Integrand size = 403, antiderivative size = 35 \[ \int \frac {\left (2 e^{e^x+x} x^4+12 x^5+\left (-12 x^5+6 x^6+e^{e^x} \left (-4 x^3+2 x^4\right )\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )\right ) \log \left (\frac {e^{-x} \left (x^2-5 e^x \log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )\right )}{\log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )}\right )+\left (\left (-2 e^{e^x} x^3-6 x^5\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )+\left (10 e^{e^x+x} x+30 e^x x^3\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \log ^2\left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )\right ) \log ^2\left (\frac {e^{-x} \left (x^2-5 e^x \log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )\right )}{\log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )}\right )}{\left (-e^{e^x} x^2-3 x^4\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )+\left (5 e^{e^x+x}+15 e^x x^2\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \log ^2\left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )} \, dx=x^2 \log ^2\left (-5+\frac {e^{-x} x^2}{\log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )}\right ) \]
[Out]
\[ \int \frac {\left (2 e^{e^x+x} x^4+12 x^5+\left (-12 x^5+6 x^6+e^{e^x} \left (-4 x^3+2 x^4\right )\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )\right ) \log \left (\frac {e^{-x} \left (x^2-5 e^x \log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )\right )}{\log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )}\right )+\left (\left (-2 e^{e^x} x^3-6 x^5\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )+\left (10 e^{e^x+x} x+30 e^x x^3\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \log ^2\left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )\right ) \log ^2\left (\frac {e^{-x} \left (x^2-5 e^x \log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )\right )}{\log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )}\right )}{\left (-e^{e^x} x^2-3 x^4\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )+\left (5 e^{e^x+x}+15 e^x x^2\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \log ^2\left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )} \, dx=\int \frac {\left (2 e^{e^x+x} x^4+12 x^5+\left (-12 x^5+6 x^6+e^{e^x} \left (-4 x^3+2 x^4\right )\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )\right ) \log \left (\frac {e^{-x} \left (x^2-5 e^x \log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )\right )}{\log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )}\right )+\left (\left (-2 e^{e^x} x^3-6 x^5\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )+\left (10 e^{e^x+x} x+30 e^x x^3\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \log ^2\left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )\right ) \log ^2\left (\frac {e^{-x} \left (x^2-5 e^x \log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )\right )}{\log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )}\right )}{\left (-e^{e^x} x^2-3 x^4\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )+\left (5 e^{e^x+x}+15 e^x x^2\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \log ^2\left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )} \, dx \]
[In]
[Out]
Rubi steps \begin{align*} \text {integral}& = \int \frac {2 x \log \left (-5+\frac {e^{-x} x^2}{\log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )}\right ) \left (-x^3 \left (e^{e^x+x}+6 x\right )-\left (e^{e^x}+3 x^2\right ) \log \left (\frac {e^{e^x}}{3}+x^2\right ) \log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right ) \left ((-2+x) x^2-\left (x^2-5 e^x \log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )\right ) \log \left (-5+\frac {e^{-x} x^2}{\log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )}\right )\right )\right )}{\left (e^{e^x}+3 x^2\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \left (x^2-5 e^x \log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )\right ) \log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )} \, dx \\ & = 2 \int \frac {x \log \left (-5+\frac {e^{-x} x^2}{\log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )}\right ) \left (-x^3 \left (e^{e^x+x}+6 x\right )-\left (e^{e^x}+3 x^2\right ) \log \left (\frac {e^{e^x}}{3}+x^2\right ) \log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right ) \left ((-2+x) x^2-\left (x^2-5 e^x \log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )\right ) \log \left (-5+\frac {e^{-x} x^2}{\log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )}\right )\right )\right )}{\left (e^{e^x}+3 x^2\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \left (x^2-5 e^x \log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )\right ) \log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )} \, dx \\ & = 2 \int \left (\frac {x^3 \left (-e^{e^x} x^3-30 x^2 \log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )+10 e^{e^x} \log \left (\frac {e^{e^x}}{3}+x^2\right ) \log ^2\left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )-5 e^{e^x} x \log \left (\frac {e^{e^x}}{3}+x^2\right ) \log ^2\left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )+30 x^2 \log \left (\frac {e^{e^x}}{3}+x^2\right ) \log ^2\left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )-15 x^3 \log \left (\frac {e^{e^x}}{3}+x^2\right ) \log ^2\left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )\right ) \log \left (-5+\frac {e^{-x} x^2}{\log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )}\right )}{5 \left (e^{e^x}+3 x^2\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \left (x^2-5 e^x \log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )\right ) \log ^2\left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )}+\frac {x \log \left (-5+\frac {e^{-x} x^2}{\log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )}\right ) \left (e^{e^x} x^3+5 e^{e^x} \log \left (\frac {e^{e^x}}{3}+x^2\right ) \log ^2\left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right ) \log \left (-5+\frac {e^{-x} x^2}{\log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )}\right )+15 x^2 \log \left (\frac {e^{e^x}}{3}+x^2\right ) \log ^2\left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right ) \log \left (-5+\frac {e^{-x} x^2}{\log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )}\right )\right )}{5 \left (e^{e^x}+3 x^2\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \log ^2\left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )}\right ) \, dx \\ & = \frac {2}{5} \int \frac {x^3 \left (-e^{e^x} x^3-30 x^2 \log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )+10 e^{e^x} \log \left (\frac {e^{e^x}}{3}+x^2\right ) \log ^2\left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )-5 e^{e^x} x \log \left (\frac {e^{e^x}}{3}+x^2\right ) \log ^2\left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )+30 x^2 \log \left (\frac {e^{e^x}}{3}+x^2\right ) \log ^2\left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )-15 x^3 \log \left (\frac {e^{e^x}}{3}+x^2\right ) \log ^2\left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )\right ) \log \left (-5+\frac {e^{-x} x^2}{\log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )}\right )}{\left (e^{e^x}+3 x^2\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \left (x^2-5 e^x \log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )\right ) \log ^2\left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )} \, dx+\frac {2}{5} \int \frac {x \log \left (-5+\frac {e^{-x} x^2}{\log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )}\right ) \left (e^{e^x} x^3+5 e^{e^x} \log \left (\frac {e^{e^x}}{3}+x^2\right ) \log ^2\left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right ) \log \left (-5+\frac {e^{-x} x^2}{\log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )}\right )+15 x^2 \log \left (\frac {e^{e^x}}{3}+x^2\right ) \log ^2\left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right ) \log \left (-5+\frac {e^{-x} x^2}{\log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )}\right )\right )}{\left (e^{e^x}+3 x^2\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \log ^2\left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )} \, dx \\ & = \frac {2}{5} \int \frac {x^3 \left (-e^{e^x} x^3-30 x^2 \log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )-5 (-2+x) \left (e^{e^x}+3 x^2\right ) \log \left (\frac {e^{e^x}}{3}+x^2\right ) \log ^2\left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )\right ) \log \left (-5+\frac {e^{-x} x^2}{\log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )}\right )}{\left (e^{e^x}+3 x^2\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \left (x^2-5 e^x \log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )\right ) \log ^2\left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )} \, dx+\frac {2}{5} \int x \log \left (-5+\frac {e^{-x} x^2}{\log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )}\right ) \left (\frac {e^{e^x} x^3}{\left (e^{e^x}+3 x^2\right ) \log \left (\frac {e^{e^x}}{3}+x^2\right ) \log ^2\left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )}+5 \log \left (-5+\frac {e^{-x} x^2}{\log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )}\right )\right ) \, dx \\ & = \frac {2}{5} \int \left (\frac {10 e^{e^x} x^3 \log \left (-5+\frac {e^{-x} x^2}{\log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )}\right )}{\left (e^{e^x}+3 x^2\right ) \left (x^2-5 e^x \log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )\right )}-\frac {5 e^{e^x} x^4 \log \left (-5+\frac {e^{-x} x^2}{\log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )}\right )}{\left (e^{e^x}+3 x^2\right ) \left (x^2-5 e^x \log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )\right )}+\frac {30 x^5 \log \left (-5+\frac {e^{-x} x^2}{\log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )}\right )}{\left (e^{e^x}+3 x^2\right ) \left (x^2-5 e^x \log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )\right )}-\frac {15 x^6 \log \left (-5+\frac {e^{-x} x^2}{\log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )}\right )}{\left (e^{e^x}+3 x^2\right ) \left (x^2-5 e^x \log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )\right )}+\frac {e^{e^x} x^6 \log \left (-5+\frac {e^{-x} x^2}{\log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )}\right )}{\left (-e^{e^x}-3 x^2\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \left (x^2-5 e^x \log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )\right ) \log ^2\left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )}+\frac {30 x^5 \log \left (-5+\frac {e^{-x} x^2}{\log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )}\right )}{\left (-e^{e^x}-3 x^2\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \left (x^2-5 e^x \log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )\right ) \log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )}\right ) \, dx+\frac {2}{5} \int \left (\frac {3 x^6 \log \left (-5+\frac {e^{-x} x^2}{\log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )}\right )}{\left (-e^{e^x}-3 x^2\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \log ^2\left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )}+\frac {x \log \left (-5+\frac {e^{-x} x^2}{\log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )}\right ) \left (x^3+5 \log \left (\frac {e^{e^x}}{3}+x^2\right ) \log ^2\left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right ) \log \left (-5+\frac {e^{-x} x^2}{\log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )}\right )\right )}{\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \log ^2\left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )}\right ) \, dx \\ & = \frac {2}{5} \int \frac {e^{e^x} x^6 \log \left (-5+\frac {e^{-x} x^2}{\log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )}\right )}{\left (-e^{e^x}-3 x^2\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \left (x^2-5 e^x \log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )\right ) \log ^2\left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )} \, dx+\frac {2}{5} \int \frac {x \log \left (-5+\frac {e^{-x} x^2}{\log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )}\right ) \left (x^3+5 \log \left (\frac {e^{e^x}}{3}+x^2\right ) \log ^2\left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right ) \log \left (-5+\frac {e^{-x} x^2}{\log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )}\right )\right )}{\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \log ^2\left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )} \, dx+\frac {6}{5} \int \frac {x^6 \log \left (-5+\frac {e^{-x} x^2}{\log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )}\right )}{\left (-e^{e^x}-3 x^2\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \log ^2\left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )} \, dx-2 \int \frac {e^{e^x} x^4 \log \left (-5+\frac {e^{-x} x^2}{\log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )}\right )}{\left (e^{e^x}+3 x^2\right ) \left (x^2-5 e^x \log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )\right )} \, dx+4 \int \frac {e^{e^x} x^3 \log \left (-5+\frac {e^{-x} x^2}{\log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )}\right )}{\left (e^{e^x}+3 x^2\right ) \left (x^2-5 e^x \log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )\right )} \, dx-6 \int \frac {x^6 \log \left (-5+\frac {e^{-x} x^2}{\log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )}\right )}{\left (e^{e^x}+3 x^2\right ) \left (x^2-5 e^x \log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )\right )} \, dx+12 \int \frac {x^5 \log \left (-5+\frac {e^{-x} x^2}{\log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )}\right )}{\left (e^{e^x}+3 x^2\right ) \left (x^2-5 e^x \log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )\right )} \, dx+12 \int \frac {x^5 \log \left (-5+\frac {e^{-x} x^2}{\log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )}\right )}{\left (-e^{e^x}-3 x^2\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \left (x^2-5 e^x \log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )\right ) \log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )} \, dx \\ & = \frac {2}{5} \int \frac {e^{e^x} x^6 \log \left (-5+\frac {e^{-x} x^2}{\log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )}\right )}{\left (-e^{e^x}-3 x^2\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \left (x^2-5 e^x \log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )\right ) \log ^2\left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )} \, dx+\frac {2}{5} \int x \log \left (-5+\frac {e^{-x} x^2}{\log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )}\right ) \left (\frac {x^3}{\log \left (\frac {e^{e^x}}{3}+x^2\right ) \log ^2\left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )}+5 \log \left (-5+\frac {e^{-x} x^2}{\log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )}\right )\right ) \, dx+\frac {6}{5} \int \frac {x^6 \log \left (-5+\frac {e^{-x} x^2}{\log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )}\right )}{\left (-e^{e^x}-3 x^2\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \log ^2\left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )} \, dx-2 \int \frac {e^{e^x} x^4 \log \left (-5+\frac {e^{-x} x^2}{\log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )}\right )}{\left (e^{e^x}+3 x^2\right ) \left (x^2-5 e^x \log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )\right )} \, dx+4 \int \frac {e^{e^x} x^3 \log \left (-5+\frac {e^{-x} x^2}{\log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )}\right )}{\left (e^{e^x}+3 x^2\right ) \left (x^2-5 e^x \log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )\right )} \, dx-6 \int \frac {x^6 \log \left (-5+\frac {e^{-x} x^2}{\log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )}\right )}{\left (e^{e^x}+3 x^2\right ) \left (x^2-5 e^x \log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )\right )} \, dx+12 \int \frac {x^5 \log \left (-5+\frac {e^{-x} x^2}{\log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )}\right )}{\left (e^{e^x}+3 x^2\right ) \left (x^2-5 e^x \log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )\right )} \, dx+12 \int \frac {x^5 \log \left (-5+\frac {e^{-x} x^2}{\log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )}\right )}{\left (-e^{e^x}-3 x^2\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \left (x^2-5 e^x \log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )\right ) \log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )} \, dx \\ & = \frac {2}{5} \int \frac {e^{e^x} x^6 \log \left (-5+\frac {e^{-x} x^2}{\log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )}\right )}{\left (-e^{e^x}-3 x^2\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \left (x^2-5 e^x \log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )\right ) \log ^2\left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )} \, dx+\frac {2}{5} \int \left (\frac {x^4 \log \left (-5+\frac {e^{-x} x^2}{\log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )}\right )}{\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \log ^2\left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )}+5 x \log ^2\left (-5+\frac {e^{-x} x^2}{\log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )}\right )\right ) \, dx+\frac {6}{5} \int \frac {x^6 \log \left (-5+\frac {e^{-x} x^2}{\log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )}\right )}{\left (-e^{e^x}-3 x^2\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \log ^2\left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )} \, dx-2 \int \frac {e^{e^x} x^4 \log \left (-5+\frac {e^{-x} x^2}{\log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )}\right )}{\left (e^{e^x}+3 x^2\right ) \left (x^2-5 e^x \log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )\right )} \, dx+4 \int \frac {e^{e^x} x^3 \log \left (-5+\frac {e^{-x} x^2}{\log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )}\right )}{\left (e^{e^x}+3 x^2\right ) \left (x^2-5 e^x \log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )\right )} \, dx-6 \int \frac {x^6 \log \left (-5+\frac {e^{-x} x^2}{\log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )}\right )}{\left (e^{e^x}+3 x^2\right ) \left (x^2-5 e^x \log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )\right )} \, dx+12 \int \frac {x^5 \log \left (-5+\frac {e^{-x} x^2}{\log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )}\right )}{\left (e^{e^x}+3 x^2\right ) \left (x^2-5 e^x \log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )\right )} \, dx+12 \int \frac {x^5 \log \left (-5+\frac {e^{-x} x^2}{\log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )}\right )}{\left (-e^{e^x}-3 x^2\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \left (x^2-5 e^x \log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )\right ) \log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )} \, dx \\ & = \frac {2}{5} \int \frac {x^4 \log \left (-5+\frac {e^{-x} x^2}{\log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )}\right )}{\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \log ^2\left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )} \, dx+\frac {2}{5} \int \frac {e^{e^x} x^6 \log \left (-5+\frac {e^{-x} x^2}{\log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )}\right )}{\left (-e^{e^x}-3 x^2\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \left (x^2-5 e^x \log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )\right ) \log ^2\left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )} \, dx+\frac {6}{5} \int \frac {x^6 \log \left (-5+\frac {e^{-x} x^2}{\log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )}\right )}{\left (-e^{e^x}-3 x^2\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \log ^2\left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )} \, dx-2 \int \frac {e^{e^x} x^4 \log \left (-5+\frac {e^{-x} x^2}{\log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )}\right )}{\left (e^{e^x}+3 x^2\right ) \left (x^2-5 e^x \log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )\right )} \, dx+2 \int x \log ^2\left (-5+\frac {e^{-x} x^2}{\log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )}\right ) \, dx+4 \int \frac {e^{e^x} x^3 \log \left (-5+\frac {e^{-x} x^2}{\log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )}\right )}{\left (e^{e^x}+3 x^2\right ) \left (x^2-5 e^x \log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )\right )} \, dx-6 \int \frac {x^6 \log \left (-5+\frac {e^{-x} x^2}{\log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )}\right )}{\left (e^{e^x}+3 x^2\right ) \left (x^2-5 e^x \log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )\right )} \, dx+12 \int \frac {x^5 \log \left (-5+\frac {e^{-x} x^2}{\log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )}\right )}{\left (e^{e^x}+3 x^2\right ) \left (x^2-5 e^x \log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )\right )} \, dx+12 \int \frac {x^5 \log \left (-5+\frac {e^{-x} x^2}{\log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )}\right )}{\left (-e^{e^x}-3 x^2\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \left (x^2-5 e^x \log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )\right ) \log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )} \, dx \\ \end{align*}
Time = 0.35 (sec) , antiderivative size = 35, normalized size of antiderivative = 1.00 \[ \int \frac {\left (2 e^{e^x+x} x^4+12 x^5+\left (-12 x^5+6 x^6+e^{e^x} \left (-4 x^3+2 x^4\right )\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )\right ) \log \left (\frac {e^{-x} \left (x^2-5 e^x \log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )\right )}{\log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )}\right )+\left (\left (-2 e^{e^x} x^3-6 x^5\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )+\left (10 e^{e^x+x} x+30 e^x x^3\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \log ^2\left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )\right ) \log ^2\left (\frac {e^{-x} \left (x^2-5 e^x \log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )\right )}{\log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )}\right )}{\left (-e^{e^x} x^2-3 x^4\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )+\left (5 e^{e^x+x}+15 e^x x^2\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \log ^2\left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )} \, dx=x^2 \log ^2\left (-5+\frac {e^{-x} x^2}{\log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )}\right ) \]
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Result contains higher order function than in optimal. Order 9 vs. order 3.
Time = 0.50 (sec) , antiderivative size = 5397, normalized size of antiderivative = 154.20
\[\text {output too large to display}\]
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Leaf count of result is larger than twice the leaf count of optimal. 64 vs. \(2 (30) = 60\).
Time = 0.28 (sec) , antiderivative size = 64, normalized size of antiderivative = 1.83 \[ \int \frac {\left (2 e^{e^x+x} x^4+12 x^5+\left (-12 x^5+6 x^6+e^{e^x} \left (-4 x^3+2 x^4\right )\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )\right ) \log \left (\frac {e^{-x} \left (x^2-5 e^x \log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )\right )}{\log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )}\right )+\left (\left (-2 e^{e^x} x^3-6 x^5\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )+\left (10 e^{e^x+x} x+30 e^x x^3\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \log ^2\left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )\right ) \log ^2\left (\frac {e^{-x} \left (x^2-5 e^x \log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )\right )}{\log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )}\right )}{\left (-e^{e^x} x^2-3 x^4\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )+\left (5 e^{e^x+x}+15 e^x x^2\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \log ^2\left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )} \, dx=x^{2} \log \left (\frac {{\left (x^{2} - 5 \, e^{x} \log \left (\log \left (\frac {1}{3} \, {\left (3 \, x^{2} e^{x} + e^{\left (x + e^{x}\right )}\right )} e^{\left (-x\right )}\right )\right )\right )} e^{\left (-x\right )}}{\log \left (\log \left (\frac {1}{3} \, {\left (3 \, x^{2} e^{x} + e^{\left (x + e^{x}\right )}\right )} e^{\left (-x\right )}\right )\right )}\right )^{2} \]
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Timed out. \[ \int \frac {\left (2 e^{e^x+x} x^4+12 x^5+\left (-12 x^5+6 x^6+e^{e^x} \left (-4 x^3+2 x^4\right )\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )\right ) \log \left (\frac {e^{-x} \left (x^2-5 e^x \log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )\right )}{\log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )}\right )+\left (\left (-2 e^{e^x} x^3-6 x^5\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )+\left (10 e^{e^x+x} x+30 e^x x^3\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \log ^2\left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )\right ) \log ^2\left (\frac {e^{-x} \left (x^2-5 e^x \log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )\right )}{\log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )}\right )}{\left (-e^{e^x} x^2-3 x^4\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )+\left (5 e^{e^x+x}+15 e^x x^2\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \log ^2\left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )} \, dx=\text {Timed out} \]
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Leaf count of result is larger than twice the leaf count of optimal. 132 vs. \(2 (30) = 60\).
Time = 0.97 (sec) , antiderivative size = 132, normalized size of antiderivative = 3.77 \[ \int \frac {\left (2 e^{e^x+x} x^4+12 x^5+\left (-12 x^5+6 x^6+e^{e^x} \left (-4 x^3+2 x^4\right )\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )\right ) \log \left (\frac {e^{-x} \left (x^2-5 e^x \log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )\right )}{\log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )}\right )+\left (\left (-2 e^{e^x} x^3-6 x^5\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )+\left (10 e^{e^x+x} x+30 e^x x^3\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \log ^2\left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )\right ) \log ^2\left (\frac {e^{-x} \left (x^2-5 e^x \log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )\right )}{\log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )}\right )}{\left (-e^{e^x} x^2-3 x^4\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )+\left (5 e^{e^x+x}+15 e^x x^2\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \log ^2\left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )} \, dx=x^{4} + x^{2} \log \left (x^{2} - 5 \, e^{x} \log \left (-\log \left (3\right ) + \log \left (3 \, x^{2} + e^{\left (e^{x}\right )}\right )\right )\right )^{2} + 2 \, x^{3} \log \left (\log \left (-\log \left (3\right ) + \log \left (3 \, x^{2} + e^{\left (e^{x}\right )}\right )\right )\right ) + x^{2} \log \left (\log \left (-\log \left (3\right ) + \log \left (3 \, x^{2} + e^{\left (e^{x}\right )}\right )\right )\right )^{2} - 2 \, {\left (x^{3} + x^{2} \log \left (\log \left (-\log \left (3\right ) + \log \left (3 \, x^{2} + e^{\left (e^{x}\right )}\right )\right )\right )\right )} \log \left (x^{2} - 5 \, e^{x} \log \left (-\log \left (3\right ) + \log \left (3 \, x^{2} + e^{\left (e^{x}\right )}\right )\right )\right ) \]
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Leaf count of result is larger than twice the leaf count of optimal. 211 vs. \(2 (30) = 60\).
Time = 0.56 (sec) , antiderivative size = 211, normalized size of antiderivative = 6.03 \[ \int \frac {\left (2 e^{e^x+x} x^4+12 x^5+\left (-12 x^5+6 x^6+e^{e^x} \left (-4 x^3+2 x^4\right )\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )\right ) \log \left (\frac {e^{-x} \left (x^2-5 e^x \log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )\right )}{\log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )}\right )+\left (\left (-2 e^{e^x} x^3-6 x^5\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )+\left (10 e^{e^x+x} x+30 e^x x^3\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \log ^2\left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )\right ) \log ^2\left (\frac {e^{-x} \left (x^2-5 e^x \log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )\right )}{\log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )}\right )}{\left (-e^{e^x} x^2-3 x^4\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )+\left (5 e^{e^x+x}+15 e^x x^2\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \log ^2\left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )} \, dx=x^{4} - 2 \, x^{3} \log \left (x^{2} - 5 \, e^{x} \log \left (-\log \left (3\right ) + \log \left ({\left (3 \, x^{2} e^{x} + e^{\left (x + e^{x}\right )}\right )} e^{\left (-x\right )}\right )\right )\right ) + x^{2} \log \left (x^{2} - 5 \, e^{x} \log \left (-\log \left (3\right ) + \log \left ({\left (3 \, x^{2} e^{x} + e^{\left (x + e^{x}\right )}\right )} e^{\left (-x\right )}\right )\right )\right )^{2} + 2 \, x^{3} \log \left (\log \left (-\log \left (3\right ) + \log \left ({\left (3 \, x^{2} e^{x} + e^{\left (x + e^{x}\right )}\right )} e^{\left (-x\right )}\right )\right )\right ) - 2 \, x^{2} \log \left (x^{2} - 5 \, e^{x} \log \left (-\log \left (3\right ) + \log \left ({\left (3 \, x^{2} e^{x} + e^{\left (x + e^{x}\right )}\right )} e^{\left (-x\right )}\right )\right )\right ) \log \left (\log \left (-\log \left (3\right ) + \log \left ({\left (3 \, x^{2} e^{x} + e^{\left (x + e^{x}\right )}\right )} e^{\left (-x\right )}\right )\right )\right ) + x^{2} \log \left (\log \left (-\log \left (3\right ) + \log \left ({\left (3 \, x^{2} e^{x} + e^{\left (x + e^{x}\right )}\right )} e^{\left (-x\right )}\right )\right )\right )^{2} \]
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Time = 14.76 (sec) , antiderivative size = 45, normalized size of antiderivative = 1.29 \[ \int \frac {\left (2 e^{e^x+x} x^4+12 x^5+\left (-12 x^5+6 x^6+e^{e^x} \left (-4 x^3+2 x^4\right )\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )\right ) \log \left (\frac {e^{-x} \left (x^2-5 e^x \log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )\right )}{\log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )}\right )+\left (\left (-2 e^{e^x} x^3-6 x^5\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )+\left (10 e^{e^x+x} x+30 e^x x^3\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \log ^2\left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )\right ) \log ^2\left (\frac {e^{-x} \left (x^2-5 e^x \log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )\right )}{\log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )}\right )}{\left (-e^{e^x} x^2-3 x^4\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )+\left (5 e^{e^x+x}+15 e^x x^2\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \log ^2\left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )} \, dx=x^2\,{\ln \left (-\frac {5\,\ln \left (\ln \left (\frac {{\mathrm {e}}^{{\mathrm {e}}^x}}{3}+x^2\right )\right )-x^2\,{\mathrm {e}}^{-x}}{\ln \left (\ln \left (\frac {{\mathrm {e}}^{{\mathrm {e}}^x}}{3}+x^2\right )\right )}\right )}^2 \]
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