\[ \int \frac {\left (6 x^2+2 x^3\right ) \log (1-x)+\left (3+x-4 x^2\right ) \log ^2(1-x)+\left (\left (6 x+2 x^2\right ) \log (1-x)+\left (-x+x^2\right ) \log ^2(1-x)\right ) \log (x)}{-x^3+x^4+\left (-2 x^2+2 x^3\right ) \log (x)+\left (-x+x^2\right ) \log ^2(x)} \, dx \]
Optimal antiderivative \[ \frac {\ln \! \left (1-x \right )^{2} \left (3+x \right )}{x +\ln \! \left (x \right )} \]
command
integrate((((x**2-x)*ln(1-x)**2+(2*x**2+6*x)*ln(1-x))*ln(x)+(-4*x**2+x+3)*ln(1-x)**2+(2*x**3+6*x**2)*ln(1-x))/((x**2-x)*ln(x)**2+(2*x**3-2*x**2)*ln(x)+x**4-x**3),x)
Sympy 1.10.1 under Python 3.10.4 output
\[ \text {Exception raised: TypeError} \]
Sympy 1.8 under Python 3.8.8 output
\[ \frac {\left (x + 3\right ) \log {\left (1 - x \right )}^{2}}{x + \log {\left (x \right )}} \]