Integrand size = 212, antiderivative size = 30 \[ \int \frac {\left (96 x^2-3 x^3+e^x \left (-32 x^3+x^4\right )\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right )+\left (-1728 x+54 x^2+e^x \left (-576 x+18 x^2\right )+\left (54 x-18 e^x x^2\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right )\right ) \log \left (-\frac {16 \log \left (e^{-x} \left (-3+e^x x\right )\right )}{-32+x}\right )+\left (-864+27 x+e^x \left (288 x-9 x^2\right )\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right ) \log ^2\left (-\frac {16 \log \left (e^{-x} \left (-3+e^x x\right )\right )}{-32+x}\right )}{\left (96 x^2-3 x^3+e^x \left (-32 x^3+x^4\right )\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right )} \, dx=x+\frac {9 \log ^2\left (\frac {\log \left (-3 e^{-x}+x\right )}{2-\frac {x}{16}}\right )}{x} \]
[Out]
\[ \int \frac {\left (96 x^2-3 x^3+e^x \left (-32 x^3+x^4\right )\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right )+\left (-1728 x+54 x^2+e^x \left (-576 x+18 x^2\right )+\left (54 x-18 e^x x^2\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right )\right ) \log \left (-\frac {16 \log \left (e^{-x} \left (-3+e^x x\right )\right )}{-32+x}\right )+\left (-864+27 x+e^x \left (288 x-9 x^2\right )\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right ) \log ^2\left (-\frac {16 \log \left (e^{-x} \left (-3+e^x x\right )\right )}{-32+x}\right )}{\left (96 x^2-3 x^3+e^x \left (-32 x^3+x^4\right )\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right )} \, dx=\int \frac {\left (96 x^2-3 x^3+e^x \left (-32 x^3+x^4\right )\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right )+\left (-1728 x+54 x^2+e^x \left (-576 x+18 x^2\right )+\left (54 x-18 e^x x^2\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right )\right ) \log \left (-\frac {16 \log \left (e^{-x} \left (-3+e^x x\right )\right )}{-32+x}\right )+\left (-864+27 x+e^x \left (288 x-9 x^2\right )\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right ) \log ^2\left (-\frac {16 \log \left (e^{-x} \left (-3+e^x x\right )\right )}{-32+x}\right )}{\left (96 x^2-3 x^3+e^x \left (-32 x^3+x^4\right )\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right )} \, dx \]
[In]
[Out]
Rubi steps \begin{align*} \text {integral}& = \int \left (1-\frac {18 \left (-\left (\left (3+e^x\right ) (-32+x)\right )+\left (-3+e^x x\right ) \log \left (-3 e^{-x}+x\right )\right ) \log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{(-32+x) x \left (-3+e^x x\right ) \log \left (-3 e^{-x}+x\right )}-\frac {9 \log ^2\left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x^2}\right ) \, dx \\ & = x-9 \int \frac {\log ^2\left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x^2} \, dx-18 \int \frac {\left (-\left (\left (3+e^x\right ) (-32+x)\right )+\left (-3+e^x x\right ) \log \left (-3 e^{-x}+x\right )\right ) \log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{(-32+x) x \left (-3+e^x x\right ) \log \left (-3 e^{-x}+x\right )} \, dx \\ & = x-9 \int \frac {\log ^2\left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x^2} \, dx-18 \int \left (-\frac {3 (1+x) \log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x^2 \left (-3+e^x x\right ) \log \left (-3 e^{-x}+x\right )}+\frac {\left (32-x+x \log \left (-3 e^{-x}+x\right )\right ) \log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{(-32+x) x^2 \log \left (-3 e^{-x}+x\right )}\right ) \, dx \\ & = x-9 \int \frac {\log ^2\left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x^2} \, dx-18 \int \frac {\left (32-x+x \log \left (-3 e^{-x}+x\right )\right ) \log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{(-32+x) x^2 \log \left (-3 e^{-x}+x\right )} \, dx+54 \int \frac {(1+x) \log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x^2 \left (-3+e^x x\right ) \log \left (-3 e^{-x}+x\right )} \, dx \\ & = x-9 \int \frac {\log ^2\left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x^2} \, dx-18 \int \left (\frac {\left (32-x+x \log \left (-3 e^{-x}+x\right )\right ) \log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{1024 (-32+x) \log \left (-3 e^{-x}+x\right )}-\frac {\left (32-x+x \log \left (-3 e^{-x}+x\right )\right ) \log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{32 x^2 \log \left (-3 e^{-x}+x\right )}-\frac {\left (32-x+x \log \left (-3 e^{-x}+x\right )\right ) \log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{1024 x \log \left (-3 e^{-x}+x\right )}\right ) \, dx+54 \int \left (\frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x^2 \left (-3+e^x x\right ) \log \left (-3 e^{-x}+x\right )}+\frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x \left (-3+e^x x\right ) \log \left (-3 e^{-x}+x\right )}\right ) \, dx \\ & = x-\frac {9}{512} \int \frac {\left (32-x+x \log \left (-3 e^{-x}+x\right )\right ) \log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{(-32+x) \log \left (-3 e^{-x}+x\right )} \, dx+\frac {9}{512} \int \frac {\left (32-x+x \log \left (-3 e^{-x}+x\right )\right ) \log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x \log \left (-3 e^{-x}+x\right )} \, dx+\frac {9}{16} \int \frac {\left (32-x+x \log \left (-3 e^{-x}+x\right )\right ) \log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x^2 \log \left (-3 e^{-x}+x\right )} \, dx-9 \int \frac {\log ^2\left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x^2} \, dx+54 \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x^2 \left (-3+e^x x\right ) \log \left (-3 e^{-x}+x\right )} \, dx+54 \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x \left (-3+e^x x\right ) \log \left (-3 e^{-x}+x\right )} \, dx \\ & = x+\frac {9}{512} \int \left (\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )-\frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{\log \left (-3 e^{-x}+x\right )}+\frac {32 \log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x \log \left (-3 e^{-x}+x\right )}\right ) \, dx-\frac {9}{512} \int \left (\frac {x \log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{-32+x}+\frac {32 \log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{(-32+x) \log \left (-3 e^{-x}+x\right )}-\frac {x \log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{(-32+x) \log \left (-3 e^{-x}+x\right )}\right ) \, dx+\frac {9}{16} \int \left (\frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x}+\frac {32 \log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x^2 \log \left (-3 e^{-x}+x\right )}-\frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x \log \left (-3 e^{-x}+x\right )}\right ) \, dx-9 \int \frac {\log ^2\left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x^2} \, dx+54 \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x^2 \left (-3+e^x x\right ) \log \left (-3 e^{-x}+x\right )} \, dx+54 \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x \left (-3+e^x x\right ) \log \left (-3 e^{-x}+x\right )} \, dx \\ & = x+\frac {9}{512} \int \log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right ) \, dx-\frac {9}{512} \int \frac {x \log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{-32+x} \, dx-\frac {9}{512} \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{\log \left (-3 e^{-x}+x\right )} \, dx+\frac {9}{512} \int \frac {x \log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{(-32+x) \log \left (-3 e^{-x}+x\right )} \, dx+\frac {9}{16} \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x} \, dx-\frac {9}{16} \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{(-32+x) \log \left (-3 e^{-x}+x\right )} \, dx-9 \int \frac {\log ^2\left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x^2} \, dx+18 \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x^2 \log \left (-3 e^{-x}+x\right )} \, dx+54 \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x^2 \left (-3+e^x x\right ) \log \left (-3 e^{-x}+x\right )} \, dx+54 \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x \left (-3+e^x x\right ) \log \left (-3 e^{-x}+x\right )} \, dx \\ & = x+\frac {9}{512} x \log \left (\frac {16 \log \left (-3 e^{-x}+x\right )}{32-x}\right )-\frac {9}{512} \int \frac {x \left (\frac {3-e^x x}{-32+x}+\frac {3+e^x}{\log \left (-3 e^{-x}+x\right )}\right )}{-3+e^x x} \, dx-\frac {9}{512} \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{\log \left (-3 e^{-x}+x\right )} \, dx-\frac {9}{512} \int \left (\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )+\frac {32 \log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{-32+x}\right ) \, dx+\frac {9}{512} \int \left (\frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{\log \left (-3 e^{-x}+x\right )}+\frac {32 \log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{(-32+x) \log \left (-3 e^{-x}+x\right )}\right ) \, dx+\frac {9}{16} \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x} \, dx-\frac {9}{16} \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{(-32+x) \log \left (-3 e^{-x}+x\right )} \, dx-9 \int \frac {\log ^2\left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x^2} \, dx+18 \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x^2 \log \left (-3 e^{-x}+x\right )} \, dx+54 \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x^2 \left (-3+e^x x\right ) \log \left (-3 e^{-x}+x\right )} \, dx+54 \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x \left (-3+e^x x\right ) \log \left (-3 e^{-x}+x\right )} \, dx \\ & = x+\frac {9}{512} x \log \left (\frac {16 \log \left (-3 e^{-x}+x\right )}{32-x}\right )-\frac {9}{512} \int \left (\frac {3 (1+x)}{\left (-3+e^x x\right ) \log \left (-3 e^{-x}+x\right )}+\frac {-32+x-x \log \left (-3 e^{-x}+x\right )}{(-32+x) \log \left (-3 e^{-x}+x\right )}\right ) \, dx-\frac {9}{512} \int \log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right ) \, dx-\frac {9}{16} \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{-32+x} \, dx+\frac {9}{16} \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x} \, dx-9 \int \frac {\log ^2\left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x^2} \, dx+18 \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x^2 \log \left (-3 e^{-x}+x\right )} \, dx+54 \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x^2 \left (-3+e^x x\right ) \log \left (-3 e^{-x}+x\right )} \, dx+54 \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x \left (-3+e^x x\right ) \log \left (-3 e^{-x}+x\right )} \, dx \\ & = x+\frac {9}{512} \int \frac {x \left (\frac {3-e^x x}{-32+x}+\frac {3+e^x}{\log \left (-3 e^{-x}+x\right )}\right )}{-3+e^x x} \, dx-\frac {9}{512} \int \frac {-32+x-x \log \left (-3 e^{-x}+x\right )}{(-32+x) \log \left (-3 e^{-x}+x\right )} \, dx-\frac {27}{512} \int \frac {1+x}{\left (-3+e^x x\right ) \log \left (-3 e^{-x}+x\right )} \, dx-\frac {9}{16} \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{-32+x} \, dx+\frac {9}{16} \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x} \, dx-9 \int \frac {\log ^2\left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x^2} \, dx+18 \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x^2 \log \left (-3 e^{-x}+x\right )} \, dx+54 \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x^2 \left (-3+e^x x\right ) \log \left (-3 e^{-x}+x\right )} \, dx+54 \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x \left (-3+e^x x\right ) \log \left (-3 e^{-x}+x\right )} \, dx \\ & = x-\frac {9}{512} \int \left (-\frac {x}{-32+x}+\frac {1}{\log \left (-3 e^{-x}+x\right )}\right ) \, dx+\frac {9}{512} \int \left (\frac {3 (1+x)}{\left (-3+e^x x\right ) \log \left (-3 e^{-x}+x\right )}+\frac {-32+x-x \log \left (-3 e^{-x}+x\right )}{(-32+x) \log \left (-3 e^{-x}+x\right )}\right ) \, dx-\frac {27}{512} \int \left (\frac {1}{\left (-3+e^x x\right ) \log \left (-3 e^{-x}+x\right )}+\frac {x}{\left (-3+e^x x\right ) \log \left (-3 e^{-x}+x\right )}\right ) \, dx-\frac {9}{16} \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{-32+x} \, dx+\frac {9}{16} \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x} \, dx-9 \int \frac {\log ^2\left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x^2} \, dx+18 \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x^2 \log \left (-3 e^{-x}+x\right )} \, dx+54 \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x^2 \left (-3+e^x x\right ) \log \left (-3 e^{-x}+x\right )} \, dx+54 \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x \left (-3+e^x x\right ) \log \left (-3 e^{-x}+x\right )} \, dx \\ & = x+\frac {9}{512} \int \frac {x}{-32+x} \, dx-\frac {9}{512} \int \frac {1}{\log \left (-3 e^{-x}+x\right )} \, dx+\frac {9}{512} \int \frac {-32+x-x \log \left (-3 e^{-x}+x\right )}{(-32+x) \log \left (-3 e^{-x}+x\right )} \, dx-\frac {27}{512} \int \frac {1}{\left (-3+e^x x\right ) \log \left (-3 e^{-x}+x\right )} \, dx-\frac {27}{512} \int \frac {x}{\left (-3+e^x x\right ) \log \left (-3 e^{-x}+x\right )} \, dx+\frac {27}{512} \int \frac {1+x}{\left (-3+e^x x\right ) \log \left (-3 e^{-x}+x\right )} \, dx-\frac {9}{16} \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{-32+x} \, dx+\frac {9}{16} \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x} \, dx-9 \int \frac {\log ^2\left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x^2} \, dx+18 \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x^2 \log \left (-3 e^{-x}+x\right )} \, dx+54 \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x^2 \left (-3+e^x x\right ) \log \left (-3 e^{-x}+x\right )} \, dx+54 \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x \left (-3+e^x x\right ) \log \left (-3 e^{-x}+x\right )} \, dx \\ & = x+\frac {9}{512} \int \left (1+\frac {32}{-32+x}\right ) \, dx+\frac {9}{512} \int \left (-\frac {x}{-32+x}+\frac {1}{\log \left (-3 e^{-x}+x\right )}\right ) \, dx-\frac {9}{512} \int \frac {1}{\log \left (-3 e^{-x}+x\right )} \, dx+\frac {27}{512} \int \left (\frac {1}{\left (-3+e^x x\right ) \log \left (-3 e^{-x}+x\right )}+\frac {x}{\left (-3+e^x x\right ) \log \left (-3 e^{-x}+x\right )}\right ) \, dx-\frac {27}{512} \int \frac {1}{\left (-3+e^x x\right ) \log \left (-3 e^{-x}+x\right )} \, dx-\frac {27}{512} \int \frac {x}{\left (-3+e^x x\right ) \log \left (-3 e^{-x}+x\right )} \, dx-\frac {9}{16} \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{-32+x} \, dx+\frac {9}{16} \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x} \, dx-9 \int \frac {\log ^2\left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x^2} \, dx+18 \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x^2 \log \left (-3 e^{-x}+x\right )} \, dx+54 \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x^2 \left (-3+e^x x\right ) \log \left (-3 e^{-x}+x\right )} \, dx+54 \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x \left (-3+e^x x\right ) \log \left (-3 e^{-x}+x\right )} \, dx \\ & = \frac {521 x}{512}+\frac {9}{16} \log (32-x)-\frac {9}{512} \int \frac {x}{-32+x} \, dx-\frac {9}{16} \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{-32+x} \, dx+\frac {9}{16} \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x} \, dx-9 \int \frac {\log ^2\left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x^2} \, dx+18 \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x^2 \log \left (-3 e^{-x}+x\right )} \, dx+54 \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x^2 \left (-3+e^x x\right ) \log \left (-3 e^{-x}+x\right )} \, dx+54 \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x \left (-3+e^x x\right ) \log \left (-3 e^{-x}+x\right )} \, dx \\ & = \frac {521 x}{512}+\frac {9}{16} \log (32-x)-\frac {9}{512} \int \left (1+\frac {32}{-32+x}\right ) \, dx-\frac {9}{16} \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{-32+x} \, dx+\frac {9}{16} \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x} \, dx-9 \int \frac {\log ^2\left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x^2} \, dx+18 \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x^2 \log \left (-3 e^{-x}+x\right )} \, dx+54 \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x^2 \left (-3+e^x x\right ) \log \left (-3 e^{-x}+x\right )} \, dx+54 \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x \left (-3+e^x x\right ) \log \left (-3 e^{-x}+x\right )} \, dx \\ & = x-\frac {9}{16} \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{-32+x} \, dx+\frac {9}{16} \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x} \, dx-9 \int \frac {\log ^2\left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x^2} \, dx+18 \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x^2 \log \left (-3 e^{-x}+x\right )} \, dx+54 \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x^2 \left (-3+e^x x\right ) \log \left (-3 e^{-x}+x\right )} \, dx+54 \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x \left (-3+e^x x\right ) \log \left (-3 e^{-x}+x\right )} \, dx \\ \end{align*}
\[ \int \frac {\left (96 x^2-3 x^3+e^x \left (-32 x^3+x^4\right )\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right )+\left (-1728 x+54 x^2+e^x \left (-576 x+18 x^2\right )+\left (54 x-18 e^x x^2\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right )\right ) \log \left (-\frac {16 \log \left (e^{-x} \left (-3+e^x x\right )\right )}{-32+x}\right )+\left (-864+27 x+e^x \left (288 x-9 x^2\right )\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right ) \log ^2\left (-\frac {16 \log \left (e^{-x} \left (-3+e^x x\right )\right )}{-32+x}\right )}{\left (96 x^2-3 x^3+e^x \left (-32 x^3+x^4\right )\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right )} \, dx=\int \frac {\left (96 x^2-3 x^3+e^x \left (-32 x^3+x^4\right )\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right )+\left (-1728 x+54 x^2+e^x \left (-576 x+18 x^2\right )+\left (54 x-18 e^x x^2\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right )\right ) \log \left (-\frac {16 \log \left (e^{-x} \left (-3+e^x x\right )\right )}{-32+x}\right )+\left (-864+27 x+e^x \left (288 x-9 x^2\right )\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right ) \log ^2\left (-\frac {16 \log \left (e^{-x} \left (-3+e^x x\right )\right )}{-32+x}\right )}{\left (96 x^2-3 x^3+e^x \left (-32 x^3+x^4\right )\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right )} \, dx \]
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Time = 13.19 (sec) , antiderivative size = 39, normalized size of antiderivative = 1.30
method | result | size |
parallelrisch | \(-\frac {-384 x^{2}-3456 {\ln \left (-\frac {16 \ln \left (\left ({\mathrm e}^{x} x -3\right ) {\mathrm e}^{-x}\right )}{x -32}\right )}^{2}-6144 x}{384 x}\) | \(39\) |
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Time = 0.26 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.07 \[ \int \frac {\left (96 x^2-3 x^3+e^x \left (-32 x^3+x^4\right )\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right )+\left (-1728 x+54 x^2+e^x \left (-576 x+18 x^2\right )+\left (54 x-18 e^x x^2\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right )\right ) \log \left (-\frac {16 \log \left (e^{-x} \left (-3+e^x x\right )\right )}{-32+x}\right )+\left (-864+27 x+e^x \left (288 x-9 x^2\right )\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right ) \log ^2\left (-\frac {16 \log \left (e^{-x} \left (-3+e^x x\right )\right )}{-32+x}\right )}{\left (96 x^2-3 x^3+e^x \left (-32 x^3+x^4\right )\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right )} \, dx=\frac {x^{2} + 9 \, \log \left (-\frac {16 \, \log \left ({\left (x e^{x} - 3\right )} e^{\left (-x\right )}\right )}{x - 32}\right )^{2}}{x} \]
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Time = 0.78 (sec) , antiderivative size = 26, normalized size of antiderivative = 0.87 \[ \int \frac {\left (96 x^2-3 x^3+e^x \left (-32 x^3+x^4\right )\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right )+\left (-1728 x+54 x^2+e^x \left (-576 x+18 x^2\right )+\left (54 x-18 e^x x^2\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right )\right ) \log \left (-\frac {16 \log \left (e^{-x} \left (-3+e^x x\right )\right )}{-32+x}\right )+\left (-864+27 x+e^x \left (288 x-9 x^2\right )\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right ) \log ^2\left (-\frac {16 \log \left (e^{-x} \left (-3+e^x x\right )\right )}{-32+x}\right )}{\left (96 x^2-3 x^3+e^x \left (-32 x^3+x^4\right )\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right )} \, dx=x + \frac {9 \log {\left (- \frac {16 \log {\left (\left (x e^{x} - 3\right ) e^{- x} \right )}}{x - 32} \right )}^{2}}{x} \]
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Leaf count of result is larger than twice the leaf count of optimal. 71 vs. \(2 (26) = 52\).
Time = 0.37 (sec) , antiderivative size = 71, normalized size of antiderivative = 2.37 \[ \int \frac {\left (96 x^2-3 x^3+e^x \left (-32 x^3+x^4\right )\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right )+\left (-1728 x+54 x^2+e^x \left (-576 x+18 x^2\right )+\left (54 x-18 e^x x^2\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right )\right ) \log \left (-\frac {16 \log \left (e^{-x} \left (-3+e^x x\right )\right )}{-32+x}\right )+\left (-864+27 x+e^x \left (288 x-9 x^2\right )\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right ) \log ^2\left (-\frac {16 \log \left (e^{-x} \left (-3+e^x x\right )\right )}{-32+x}\right )}{\left (96 x^2-3 x^3+e^x \left (-32 x^3+x^4\right )\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right )} \, dx=\frac {x^{2} + 144 \, \log \left (2\right )^{2} + 18 \, {\left (4 \, \log \left (2\right ) - \log \left (x - 32\right )\right )} \log \left (x - \log \left (x e^{x} - 3\right )\right ) + 9 \, \log \left (x - \log \left (x e^{x} - 3\right )\right )^{2} - 72 \, \log \left (2\right ) \log \left (x - 32\right ) + 9 \, \log \left (x - 32\right )^{2}}{x} \]
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Leaf count of result is larger than twice the leaf count of optimal. 426 vs. \(2 (26) = 52\).
Time = 3.87 (sec) , antiderivative size = 426, normalized size of antiderivative = 14.20 \[ \int \frac {\left (96 x^2-3 x^3+e^x \left (-32 x^3+x^4\right )\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right )+\left (-1728 x+54 x^2+e^x \left (-576 x+18 x^2\right )+\left (54 x-18 e^x x^2\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right )\right ) \log \left (-\frac {16 \log \left (e^{-x} \left (-3+e^x x\right )\right )}{-32+x}\right )+\left (-864+27 x+e^x \left (288 x-9 x^2\right )\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right ) \log ^2\left (-\frac {16 \log \left (e^{-x} \left (-3+e^x x\right )\right )}{-32+x}\right )}{\left (96 x^2-3 x^3+e^x \left (-32 x^3+x^4\right )\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right )} \, dx=-\frac {9 \, \pi ^{2} \mathrm {sgn}\left (-8 \, \pi + 8 \, \pi \mathrm {sgn}\left (x e^{x} - 3\right )\right ) \mathrm {sgn}\left (x - 32\right ) \mathrm {sgn}\left (\log \left ({\left | x e^{x} - 3 \right |} e^{\left (-x\right )}\right )\right ) + 9 \, \pi ^{2} \mathrm {sgn}\left (-8 \, \pi + 8 \, \pi \mathrm {sgn}\left (x e^{x} - 3\right )\right ) \mathrm {sgn}\left (x - 32\right ) + 27 \, \pi ^{2} \mathrm {sgn}\left (-8 \, \pi + 8 \, \pi \mathrm {sgn}\left (x e^{x} - 3\right )\right ) \mathrm {sgn}\left (\log \left ({\left | x e^{x} - 3 \right |} e^{\left (-x\right )}\right )\right ) - 18 \, \pi \arctan \left (-\frac {\pi - \pi \mathrm {sgn}\left (x e^{x} - 3\right )}{2 \, \log \left ({\left | x e^{x} - 3 \right |} e^{\left (-x\right )}\right )}\right ) \mathrm {sgn}\left (-8 \, \pi + 8 \, \pi \mathrm {sgn}\left (x e^{x} - 3\right )\right ) \mathrm {sgn}\left (\log \left ({\left | x e^{x} - 3 \right |} e^{\left (-x\right )}\right )\right ) + 27 \, \pi ^{2} \mathrm {sgn}\left (-8 \, \pi + 8 \, \pi \mathrm {sgn}\left (x e^{x} - 3\right )\right ) - 18 \, \pi \arctan \left (-\frac {\pi - \pi \mathrm {sgn}\left (x e^{x} - 3\right )}{2 \, \log \left ({\left | x e^{x} - 3 \right |} e^{\left (-x\right )}\right )}\right ) \mathrm {sgn}\left (-8 \, \pi + 8 \, \pi \mathrm {sgn}\left (x e^{x} - 3\right )\right ) + 27 \, \pi ^{2} \mathrm {sgn}\left (x - 32\right ) - 18 \, \pi \arctan \left (-\frac {\pi - \pi \mathrm {sgn}\left (x e^{x} - 3\right )}{2 \, \log \left ({\left | x e^{x} - 3 \right |} e^{\left (-x\right )}\right )}\right ) \mathrm {sgn}\left (x - 32\right ) + 9 \, \pi ^{2} \mathrm {sgn}\left (\log \left ({\left | x e^{x} - 3 \right |} e^{\left (-x\right )}\right )\right ) + 54 \, \pi ^{2} - 2 \, x^{2} - 54 \, \pi \arctan \left (-\frac {\pi - \pi \mathrm {sgn}\left (x e^{x} - 3\right )}{2 \, \log \left ({\left | x e^{x} - 3 \right |} e^{\left (-x\right )}\right )}\right ) + 18 \, \arctan \left (-\frac {\pi - \pi \mathrm {sgn}\left (x e^{x} - 3\right )}{2 \, \log \left ({\left | x e^{x} - 3 \right |} e^{\left (-x\right )}\right )}\right )^{2} - 18 \, \log \left (16 \, {\left | \log \left ({\left (x e^{x} - 3\right )} e^{\left (-x\right )}\right ) \right |}\right )^{2} + 36 \, \log \left (16 \, {\left | \log \left ({\left (x e^{x} - 3\right )} e^{\left (-x\right )}\right ) \right |}\right ) \log \left ({\left | x - 32 \right |}\right ) - 18 \, \log \left ({\left | x - 32 \right |}\right )^{2}}{2 \, x} \]
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Time = 9.66 (sec) , antiderivative size = 26, normalized size of antiderivative = 0.87 \[ \int \frac {\left (96 x^2-3 x^3+e^x \left (-32 x^3+x^4\right )\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right )+\left (-1728 x+54 x^2+e^x \left (-576 x+18 x^2\right )+\left (54 x-18 e^x x^2\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right )\right ) \log \left (-\frac {16 \log \left (e^{-x} \left (-3+e^x x\right )\right )}{-32+x}\right )+\left (-864+27 x+e^x \left (288 x-9 x^2\right )\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right ) \log ^2\left (-\frac {16 \log \left (e^{-x} \left (-3+e^x x\right )\right )}{-32+x}\right )}{\left (96 x^2-3 x^3+e^x \left (-32 x^3+x^4\right )\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right )} \, dx=x+\frac {9\,{\ln \left (-\frac {16\,\ln \left (x-3\,{\mathrm {e}}^{-x}\right )}{x-32}\right )}^2}{x} \]
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