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