\[ \int \frac {\left (-40 x^2+40 x^3-10 x^4\right ) \log ^2(x)+\left (2-3 x+x^2\right ) \log \left (x-x^2\right )+\log (x) \left (-2+5 x-2 x^2+\left (2-2 x+x^2\right ) \log \left (x-x^2\right )\right )}{\left (120 x^2-120 x^3+30 x^4\right ) \log ^2(x)} \, dx \]
Optimal antiderivative \[ \frac {\ln \! \left (\left (1-x \right ) x \right )}{30 \left (\frac {x}{-1+x}-x \right ) \ln \! \left (x \right )}-\frac {x}{3} \]
command
integrate(((-10*x**4+40*x**3-40*x**2)*ln(x)**2+((x**2-2*x+2)*ln(-x**2+x)-2*x**2+5*x-2)*ln(x)+(x**2-3*x+2)*ln(-x**2+x))/(30*x**4-120*x**3+120*x**2)/ln(x)**2,x)
Sympy 1.10.1 under Python 3.10.4 output
\[ \text {Exception raised: TypeError} \]
Sympy 1.8 under Python 3.8.8 output
\[ - \frac {x}{3} + \frac {\left (1 - x\right ) \log {\left (- x^{2} + x \right )}}{30 x^{2} \log {\left (x \right )} - 60 x \log {\left (x \right )}} \]