\[ \int \frac {-2 x+2 \log (x)+(x-\log (x)) \log \left (2 x^2\right )+(1-x) \log \left (2 x^2\right ) \log \left (\frac {x}{\log \left (2 x^2\right )}\right )}{\left (x^3-2 x^2 \log (x)+x \log ^2(x)\right ) \log \left (2 x^2\right )} \, dx \]
Optimal antiderivative \[ 1+\frac {\ln \! \left (\frac {x}{\ln \left (2 x^{2}\right )}\right )}{x -\ln \! \left (x \right )} \]
command
integrate(((1-x)*ln(2*x**2)*ln(x/ln(2*x**2))+(x-ln(x))*ln(2*x**2)+2*ln(x)-2*x)/(x*ln(x)**2-2*x**2*ln(x)+x**3)/ln(2*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
\[ \frac {\log {\left (\frac {x}{2 \log {\left (x \right )} + \log {\left (2 \right )}} \right )}}{x - \log {\left (x \right )}} \]