{\left (-x^2+\log (6)\right ) \log ^2\left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )} \, dx}{\log (6)}-\int e^{-x+\frac {e^{2/x} x}{\log \left (3 \left (x^2-\log (6)\right )^2\right )}} \, dx+\int \frac {e^{\frac {2}{x}-x+\frac {e^{2/x} x}{\log \left (3 \left (x^2-\log (6)\right )^2\right )}}}{\log \left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )} \, dx+\int \frac {e^{\frac {2}{x}-x+\frac {e^{2/x} x}{\log \left (3 \left (x^2-\log (6)\right )^2\right )}} x^2}{\left (-x^2+\log (6)\right ) \log \left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )} \, dx \\ & = \text {Too large to display} \\ \end{align*}
Time = 0.17 (sec) , antiderivative size = 29, normalized size of antiderivative = 0.94 \[ \int \frac {e^{\frac {e^{2/x} x-x \log \left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )}{\log \left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )}} \left (4 e^{2/x} x^3+e^{2/x} \left (2 x^2-x^3+(-2+x) \log (6)\right ) \log \left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )+\left (x^3-x \log (6)\right ) \log ^2\left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )\right )}{\left (-x^3+x \log (6)\right ) \log ^2\left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )} \, dx=e^{x \left (-1+\frac {e^{2/x}}{\log \left (3 \left (x^2-\log (6)\right )^2\right )}\right )} \]
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Time = 137.58 (sec) , antiderivative size = 56, normalized size of antiderivative = 1.81
method | result | size |
parallelrisch | \({\mathrm e}^{-\frac {x \left (\ln \left (3 \ln \left (6\right )^{2}-6 x^{2} \ln \left (6\right )+3 x^{4}\right )-{\mathrm e}^{\frac {2}{x}}\right )}{\ln \left (3 \ln \left (6\right )^{2}-6 x^{2} \ln \left (6\right )+3 x^{4}\right )}}\) | \(56\) |
risch | \({\mathrm e}^{-\frac {x \left (-i \pi {\operatorname {csgn}\left (i \left (-x^{2}+\ln \left (6\right )\right )^{2}\right )}^{3}+2 i \pi {\operatorname {csgn}\left (i \left (-x^{2}+\ln \left (6\right )\right )^{2}\right )}^{2} \operatorname {csgn}\left (i \left (-x^{2}+\ln \left (6\right )\right )\right )-i \pi \,\operatorname {csgn}\left (i \left (-x^{2}+\ln \left (6\right )\right )^{2}\right ) {\operatorname {csgn}\left (i \left (-x^{2}+\ln \left (6\right )\right )\right )}^{2}-2 \,{\mathrm e}^{\frac {2}{x}}+2 \ln \left (3\right )+4 \ln \left (-x^{2}+\ln \left (2\right )+\ln \left (3\right )\right )\right )}{-i \pi {\operatorname {csgn}\left (i \left (-x^{2}+\ln \left (6\right )\right )^{2}\right )}^{3}+2 i \pi {\operatorname {csgn}\left (i \left (-x^{2}+\ln \left (6\right )\right )^{2}\right )}^{2} \operatorname {csgn}\left (i \left (-x^{2}+\ln \left (6\right )\right )\right )-i \pi \,\operatorname {csgn}\left (i \left (-x^{2}+\ln \left (6\right )\right )^{2}\right ) {\operatorname {csgn}\left (i \left (-x^{2}+\ln \left (6\right )\right )\right )}^{2}+2 \ln \left (3\right )+4 \ln \left (-x^{2}+\ln \left (2\right )+\ln \left (3\right )\right )}}\) | \(219\) |
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Time = 0.28 (sec) , antiderivative size = 56, normalized size of antiderivative = 1.81 \[ \int \frac {e^{\frac {e^{2/x} x-x \log \left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )}{\log \left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )}} \left (4 e^{2/x} x^3+e^{2/x} \left (2 x^2-x^3+(-2+x) \log (6)\right ) \log \left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )+\left (x^3-x \log (6)\right ) \log ^2\left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )\right )}{\left (-x^3+x \log (6)\right ) \log ^2\left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )} \, dx=e^{\left (\frac {x e^{\frac {2}{x}} - x \log \left (3 \, x^{4} - 6 \, x^{2} \log \left (6\right ) + 3 \, \log \left (6\right )^{2}\right )}{\log \left (3 \, x^{4} - 6 \, x^{2} \log \left (6\right ) + 3 \, \log \left (6\right )^{2}\right )}\right )} \]
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Leaf count of result is larger than twice the leaf count of optimal. 53 vs. \(2 (22) = 44\).
Time = 0.54 (sec) , antiderivative size = 53, normalized size of antiderivative = 1.71 \[ \int \frac {e^{\frac {e^{2/x} x-x \log \left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )}{\log \left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )}} \left (4 e^{2/x} x^3+e^{2/x} \left (2 x^2-x^3+(-2+x) \log (6)\right ) \log \left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )+\left (x^3-x \log (6)\right ) \log ^2\left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )\right )}{\left (-x^3+x \log (6)\right ) \log ^2\left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )} \, dx=e^{\frac {x e^{\frac {2}{x}} - x \log {\left (3 x^{4} - 6 x^{2} \log {\left (6 \right )} + 3 \log {\left (6 \right )}^{2} \right )}}{\log {\left (3 x^{4} - 6 x^{2} \log {\left (6 \right )} + 3 \log {\left (6 \right )}^{2} \right )}}} \]
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Exception generated. \[ \int \frac {e^{\frac {e^{2/x} x-x \log \left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )}{\log \left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )}} \left (4 e^{2/x} x^3+e^{2/x} \left (2 x^2-x^3+(-2+x) \log (6)\right ) \log \left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )+\left (x^3-x \log (6)\right ) \log ^2\left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )\right )}{\left (-x^3+x \log (6)\right ) \log ^2\left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )} \, dx=\text {Exception raised: RuntimeError} \]
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Time = 6.35 (sec) , antiderivative size = 35, normalized size of antiderivative = 1.13 \[ \int \frac {e^{\frac {e^{2/x} x-x \log \left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )}{\log \left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )}} \left (4 e^{2/x} x^3+e^{2/x} \left (2 x^2-x^3+(-2+x) \log (6)\right ) \log \left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )+\left (x^3-x \log (6)\right ) \log ^2\left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )\right )}{\left (-x^3+x \log (6)\right ) \log ^2\left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )} \, dx=e^{\left (-x + \frac {x e^{\frac {2}{x}}}{\log \left (3 \, x^{4} - 6 \, x^{2} \log \left (6\right ) + 3 \, \log \left (6\right )^{2}\right )}\right )} \]
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Time = 13.12 (sec) , antiderivative size = 36, normalized size of antiderivative = 1.16 \[ \int \frac {e^{\frac {e^{2/x} x-x \log \left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )}{\log \left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )}} \left (4 e^{2/x} x^3+e^{2/x} \left (2 x^2-x^3+(-2+x) \log (6)\right ) \log \left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )+\left (x^3-x \log (6)\right ) \log ^2\left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )\right )}{\left (-x^3+x \log (6)\right ) \log ^2\left (3 x^4-6 x^2 \log (6)+3 \log ^2(6)\right )} \, dx={\mathrm {e}}^{\frac {x\,{\mathrm {e}}^{2/x}}{\ln \left (3\,x^4-6\,\ln \left (6\right )\,x^2+3\,{\ln \left (6\right )}^2\right )}}\,{\mathrm {e}}^{-x} \]
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