\[ \int \frac {18-12 x+2 x^2+x^2 \left (i \pi +\log \left (\frac {25}{4}\right )\right )+\left (-9+6 x-x^2\right ) \log \left (x^2\right )}{\left (3 x^2-x^3\right ) \left (i \pi +\log \left (\frac {25}{4}\right )\right )+\left (9 x-6 x^2+x^3\right ) \log \left (x^2\right )} \, dx \]
Optimal antiderivative \[ \ln \left (\frac {\ln \left (\frac {25}{4}\right )+i \pi }{-3 x +9}+\frac {\ln \left (x^{2}\right )}{3 x}\right ) \]
command
integrate(((-x**2+6*x-9)*ln(x**2)+x**2*(ln(25/4)+I*pi)+2*x**2-12*x+18)/((x**3-6*x**2+9*x)*ln(x**2)+(-x**3+3*x**2)*(ln(25/4)+I*pi)),x)
Sympy 1.10.1 under Python 3.10.4 output
\[ - \log {\left (x \right )} + \log {\left (\log {\left (x^{2} \right )} + \frac {- 2 x \log {\left (5 \right )} + 2 x \log {\left (2 \right )} - i \pi x}{x - 3} \right )} \]
Sympy 1.8 under Python 3.8.8 output
\[ \text {Timed out} \]________________________________________________________________________________________