Integrand size = 144, antiderivative size = 24 \[ \int \frac {-12 e^{e^x}+(-6 x+6 x \log (3)) \log \left (x^2\right )-6 e^{e^x+x} x \log \left (x^2\right ) \log \left (\log \left (x^2\right )\right )+\left ((3 x-3 x \log (3)) \log \left (x^2\right )+3 e^{e^x} \log \left (x^2\right ) \log \left (\log \left (x^2\right )\right )\right ) \log \left (x-x \log (3)+e^{e^x} \log \left (\log \left (x^2\right )\right )\right )}{\left ((x-x \log (3)) \log \left (x^2\right )+e^{e^x} \log \left (x^2\right ) \log \left (\log \left (x^2\right )\right )\right ) \log ^3\left (x-x \log (3)+e^{e^x} \log \left (\log \left (x^2\right )\right )\right )} \, dx=\frac {3 x}{\log ^2\left (x-x \log (3)+e^{e^x} \log \left (\log \left (x^2\right )\right )\right )} \]
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\[ \int \frac {-12 e^{e^x}+(-6 x+6 x \log (3)) \log \left (x^2\right )-6 e^{e^x+x} x \log \left (x^2\right ) \log \left (\log \left (x^2\right )\right )+\left ((3 x-3 x \log (3)) \log \left (x^2\right )+3 e^{e^x} \log \left (x^2\right ) \log \left (\log \left (x^2\right )\right )\right ) \log \left (x-x \log (3)+e^{e^x} \log \left (\log \left (x^2\right )\right )\right )}{\left ((x-x \log (3)) \log \left (x^2\right )+e^{e^x} \log \left (x^2\right ) \log \left (\log \left (x^2\right )\right )\right ) \log ^3\left (x-x \log (3)+e^{e^x} \log \left (\log \left (x^2\right )\right )\right )} \, dx=\int \frac {-12 e^{e^x}+(-6 x+6 x \log (3)) \log \left (x^2\right )-6 e^{e^x+x} x \log \left (x^2\right ) \log \left (\log \left (x^2\right )\right )+\left ((3 x-3 x \log (3)) \log \left (x^2\right )+3 e^{e^x} \log \left (x^2\right ) \log \left (\log \left (x^2\right )\right )\right ) \log \left (x-x \log (3)+e^{e^x} \log \left (\log \left (x^2\right )\right )\right )}{\left ((x-x \log (3)) \log \left (x^2\right )+e^{e^x} \log \left (x^2\right ) \log \left (\log \left (x^2\right )\right )\right ) \log ^3\left (x-x \log (3)+e^{e^x} \log \left (\log \left (x^2\right )\right )\right )} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {-12 e^{e^x}+(-6 x+6 x \log (3)) \log \left (x^2\right )-6 e^{e^x+x} x \log \left (x^2\right ) \log \left (\log \left (x^2\right )\right )+\left ((3 x-3 x \log (3)) \log \left (x^2\right )+3 e^{e^x} \log \left (x^2\right ) \log \left (\log \left (x^2\right )\right )\right ) \log \left (x-x \log (3)+e^{e^x} \log \left (\log \left (x^2\right )\right )\right )}{\log \left (x^2\right ) \left (x (1-\log (3))+e^{e^x} \log \left (\log \left (x^2\right )\right )\right ) \log ^3\left (x (1-\log (3))+e^{e^x} \log \left (\log \left (x^2\right )\right )\right )} \, dx \\ & = \int \left (\frac {6 e^{e^x+x} x \log \left (\log \left (x^2\right )\right )}{\left (-x (1-\log (3))-e^{e^x} \log \left (\log \left (x^2\right )\right )\right ) \log ^3\left (x (1-\log (3))+e^{e^x} \log \left (\log \left (x^2\right )\right )\right )}+\frac {3 \left (-4 e^{e^x}-2 x (1-\log (3)) \log \left (x^2\right )+x (1-\log (3)) \log \left (x^2\right ) \log \left (x-x \log (3)+e^{e^x} \log \left (\log \left (x^2\right )\right )\right )+e^{e^x} \log \left (x^2\right ) \log \left (\log \left (x^2\right )\right ) \log \left (x-x \log (3)+e^{e^x} \log \left (\log \left (x^2\right )\right )\right )\right )}{\log \left (x^2\right ) \left (x (1-\log (3))+e^{e^x} \log \left (\log \left (x^2\right )\right )\right ) \log ^3\left (x (1-\log (3))+e^{e^x} \log \left (\log \left (x^2\right )\right )\right )}\right ) \, dx \\ & = 3 \int \frac {-4 e^{e^x}-2 x (1-\log (3)) \log \left (x^2\right )+x (1-\log (3)) \log \left (x^2\right ) \log \left (x-x \log (3)+e^{e^x} \log \left (\log \left (x^2\right )\right )\right )+e^{e^x} \log \left (x^2\right ) \log \left (\log \left (x^2\right )\right ) \log \left (x-x \log (3)+e^{e^x} \log \left (\log \left (x^2\right )\right )\right )}{\log \left (x^2\right ) \left (x (1-\log (3))+e^{e^x} \log \left (\log \left (x^2\right )\right )\right ) \log ^3\left (x (1-\log (3))+e^{e^x} \log \left (\log \left (x^2\right )\right )\right )} \, dx+6 \int \frac {e^{e^x+x} x \log \left (\log \left (x^2\right )\right )}{\left (-x (1-\log (3))-e^{e^x} \log \left (\log \left (x^2\right )\right )\right ) \log ^3\left (x (1-\log (3))+e^{e^x} \log \left (\log \left (x^2\right )\right )\right )} \, dx \\ & = 3 \int \left (\frac {2 x (1-\log (3)) \left (2-\log \left (x^2\right ) \log \left (\log \left (x^2\right )\right )\right )}{\log \left (x^2\right ) \log \left (\log \left (x^2\right )\right ) \left (x (1-\log (3))+e^{e^x} \log \left (\log \left (x^2\right )\right )\right ) \log ^3\left (x (1-\log (3))+e^{e^x} \log \left (\log \left (x^2\right )\right )\right )}+\frac {-4+\log \left (x^2\right ) \log \left (\log \left (x^2\right )\right ) \log \left (x-x \log (3)+e^{e^x} \log \left (\log \left (x^2\right )\right )\right )}{\log \left (x^2\right ) \log \left (\log \left (x^2\right )\right ) \log ^3\left (x (1-\log (3))+e^{e^x} \log \left (\log \left (x^2\right )\right )\right )}\right ) \, dx+6 \int \frac {e^{e^x+x} x \log \left (\log \left (x^2\right )\right )}{\left (-x (1-\log (3))-e^{e^x} \log \left (\log \left (x^2\right )\right )\right ) \log ^3\left (x (1-\log (3))+e^{e^x} \log \left (\log \left (x^2\right )\right )\right )} \, dx \\ & = 3 \int \frac {-4+\log \left (x^2\right ) \log \left (\log \left (x^2\right )\right ) \log \left (x-x \log (3)+e^{e^x} \log \left (\log \left (x^2\right )\right )\right )}{\log \left (x^2\right ) \log \left (\log \left (x^2\right )\right ) \log ^3\left (x (1-\log (3))+e^{e^x} \log \left (\log \left (x^2\right )\right )\right )} \, dx+6 \int \frac {e^{e^x+x} x \log \left (\log \left (x^2\right )\right )}{\left (-x (1-\log (3))-e^{e^x} \log \left (\log \left (x^2\right )\right )\right ) \log ^3\left (x (1-\log (3))+e^{e^x} \log \left (\log \left (x^2\right )\right )\right )} \, dx+(6 (1-\log (3))) \int \frac {x \left (2-\log \left (x^2\right ) \log \left (\log \left (x^2\right )\right )\right )}{\log \left (x^2\right ) \log \left (\log \left (x^2\right )\right ) \left (x (1-\log (3))+e^{e^x} \log \left (\log \left (x^2\right )\right )\right ) \log ^3\left (x (1-\log (3))+e^{e^x} \log \left (\log \left (x^2\right )\right )\right )} \, dx \\ & = 3 \int \left (-\frac {4}{\log \left (x^2\right ) \log \left (\log \left (x^2\right )\right ) \log ^3\left (x (1-\log (3))+e^{e^x} \log \left (\log \left (x^2\right )\right )\right )}+\frac {1}{\log ^2\left (x (1-\log (3))+e^{e^x} \log \left (\log \left (x^2\right )\right )\right )}\right ) \, dx+6 \int \frac {e^{e^x+x} x \log \left (\log \left (x^2\right )\right )}{\left (-x (1-\log (3))-e^{e^x} \log \left (\log \left (x^2\right )\right )\right ) \log ^3\left (x (1-\log (3))+e^{e^x} \log \left (\log \left (x^2\right )\right )\right )} \, dx+(6 (1-\log (3))) \int \left (\frac {x}{\left (-x (1-\log (3))-e^{e^x} \log \left (\log \left (x^2\right )\right )\right ) \log ^3\left (x (1-\log (3))+e^{e^x} \log \left (\log \left (x^2\right )\right )\right )}+\frac {2 x}{\log \left (x^2\right ) \log \left (\log \left (x^2\right )\right ) \left (x (1-\log (3))+e^{e^x} \log \left (\log \left (x^2\right )\right )\right ) \log ^3\left (x (1-\log (3))+e^{e^x} \log \left (\log \left (x^2\right )\right )\right )}\right ) \, dx \\ & = 3 \int \frac {1}{\log ^2\left (x (1-\log (3))+e^{e^x} \log \left (\log \left (x^2\right )\right )\right )} \, dx+6 \int \frac {e^{e^x+x} x \log \left (\log \left (x^2\right )\right )}{\left (-x (1-\log (3))-e^{e^x} \log \left (\log \left (x^2\right )\right )\right ) \log ^3\left (x (1-\log (3))+e^{e^x} \log \left (\log \left (x^2\right )\right )\right )} \, dx-12 \int \frac {1}{\log \left (x^2\right ) \log \left (\log \left (x^2\right )\right ) \log ^3\left (x (1-\log (3))+e^{e^x} \log \left (\log \left (x^2\right )\right )\right )} \, dx+(6 (1-\log (3))) \int \frac {x}{\left (-x (1-\log (3))-e^{e^x} \log \left (\log \left (x^2\right )\right )\right ) \log ^3\left (x (1-\log (3))+e^{e^x} \log \left (\log \left (x^2\right )\right )\right )} \, dx+(12 (1-\log (3))) \int \frac {x}{\log \left (x^2\right ) \log \left (\log \left (x^2\right )\right ) \left (x (1-\log (3))+e^{e^x} \log \left (\log \left (x^2\right )\right )\right ) \log ^3\left (x (1-\log (3))+e^{e^x} \log \left (\log \left (x^2\right )\right )\right )} \, dx \\ \end{align*}
Time = 0.16 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.00 \[ \int \frac {-12 e^{e^x}+(-6 x+6 x \log (3)) \log \left (x^2\right )-6 e^{e^x+x} x \log \left (x^2\right ) \log \left (\log \left (x^2\right )\right )+\left ((3 x-3 x \log (3)) \log \left (x^2\right )+3 e^{e^x} \log \left (x^2\right ) \log \left (\log \left (x^2\right )\right )\right ) \log \left (x-x \log (3)+e^{e^x} \log \left (\log \left (x^2\right )\right )\right )}{\left ((x-x \log (3)) \log \left (x^2\right )+e^{e^x} \log \left (x^2\right ) \log \left (\log \left (x^2\right )\right )\right ) \log ^3\left (x-x \log (3)+e^{e^x} \log \left (\log \left (x^2\right )\right )\right )} \, dx=\frac {3 x}{\log ^2\left (x-x \log (3)+e^{e^x} \log \left (\log \left (x^2\right )\right )\right )} \]
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Result contains higher order function than in optimal. Order 9 vs. order 3.
Time = 0.61 (sec) , antiderivative size = 52, normalized size of antiderivative = 2.17
\[\frac {3 x}{\ln \left ({\mathrm e}^{{\mathrm e}^{x}} \ln \left (2 \ln \left (x \right )-\frac {i \pi \,\operatorname {csgn}\left (i x^{2}\right ) {\left (-\operatorname {csgn}\left (i x^{2}\right )+\operatorname {csgn}\left (i x \right )\right )}^{2}}{2}\right )-x \ln \left (3\right )+x \right )^{2}}\]
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Time = 0.24 (sec) , antiderivative size = 36, normalized size of antiderivative = 1.50 \[ \int \frac {-12 e^{e^x}+(-6 x+6 x \log (3)) \log \left (x^2\right )-6 e^{e^x+x} x \log \left (x^2\right ) \log \left (\log \left (x^2\right )\right )+\left ((3 x-3 x \log (3)) \log \left (x^2\right )+3 e^{e^x} \log \left (x^2\right ) \log \left (\log \left (x^2\right )\right )\right ) \log \left (x-x \log (3)+e^{e^x} \log \left (\log \left (x^2\right )\right )\right )}{\left ((x-x \log (3)) \log \left (x^2\right )+e^{e^x} \log \left (x^2\right ) \log \left (\log \left (x^2\right )\right )\right ) \log ^3\left (x-x \log (3)+e^{e^x} \log \left (\log \left (x^2\right )\right )\right )} \, dx=\frac {3 \, x}{\log \left (-{\left ({\left (x \log \left (3\right ) - x\right )} e^{x} - e^{\left (x + e^{x}\right )} \log \left (\log \left (x^{2}\right )\right )\right )} e^{\left (-x\right )}\right )^{2}} \]
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Timed out. \[ \int \frac {-12 e^{e^x}+(-6 x+6 x \log (3)) \log \left (x^2\right )-6 e^{e^x+x} x \log \left (x^2\right ) \log \left (\log \left (x^2\right )\right )+\left ((3 x-3 x \log (3)) \log \left (x^2\right )+3 e^{e^x} \log \left (x^2\right ) \log \left (\log \left (x^2\right )\right )\right ) \log \left (x-x \log (3)+e^{e^x} \log \left (\log \left (x^2\right )\right )\right )}{\left ((x-x \log (3)) \log \left (x^2\right )+e^{e^x} \log \left (x^2\right ) \log \left (\log \left (x^2\right )\right )\right ) \log ^3\left (x-x \log (3)+e^{e^x} \log \left (\log \left (x^2\right )\right )\right )} \, dx=\text {Timed out} \]
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Time = 0.64 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.12 \[ \int \frac {-12 e^{e^x}+(-6 x+6 x \log (3)) \log \left (x^2\right )-6 e^{e^x+x} x \log \left (x^2\right ) \log \left (\log \left (x^2\right )\right )+\left ((3 x-3 x \log (3)) \log \left (x^2\right )+3 e^{e^x} \log \left (x^2\right ) \log \left (\log \left (x^2\right )\right )\right ) \log \left (x-x \log (3)+e^{e^x} \log \left (\log \left (x^2\right )\right )\right )}{\left ((x-x \log (3)) \log \left (x^2\right )+e^{e^x} \log \left (x^2\right ) \log \left (\log \left (x^2\right )\right )\right ) \log ^3\left (x-x \log (3)+e^{e^x} \log \left (\log \left (x^2\right )\right )\right )} \, dx=\frac {3 \, x}{\log \left (-x {\left (\log \left (3\right ) - 1\right )} + e^{\left (e^{x}\right )} \log \left (2\right ) + e^{\left (e^{x}\right )} \log \left (\log \left (x\right )\right )\right )^{2}} \]
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Timed out. \[ \int \frac {-12 e^{e^x}+(-6 x+6 x \log (3)) \log \left (x^2\right )-6 e^{e^x+x} x \log \left (x^2\right ) \log \left (\log \left (x^2\right )\right )+\left ((3 x-3 x \log (3)) \log \left (x^2\right )+3 e^{e^x} \log \left (x^2\right ) \log \left (\log \left (x^2\right )\right )\right ) \log \left (x-x \log (3)+e^{e^x} \log \left (\log \left (x^2\right )\right )\right )}{\left ((x-x \log (3)) \log \left (x^2\right )+e^{e^x} \log \left (x^2\right ) \log \left (\log \left (x^2\right )\right )\right ) \log ^3\left (x-x \log (3)+e^{e^x} \log \left (\log \left (x^2\right )\right )\right )} \, dx=\text {Timed out} \]
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Timed out. \[ \int \frac {-12 e^{e^x}+(-6 x+6 x \log (3)) \log \left (x^2\right )-6 e^{e^x+x} x \log \left (x^2\right ) \log \left (\log \left (x^2\right )\right )+\left ((3 x-3 x \log (3)) \log \left (x^2\right )+3 e^{e^x} \log \left (x^2\right ) \log \left (\log \left (x^2\right )\right )\right ) \log \left (x-x \log (3)+e^{e^x} \log \left (\log \left (x^2\right )\right )\right )}{\left ((x-x \log (3)) \log \left (x^2\right )+e^{e^x} \log \left (x^2\right ) \log \left (\log \left (x^2\right )\right )\right ) \log ^3\left (x-x \log (3)+e^{e^x} \log \left (\log \left (x^2\right )\right )\right )} \, dx=\int -\frac {12\,{\mathrm {e}}^{{\mathrm {e}}^x}+\ln \left (x^2\right )\,\left (6\,x-6\,x\,\ln \left (3\right )\right )-\ln \left (x-x\,\ln \left (3\right )+{\mathrm {e}}^{{\mathrm {e}}^x}\,\ln \left (\ln \left (x^2\right )\right )\right )\,\left (\ln \left (x^2\right )\,\left (3\,x-3\,x\,\ln \left (3\right )\right )+3\,\ln \left (x^2\right )\,{\mathrm {e}}^{{\mathrm {e}}^x}\,\ln \left (\ln \left (x^2\right )\right )\right )+6\,x\,\ln \left (x^2\right )\,{\mathrm {e}}^{{\mathrm {e}}^x}\,{\mathrm {e}}^x\,\ln \left (\ln \left (x^2\right )\right )}{{\ln \left (x-x\,\ln \left (3\right )+{\mathrm {e}}^{{\mathrm {e}}^x}\,\ln \left (\ln \left (x^2\right )\right )\right )}^3\,\left (\ln \left (x^2\right )\,\left (x-x\,\ln \left (3\right )\right )+\ln \left (x^2\right )\,{\mathrm {e}}^{{\mathrm {e}}^x}\,\ln \left (\ln \left (x^2\right )\right )\right )} \,d x \]
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