Integrand size = 336, antiderivative size = 32 \[ \int \frac {-4 x^2+2 x^3+\left (8 x-8 x^2+2 x^3\right ) \log (1-x)+\left (-4+6 x-2 x^2\right ) \log ^2(1-x)+e^{10-2 e^x} \left (-4 x^2+2 x^3+e^x \left (-4 x^3+4 x^4\right )+\left (4 x-2 x^2+e^x \left (8 x^2-8 x^3\right )\right ) \log (1-x)+e^x \left (-4 x+4 x^2\right ) \log ^2(1-x)\right )+\left (4 x^2-2 x^3+\left (-4 x+2 x^2\right ) \log (1-x)\right ) \log \left (x^2\right )}{-x^4+x^5+e^{30-6 e^x} \left (-x+x^2\right )+\left (3 x^3-3 x^4\right ) \log \left (x^2\right )+\left (-3 x^2+3 x^3\right ) \log ^2\left (x^2\right )+\left (x-x^2\right ) \log ^3\left (x^2\right )+e^{20-4 e^x} \left (-3 x^2+3 x^3+\left (3 x-3 x^2\right ) \log \left (x^2\right )\right )+e^{10-2 e^x} \left (-3 x^3+3 x^4+\left (6 x^2-6 x^3\right ) \log \left (x^2\right )+\left (-3 x+3 x^2\right ) \log ^2\left (x^2\right )\right )} \, dx=\frac {(-x+\log (1-x))^2}{\left (e^{10-2 e^x}+x-\log \left (x^2\right )\right )^2} \]
[Out]
\[ \int \frac {-4 x^2+2 x^3+\left (8 x-8 x^2+2 x^3\right ) \log (1-x)+\left (-4+6 x-2 x^2\right ) \log ^2(1-x)+e^{10-2 e^x} \left (-4 x^2+2 x^3+e^x \left (-4 x^3+4 x^4\right )+\left (4 x-2 x^2+e^x \left (8 x^2-8 x^3\right )\right ) \log (1-x)+e^x \left (-4 x+4 x^2\right ) \log ^2(1-x)\right )+\left (4 x^2-2 x^3+\left (-4 x+2 x^2\right ) \log (1-x)\right ) \log \left (x^2\right )}{-x^4+x^5+e^{30-6 e^x} \left (-x+x^2\right )+\left (3 x^3-3 x^4\right ) \log \left (x^2\right )+\left (-3 x^2+3 x^3\right ) \log ^2\left (x^2\right )+\left (x-x^2\right ) \log ^3\left (x^2\right )+e^{20-4 e^x} \left (-3 x^2+3 x^3+\left (3 x-3 x^2\right ) \log \left (x^2\right )\right )+e^{10-2 e^x} \left (-3 x^3+3 x^4+\left (6 x^2-6 x^3\right ) \log \left (x^2\right )+\left (-3 x+3 x^2\right ) \log ^2\left (x^2\right )\right )} \, dx=\int \frac {-4 x^2+2 x^3+\left (8 x-8 x^2+2 x^3\right ) \log (1-x)+\left (-4+6 x-2 x^2\right ) \log ^2(1-x)+e^{10-2 e^x} \left (-4 x^2+2 x^3+e^x \left (-4 x^3+4 x^4\right )+\left (4 x-2 x^2+e^x \left (8 x^2-8 x^3\right )\right ) \log (1-x)+e^x \left (-4 x+4 x^2\right ) \log ^2(1-x)\right )+\left (4 x^2-2 x^3+\left (-4 x+2 x^2\right ) \log (1-x)\right ) \log \left (x^2\right )}{-x^4+x^5+e^{30-6 e^x} \left (-x+x^2\right )+\left (3 x^3-3 x^4\right ) \log \left (x^2\right )+\left (-3 x^2+3 x^3\right ) \log ^2\left (x^2\right )+\left (x-x^2\right ) \log ^3\left (x^2\right )+e^{20-4 e^x} \left (-3 x^2+3 x^3+\left (3 x-3 x^2\right ) \log \left (x^2\right )\right )+e^{10-2 e^x} \left (-3 x^3+3 x^4+\left (6 x^2-6 x^3\right ) \log \left (x^2\right )+\left (-3 x+3 x^2\right ) \log ^2\left (x^2\right )\right )} \, dx \]
[In]
[Out]
Rubi steps \begin{align*} \text {integral}& = \int \frac {2 e^{4 e^x} (x-\log (1-x)) \left (-\left ((-1+x) \left (e^{2 e^x} (-2+x)-2 e^{10+x} x\right ) \log (1-x)\right )-x \left (e^{10} (-2+x)+e^{2 e^x} (-2+x)+2 e^{10+x} (-1+x) x-e^{2 e^x} (-2+x) \log \left (x^2\right )\right )\right )}{(1-x) x \left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3} \, dx \\ & = 2 \int \frac {e^{4 e^x} (x-\log (1-x)) \left (-\left ((-1+x) \left (e^{2 e^x} (-2+x)-2 e^{10+x} x\right ) \log (1-x)\right )-x \left (e^{10} (-2+x)+e^{2 e^x} (-2+x)+2 e^{10+x} (-1+x) x-e^{2 e^x} (-2+x) \log \left (x^2\right )\right )\right )}{(1-x) x \left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3} \, dx \\ & = 2 \int \left (\frac {e^{6 e^x} (-2+x) (x-\log (1-x))}{(-1+x) \left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3}+\frac {e^{10+4 e^x} (-2+x) (x-\log (1-x))}{(-1+x) \left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3}+\frac {2 e^{10+4 e^x+x} (x-\log (1-x))^2}{\left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3}+\frac {e^{6 e^x} (-2+x) (x-\log (1-x)) \log (1-x)}{x \left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3}-\frac {e^{6 e^x} (-2+x) (x-\log (1-x)) \log \left (x^2\right )}{(-1+x) \left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3}\right ) \, dx \\ & = 2 \int \frac {e^{6 e^x} (-2+x) (x-\log (1-x))}{(-1+x) \left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3} \, dx+2 \int \frac {e^{10+4 e^x} (-2+x) (x-\log (1-x))}{(-1+x) \left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3} \, dx+2 \int \frac {e^{6 e^x} (-2+x) (x-\log (1-x)) \log (1-x)}{x \left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3} \, dx-2 \int \frac {e^{6 e^x} (-2+x) (x-\log (1-x)) \log \left (x^2\right )}{(-1+x) \left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3} \, dx+4 \int \frac {e^{10+4 e^x+x} (x-\log (1-x))^2}{\left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3} \, dx \\ & = 2 \int \frac {e^{2 \left (5+2 e^x\right )} (2-x) (x-\log (1-x))}{(1-x) \left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3} \, dx+2 \int \left (\frac {e^{6 e^x} (x-\log (1-x))}{\left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3}-\frac {e^{6 e^x} (x-\log (1-x))}{(-1+x) \left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3}\right ) \, dx+2 \int \left (\frac {e^{6 e^x} (x-\log (1-x)) \log (1-x)}{\left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3}-\frac {2 e^{6 e^x} (x-\log (1-x)) \log (1-x)}{x \left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3}\right ) \, dx-2 \int \left (\frac {e^{6 e^x} (x-\log (1-x)) \log \left (x^2\right )}{\left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3}-\frac {e^{6 e^x} (x-\log (1-x)) \log \left (x^2\right )}{(-1+x) \left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3}\right ) \, dx+4 \int \left (\frac {e^{10+4 e^x+x} x^2}{\left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3}-\frac {2 e^{10+4 e^x+x} x \log (1-x)}{\left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3}+\frac {e^{10+4 e^x+x} \log ^2(1-x)}{\left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3}\right ) \, dx \\ & = 2 \int \frac {e^{6 e^x} (x-\log (1-x))}{\left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3} \, dx-2 \int \frac {e^{6 e^x} (x-\log (1-x))}{(-1+x) \left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3} \, dx+2 \int \frac {e^{6 e^x} (x-\log (1-x)) \log (1-x)}{\left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3} \, dx-2 \int \frac {e^{6 e^x} (x-\log (1-x)) \log \left (x^2\right )}{\left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3} \, dx+2 \int \frac {e^{6 e^x} (x-\log (1-x)) \log \left (x^2\right )}{(-1+x) \left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3} \, dx+2 \int \left (\frac {e^{2 \left (5+2 e^x\right )} (x-\log (1-x))}{\left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3}-\frac {e^{2 \left (5+2 e^x\right )} (x-\log (1-x))}{(-1+x) \left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3}\right ) \, dx+4 \int \frac {e^{10+4 e^x+x} x^2}{\left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3} \, dx-4 \int \frac {e^{6 e^x} (x-\log (1-x)) \log (1-x)}{x \left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3} \, dx+4 \int \frac {e^{10+4 e^x+x} \log ^2(1-x)}{\left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3} \, dx-8 \int \frac {e^{10+4 e^x+x} x \log (1-x)}{\left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3} \, dx \\ & = 2 \int \frac {e^{2 \left (5+2 e^x\right )} (x-\log (1-x))}{\left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3} \, dx-2 \int \frac {e^{2 \left (5+2 e^x\right )} (x-\log (1-x))}{(-1+x) \left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3} \, dx+2 \int \left (\frac {e^{6 e^x} x}{\left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3}-\frac {e^{6 e^x} \log (1-x)}{\left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3}\right ) \, dx-2 \int \left (\frac {e^{6 e^x} x}{(-1+x) \left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3}-\frac {e^{6 e^x} \log (1-x)}{(-1+x) \left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3}\right ) \, dx+2 \int \left (\frac {e^{6 e^x} x \log (1-x)}{\left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3}-\frac {e^{6 e^x} \log ^2(1-x)}{\left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3}\right ) \, dx+2 \int \left (\frac {e^{6 e^x} x \log \left (x^2\right )}{(-1+x) \left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3}-\frac {e^{6 e^x} \log (1-x) \log \left (x^2\right )}{(-1+x) \left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3}\right ) \, dx-2 \int \left (\frac {e^{6 e^x} x \log \left (x^2\right )}{\left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3}+\frac {e^{6 e^x} \log (1-x) \log \left (x^2\right )}{\left (-e^{10}-e^{2 e^x} x+e^{2 e^x} \log \left (x^2\right )\right )^3}\right ) \, dx+4 \int \frac {e^{10+4 e^x+x} x^2}{\left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3} \, dx+4 \int \frac {e^{10+4 e^x+x} \log ^2(1-x)}{\left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3} \, dx-4 \int \left (\frac {e^{6 e^x} \log (1-x)}{\left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3}-\frac {e^{6 e^x} \log ^2(1-x)}{x \left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3}\right ) \, dx-8 \int \frac {e^{10+4 e^x+x} x \log (1-x)}{\left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3} \, dx \\ & = 2 \int \frac {e^{6 e^x} x}{\left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3} \, dx-2 \int \frac {e^{6 e^x} x}{(-1+x) \left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3} \, dx-2 \int \frac {e^{6 e^x} \log (1-x)}{\left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3} \, dx+2 \int \frac {e^{6 e^x} \log (1-x)}{(-1+x) \left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3} \, dx+2 \int \frac {e^{6 e^x} x \log (1-x)}{\left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3} \, dx-2 \int \frac {e^{6 e^x} \log ^2(1-x)}{\left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3} \, dx-2 \int \frac {e^{6 e^x} x \log \left (x^2\right )}{\left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3} \, dx+2 \int \frac {e^{6 e^x} x \log \left (x^2\right )}{(-1+x) \left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3} \, dx-2 \int \frac {e^{6 e^x} \log (1-x) \log \left (x^2\right )}{(-1+x) \left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3} \, dx-2 \int \frac {e^{6 e^x} \log (1-x) \log \left (x^2\right )}{\left (-e^{10}-e^{2 e^x} x+e^{2 e^x} \log \left (x^2\right )\right )^3} \, dx+2 \int \left (\frac {e^{2 \left (5+2 e^x\right )} x}{\left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3}-\frac {e^{2 \left (5+2 e^x\right )} \log (1-x)}{\left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3}\right ) \, dx-2 \int \left (\frac {e^{2 \left (5+2 e^x\right )} x}{(-1+x) \left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3}-\frac {e^{2 \left (5+2 e^x\right )} \log (1-x)}{(-1+x) \left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3}\right ) \, dx+4 \int \frac {e^{10+4 e^x+x} x^2}{\left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3} \, dx-4 \int \frac {e^{6 e^x} \log (1-x)}{\left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3} \, dx+4 \int \frac {e^{10+4 e^x+x} \log ^2(1-x)}{\left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3} \, dx+4 \int \frac {e^{6 e^x} \log ^2(1-x)}{x \left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3} \, dx-8 \int \frac {e^{10+4 e^x+x} x \log (1-x)}{\left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3} \, dx \\ & = 2 \int \frac {e^{6 e^x} x}{\left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3} \, dx+2 \int \frac {e^{2 \left (5+2 e^x\right )} x}{\left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3} \, dx-2 \int \frac {e^{2 \left (5+2 e^x\right )} x}{(-1+x) \left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3} \, dx-2 \int \frac {e^{6 e^x} \log (1-x)}{\left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3} \, dx-2 \int \frac {e^{2 \left (5+2 e^x\right )} \log (1-x)}{\left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3} \, dx+2 \int \frac {e^{6 e^x} \log (1-x)}{(-1+x) \left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3} \, dx+2 \int \frac {e^{2 \left (5+2 e^x\right )} \log (1-x)}{(-1+x) \left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3} \, dx+2 \int \frac {e^{6 e^x} x \log (1-x)}{\left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3} \, dx-2 \int \frac {e^{6 e^x} \log ^2(1-x)}{\left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3} \, dx-2 \int \frac {e^{6 e^x} x \log \left (x^2\right )}{\left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3} \, dx-2 \int \frac {e^{6 e^x} \log (1-x) \log \left (x^2\right )}{(-1+x) \left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3} \, dx-2 \int \frac {e^{6 e^x} \log (1-x) \log \left (x^2\right )}{\left (-e^{10}-e^{2 e^x} x+e^{2 e^x} \log \left (x^2\right )\right )^3} \, dx-2 \int \left (\frac {e^{6 e^x}}{\left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3}+\frac {e^{6 e^x}}{(-1+x) \left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3}\right ) \, dx+2 \int \left (\frac {e^{6 e^x} \log \left (x^2\right )}{(-1+x) \left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3}-\frac {e^{6 e^x} \log \left (x^2\right )}{\left (-e^{10}-e^{2 e^x} x+e^{2 e^x} \log \left (x^2\right )\right )^3}\right ) \, dx+4 \int \frac {e^{10+4 e^x+x} x^2}{\left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3} \, dx-4 \int \frac {e^{6 e^x} \log (1-x)}{\left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3} \, dx+4 \int \frac {e^{10+4 e^x+x} \log ^2(1-x)}{\left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3} \, dx+4 \int \frac {e^{6 e^x} \log ^2(1-x)}{x \left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3} \, dx-8 \int \frac {e^{10+4 e^x+x} x \log (1-x)}{\left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3} \, dx \\ & = -\left (2 \int \frac {e^{6 e^x}}{\left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3} \, dx\right )-2 \int \frac {e^{6 e^x}}{(-1+x) \left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3} \, dx+2 \int \frac {e^{6 e^x} x}{\left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3} \, dx+2 \int \frac {e^{2 \left (5+2 e^x\right )} x}{\left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3} \, dx-2 \int \frac {e^{6 e^x} \log (1-x)}{\left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3} \, dx-2 \int \frac {e^{2 \left (5+2 e^x\right )} \log (1-x)}{\left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3} \, dx+2 \int \frac {e^{6 e^x} \log (1-x)}{(-1+x) \left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3} \, dx+2 \int \frac {e^{2 \left (5+2 e^x\right )} \log (1-x)}{(-1+x) \left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3} \, dx+2 \int \frac {e^{6 e^x} x \log (1-x)}{\left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3} \, dx-2 \int \frac {e^{6 e^x} \log ^2(1-x)}{\left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3} \, dx+2 \int \frac {e^{6 e^x} \log \left (x^2\right )}{(-1+x) \left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3} \, dx-2 \int \frac {e^{6 e^x} x \log \left (x^2\right )}{\left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3} \, dx-2 \int \frac {e^{6 e^x} \log (1-x) \log \left (x^2\right )}{(-1+x) \left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3} \, dx-2 \int \frac {e^{6 e^x} \log \left (x^2\right )}{\left (-e^{10}-e^{2 e^x} x+e^{2 e^x} \log \left (x^2\right )\right )^3} \, dx-2 \int \frac {e^{6 e^x} \log (1-x) \log \left (x^2\right )}{\left (-e^{10}-e^{2 e^x} x+e^{2 e^x} \log \left (x^2\right )\right )^3} \, dx-2 \int \left (\frac {e^{2 \left (5+2 e^x\right )}}{\left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3}+\frac {e^{2 \left (5+2 e^x\right )}}{(-1+x) \left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3}\right ) \, dx+4 \int \frac {e^{10+4 e^x+x} x^2}{\left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3} \, dx-4 \int \frac {e^{6 e^x} \log (1-x)}{\left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3} \, dx+4 \int \frac {e^{10+4 e^x+x} \log ^2(1-x)}{\left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3} \, dx+4 \int \frac {e^{6 e^x} \log ^2(1-x)}{x \left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3} \, dx-8 \int \frac {e^{10+4 e^x+x} x \log (1-x)}{\left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3} \, dx \\ & = -\left (2 \int \frac {e^{6 e^x}}{\left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3} \, dx\right )-2 \int \frac {e^{2 \left (5+2 e^x\right )}}{\left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3} \, dx-2 \int \frac {e^{6 e^x}}{(-1+x) \left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3} \, dx-2 \int \frac {e^{2 \left (5+2 e^x\right )}}{(-1+x) \left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3} \, dx+2 \int \frac {e^{6 e^x} x}{\left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3} \, dx+2 \int \frac {e^{2 \left (5+2 e^x\right )} x}{\left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3} \, dx-2 \int \frac {e^{6 e^x} \log (1-x)}{\left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3} \, dx-2 \int \frac {e^{2 \left (5+2 e^x\right )} \log (1-x)}{\left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3} \, dx+2 \int \frac {e^{6 e^x} \log (1-x)}{(-1+x) \left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3} \, dx+2 \int \frac {e^{2 \left (5+2 e^x\right )} \log (1-x)}{(-1+x) \left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3} \, dx+2 \int \frac {e^{6 e^x} x \log (1-x)}{\left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3} \, dx-2 \int \frac {e^{6 e^x} \log ^2(1-x)}{\left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3} \, dx+2 \int \frac {e^{6 e^x} \log \left (x^2\right )}{(-1+x) \left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3} \, dx-2 \int \frac {e^{6 e^x} x \log \left (x^2\right )}{\left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3} \, dx-2 \int \frac {e^{6 e^x} \log (1-x) \log \left (x^2\right )}{(-1+x) \left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3} \, dx-2 \int \frac {e^{6 e^x} \log \left (x^2\right )}{\left (-e^{10}-e^{2 e^x} x+e^{2 e^x} \log \left (x^2\right )\right )^3} \, dx-2 \int \frac {e^{6 e^x} \log (1-x) \log \left (x^2\right )}{\left (-e^{10}-e^{2 e^x} x+e^{2 e^x} \log \left (x^2\right )\right )^3} \, dx+4 \int \frac {e^{10+4 e^x+x} x^2}{\left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3} \, dx-4 \int \frac {e^{6 e^x} \log (1-x)}{\left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3} \, dx+4 \int \frac {e^{10+4 e^x+x} \log ^2(1-x)}{\left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3} \, dx+4 \int \frac {e^{6 e^x} \log ^2(1-x)}{x \left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3} \, dx-8 \int \frac {e^{10+4 e^x+x} x \log (1-x)}{\left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^3} \, dx \\ \end{align*}
Time = 0.34 (sec) , antiderivative size = 48, normalized size of antiderivative = 1.50 \[ \int \frac {-4 x^2+2 x^3+\left (8 x-8 x^2+2 x^3\right ) \log (1-x)+\left (-4+6 x-2 x^2\right ) \log ^2(1-x)+e^{10-2 e^x} \left (-4 x^2+2 x^3+e^x \left (-4 x^3+4 x^4\right )+\left (4 x-2 x^2+e^x \left (8 x^2-8 x^3\right )\right ) \log (1-x)+e^x \left (-4 x+4 x^2\right ) \log ^2(1-x)\right )+\left (4 x^2-2 x^3+\left (-4 x+2 x^2\right ) \log (1-x)\right ) \log \left (x^2\right )}{-x^4+x^5+e^{30-6 e^x} \left (-x+x^2\right )+\left (3 x^3-3 x^4\right ) \log \left (x^2\right )+\left (-3 x^2+3 x^3\right ) \log ^2\left (x^2\right )+\left (x-x^2\right ) \log ^3\left (x^2\right )+e^{20-4 e^x} \left (-3 x^2+3 x^3+\left (3 x-3 x^2\right ) \log \left (x^2\right )\right )+e^{10-2 e^x} \left (-3 x^3+3 x^4+\left (6 x^2-6 x^3\right ) \log \left (x^2\right )+\left (-3 x+3 x^2\right ) \log ^2\left (x^2\right )\right )} \, dx=\frac {e^{4 e^x} (x-\log (1-x))^2}{\left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^2} \]
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Result contains higher order function than in optimal. Order 9 vs. order 3.
Time = 0.31 (sec) , antiderivative size = 92, normalized size of antiderivative = 2.88
\[\frac {4 x^{2}-8 x \ln \left (1-x \right )+4 \ln \left (1-x \right )^{2}}{\left (2 \,{\mathrm e}^{-2 \,{\mathrm e}^{x}+10}+i \pi \operatorname {csgn}\left (i x^{2}\right )^{3}-2 i \pi \,\operatorname {csgn}\left (i x \right ) \operatorname {csgn}\left (i x^{2}\right )^{2}+i \pi \operatorname {csgn}\left (i x \right )^{2} \operatorname {csgn}\left (i x^{2}\right )+2 x -4 \ln \left (x \right )\right )^{2}}\]
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Leaf count of result is larger than twice the leaf count of optimal. 65 vs. \(2 (30) = 60\).
Time = 0.26 (sec) , antiderivative size = 65, normalized size of antiderivative = 2.03 \[ \int \frac {-4 x^2+2 x^3+\left (8 x-8 x^2+2 x^3\right ) \log (1-x)+\left (-4+6 x-2 x^2\right ) \log ^2(1-x)+e^{10-2 e^x} \left (-4 x^2+2 x^3+e^x \left (-4 x^3+4 x^4\right )+\left (4 x-2 x^2+e^x \left (8 x^2-8 x^3\right )\right ) \log (1-x)+e^x \left (-4 x+4 x^2\right ) \log ^2(1-x)\right )+\left (4 x^2-2 x^3+\left (-4 x+2 x^2\right ) \log (1-x)\right ) \log \left (x^2\right )}{-x^4+x^5+e^{30-6 e^x} \left (-x+x^2\right )+\left (3 x^3-3 x^4\right ) \log \left (x^2\right )+\left (-3 x^2+3 x^3\right ) \log ^2\left (x^2\right )+\left (x-x^2\right ) \log ^3\left (x^2\right )+e^{20-4 e^x} \left (-3 x^2+3 x^3+\left (3 x-3 x^2\right ) \log \left (x^2\right )\right )+e^{10-2 e^x} \left (-3 x^3+3 x^4+\left (6 x^2-6 x^3\right ) \log \left (x^2\right )+\left (-3 x+3 x^2\right ) \log ^2\left (x^2\right )\right )} \, dx=\frac {x^{2} - 2 \, x \log \left (-x + 1\right ) + \log \left (-x + 1\right )^{2}}{x^{2} + 2 \, {\left (x - \log \left (x^{2}\right )\right )} e^{\left (-2 \, e^{x} + 10\right )} - 2 \, x \log \left (x^{2}\right ) + \log \left (x^{2}\right )^{2} + e^{\left (-4 \, e^{x} + 20\right )}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 63 vs. \(2 (24) = 48\).
Time = 0.39 (sec) , antiderivative size = 63, normalized size of antiderivative = 1.97 \[ \int \frac {-4 x^2+2 x^3+\left (8 x-8 x^2+2 x^3\right ) \log (1-x)+\left (-4+6 x-2 x^2\right ) \log ^2(1-x)+e^{10-2 e^x} \left (-4 x^2+2 x^3+e^x \left (-4 x^3+4 x^4\right )+\left (4 x-2 x^2+e^x \left (8 x^2-8 x^3\right )\right ) \log (1-x)+e^x \left (-4 x+4 x^2\right ) \log ^2(1-x)\right )+\left (4 x^2-2 x^3+\left (-4 x+2 x^2\right ) \log (1-x)\right ) \log \left (x^2\right )}{-x^4+x^5+e^{30-6 e^x} \left (-x+x^2\right )+\left (3 x^3-3 x^4\right ) \log \left (x^2\right )+\left (-3 x^2+3 x^3\right ) \log ^2\left (x^2\right )+\left (x-x^2\right ) \log ^3\left (x^2\right )+e^{20-4 e^x} \left (-3 x^2+3 x^3+\left (3 x-3 x^2\right ) \log \left (x^2\right )\right )+e^{10-2 e^x} \left (-3 x^3+3 x^4+\left (6 x^2-6 x^3\right ) \log \left (x^2\right )+\left (-3 x+3 x^2\right ) \log ^2\left (x^2\right )\right )} \, dx=\frac {x^{2} - 2 x \log {\left (1 - x \right )} + \log {\left (1 - x \right )}^{2}}{x^{2} - 2 x \log {\left (x^{2} \right )} + \left (2 x - 2 \log {\left (x^{2} \right )}\right ) e^{10 - 2 e^{x}} + e^{20 - 4 e^{x}} + \log {\left (x^{2} \right )}^{2}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 83 vs. \(2 (30) = 60\).
Time = 0.91 (sec) , antiderivative size = 83, normalized size of antiderivative = 2.59 \[ \int \frac {-4 x^2+2 x^3+\left (8 x-8 x^2+2 x^3\right ) \log (1-x)+\left (-4+6 x-2 x^2\right ) \log ^2(1-x)+e^{10-2 e^x} \left (-4 x^2+2 x^3+e^x \left (-4 x^3+4 x^4\right )+\left (4 x-2 x^2+e^x \left (8 x^2-8 x^3\right )\right ) \log (1-x)+e^x \left (-4 x+4 x^2\right ) \log ^2(1-x)\right )+\left (4 x^2-2 x^3+\left (-4 x+2 x^2\right ) \log (1-x)\right ) \log \left (x^2\right )}{-x^4+x^5+e^{30-6 e^x} \left (-x+x^2\right )+\left (3 x^3-3 x^4\right ) \log \left (x^2\right )+\left (-3 x^2+3 x^3\right ) \log ^2\left (x^2\right )+\left (x-x^2\right ) \log ^3\left (x^2\right )+e^{20-4 e^x} \left (-3 x^2+3 x^3+\left (3 x-3 x^2\right ) \log \left (x^2\right )\right )+e^{10-2 e^x} \left (-3 x^3+3 x^4+\left (6 x^2-6 x^3\right ) \log \left (x^2\right )+\left (-3 x+3 x^2\right ) \log ^2\left (x^2\right )\right )} \, dx=\frac {x^{2} e^{\left (4 \, e^{x}\right )} - 2 \, x e^{\left (4 \, e^{x}\right )} \log \left (-x + 1\right ) + e^{\left (4 \, e^{x}\right )} \log \left (-x + 1\right )^{2}}{{\left (x^{2} - 4 \, x \log \left (x\right ) + 4 \, \log \left (x\right )^{2}\right )} e^{\left (4 \, e^{x}\right )} + 2 \, {\left (x e^{10} - 2 \, e^{10} \log \left (x\right )\right )} e^{\left (2 \, e^{x}\right )} + e^{20}} \]
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Timed out. \[ \int \frac {-4 x^2+2 x^3+\left (8 x-8 x^2+2 x^3\right ) \log (1-x)+\left (-4+6 x-2 x^2\right ) \log ^2(1-x)+e^{10-2 e^x} \left (-4 x^2+2 x^3+e^x \left (-4 x^3+4 x^4\right )+\left (4 x-2 x^2+e^x \left (8 x^2-8 x^3\right )\right ) \log (1-x)+e^x \left (-4 x+4 x^2\right ) \log ^2(1-x)\right )+\left (4 x^2-2 x^3+\left (-4 x+2 x^2\right ) \log (1-x)\right ) \log \left (x^2\right )}{-x^4+x^5+e^{30-6 e^x} \left (-x+x^2\right )+\left (3 x^3-3 x^4\right ) \log \left (x^2\right )+\left (-3 x^2+3 x^3\right ) \log ^2\left (x^2\right )+\left (x-x^2\right ) \log ^3\left (x^2\right )+e^{20-4 e^x} \left (-3 x^2+3 x^3+\left (3 x-3 x^2\right ) \log \left (x^2\right )\right )+e^{10-2 e^x} \left (-3 x^3+3 x^4+\left (6 x^2-6 x^3\right ) \log \left (x^2\right )+\left (-3 x+3 x^2\right ) \log ^2\left (x^2\right )\right )} \, dx=\text {Timed out} \]
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Timed out. \[ \int \frac {-4 x^2+2 x^3+\left (8 x-8 x^2+2 x^3\right ) \log (1-x)+\left (-4+6 x-2 x^2\right ) \log ^2(1-x)+e^{10-2 e^x} \left (-4 x^2+2 x^3+e^x \left (-4 x^3+4 x^4\right )+\left (4 x-2 x^2+e^x \left (8 x^2-8 x^3\right )\right ) \log (1-x)+e^x \left (-4 x+4 x^2\right ) \log ^2(1-x)\right )+\left (4 x^2-2 x^3+\left (-4 x+2 x^2\right ) \log (1-x)\right ) \log \left (x^2\right )}{-x^4+x^5+e^{30-6 e^x} \left (-x+x^2\right )+\left (3 x^3-3 x^4\right ) \log \left (x^2\right )+\left (-3 x^2+3 x^3\right ) \log ^2\left (x^2\right )+\left (x-x^2\right ) \log ^3\left (x^2\right )+e^{20-4 e^x} \left (-3 x^2+3 x^3+\left (3 x-3 x^2\right ) \log \left (x^2\right )\right )+e^{10-2 e^x} \left (-3 x^3+3 x^4+\left (6 x^2-6 x^3\right ) \log \left (x^2\right )+\left (-3 x+3 x^2\right ) \log ^2\left (x^2\right )\right )} \, dx=\int \frac {{\mathrm {e}}^{10-2\,{\mathrm {e}}^x}\,\left ({\mathrm {e}}^x\,\left (4\,x^3-4\,x^4\right )-\ln \left (1-x\right )\,\left (4\,x+{\mathrm {e}}^x\,\left (8\,x^2-8\,x^3\right )-2\,x^2\right )+4\,x^2-2\,x^3+{\mathrm {e}}^x\,{\ln \left (1-x\right )}^2\,\left (4\,x-4\,x^2\right )\right )-\ln \left (1-x\right )\,\left (2\,x^3-8\,x^2+8\,x\right )+{\ln \left (1-x\right )}^2\,\left (2\,x^2-6\,x+4\right )+4\,x^2-2\,x^3+\ln \left (x^2\right )\,\left (\ln \left (1-x\right )\,\left (4\,x-2\,x^2\right )-4\,x^2+2\,x^3\right )}{{\mathrm {e}}^{10-2\,{\mathrm {e}}^x}\,\left ({\ln \left (x^2\right )}^2\,\left (3\,x-3\,x^2\right )-\ln \left (x^2\right )\,\left (6\,x^2-6\,x^3\right )+3\,x^3-3\,x^4\right )-{\ln \left (x^2\right )}^3\,\left (x-x^2\right )-{\mathrm {e}}^{20-4\,{\mathrm {e}}^x}\,\left (\ln \left (x^2\right )\,\left (3\,x-3\,x^2\right )-3\,x^2+3\,x^3\right )+{\mathrm {e}}^{30-6\,{\mathrm {e}}^x}\,\left (x-x^2\right )-\ln \left (x^2\right )\,\left (3\,x^3-3\,x^4\right )+{\ln \left (x^2\right )}^2\,\left (3\,x^2-3\,x^3\right )+x^4-x^5} \,d x \]
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