\[ \int \frac {\left (6-2 x-4 x^2\right ) \log ^2(1-x)+\left (x^2+\left (x-x^2\right ) \log (1-x)-4 x \log ^2(1-x)\right ) \log \left (-\frac {e^{-\frac {x}{4 \log (1-x)}}}{-1+x}\right )+(-2+2 x) \log ^2(1-x) \log ^2\left (-\frac {e^{-\frac {x}{4 \log (1-x)}}}{-1+x}\right )}{(-2+2 x) \log ^2(1-x)} \, dx \]
Optimal antiderivative \[ \left (\ln \left (\frac {{\mathrm e}^{-\frac {x}{4 \ln \left (1-x \right )}}}{1-x}\right )^{2}-4-x \right ) x +x \]
command
int(((2*x-2)*ln(1-x)^2*ln(-exp(-1/4*x/ln(1-x))/(x-1))^2+(-4*x*ln(1-x)^2+(-x^2+x)*ln(1-x)+x^2)*ln(-exp(-1/4*x/ln(1-x))/(x-1))+(-4*x^2-2*x+6)*ln(1-x)^2)/(2*x-2)/ln(1-x)^2,x,method=_RETURNVERBOSE)
Maple 2022.1 output
| method | result | size |
| default | \(-3 x -\frac {1}{2}-\frac {x}{2 \ln \left (1-x \right )}+\left (x -1\right ) \ln \left (x -1\right )^{2}-2 \left (x -1\right ) \ln \left (x -1\right )-2 \ln \left (-\frac {{\mathrm e}^{-\frac {x}{4 \ln \left (1-x \right )}}}{x -1}\right )-2 \left (1-x \right ) \ln \left (1-x \right )-\ln \left (1-x \right )^{2}-2 \ln \left (x -1\right )-\frac {x^{2}}{2}-2 \left (1-x \right ) \left (\ln \left (x -1\right )-\ln \left (1-x \right )\right )-\frac {\left (1-x \right )^{3}}{16 \ln \left (1-x \right )^{2}}+\frac {3 \left (1-x \right )^{2}}{16 \ln \left (1-x \right )^{2}}-\frac {3 \left (1-x \right )}{16 \ln \left (1-x \right )^{2}}+\frac {\ln \left (x -1\right )}{2 \ln \left (1-x \right )}+2 \ln \left (1-x \right ) \left (1-x \right ) \left (\ln \left (-\frac {{\mathrm e}^{-\frac {x}{4 \ln \left (1-x \right )}}}{x -1}\right )+\frac {x}{4 \ln \left (1-x \right )}+\ln \left (x -1\right )\right )+2 \left (1-x \right ) \left (\ln \left (x -1\right )-\ln \left (1-x \right )\right ) \left (\ln \left (-\frac {{\mathrm e}^{-\frac {x}{4 \ln \left (1-x \right )}}}{x -1}\right )+\frac {x}{4 \ln \left (1-x \right )}+\ln \left (x -1\right )\right )-\frac {\left (\ln \left (-\frac {{\mathrm e}^{-\frac {x}{4 \ln \left (1-x \right )}}}{x -1}\right )+\frac {x}{4 \ln \left (1-x \right )}+\ln \left (x -1\right )\right ) x^{2}}{2 \ln \left (1-x \right )}+\left (\ln \left (x -1\right )-\ln \left (1-x \right )\right ) \left (-\frac {1-x}{\ln \left (1-x \right )}-\expIntegral \left (1, -\ln \left (1-x \right )\right )\right )-\left (\ln \left (x -1\right )-\ln \left (1-x \right )\right ) \expIntegral \left (1, -2 \ln \left (1-x \right )\right )-\frac {\left (\ln \left (x -1\right )-\ln \left (1-x \right )\right ) \left (-\frac {\left (1-x \right )^{2}}{\ln \left (1-x \right )}-2 \expIntegral \left (1, -2 \ln \left (1-x \right )\right )\right )}{2}+\left (\ln \left (x -1\right )-\ln \left (1-x \right )\right ) \expIntegral \left (1, -\ln \left (1-x \right )\right )+\frac {1}{16 \ln \left (1-x \right )^{2}}+x \left (\ln \left (-\frac {{\mathrm e}^{-\frac {x}{4 \ln \left (1-x \right )}}}{x -1}\right )+\frac {x}{4 \ln \left (1-x \right )}+\ln \left (x -1\right )\right )^{2}-2 \left (\ln \left (-\frac {{\mathrm e}^{-\frac {x}{4 \ln \left (1-x \right )}}}{x -1}\right )+\frac {x}{4 \ln \left (1-x \right )}+\ln \left (x -1\right )\right ) \ln \left (x -1\right )+2 \ln \left (x -1\right ) \ln \left (1-x \right )\) | \(569\) |
Maple 2021.1 output
\[\int \frac {\left (2 x -2\right ) \ln \left (1-x \right )^{2} \ln \left (-\frac {{\mathrm e}^{-\frac {x}{4 \ln \left (1-x \right )}}}{x -1}\right )^{2}+\left (-4 x \ln \left (1-x \right )^{2}+\left (-x^{2}+x \right ) \ln \left (1-x \right )+x^{2}\right ) \ln \left (-\frac {{\mathrm e}^{-\frac {x}{4 \ln \left (1-x \right )}}}{x -1}\right )+\left (-4 x^{2}-2 x +6\right ) \ln \left (1-x \right )^{2}}{\left (2 x -2\right ) \ln \left (1-x \right )^{2}}\, dx\]________________________________________________________________________________________