\[ \int \frac {\left (-30-12 x^2-6 x^3+6 x^4\right ) \log ^2\left (\frac {5+2 x^2+x^3-x^4}{x^2}\right )+\log \left (\frac {2}{x}\right ) \left (\left (60-6 x^3+12 x^4\right ) \log \left (\frac {5+2 x^2+x^3-x^4}{x^2}\right )+\left (30+12 x^2+6 x^3-6 x^4\right ) \log ^2\left (\frac {5+2 x^2+x^3-x^4}{x^2}\right )\right )}{\left (-5 x^3-2 x^5-x^6+x^7\right ) \log ^3\left (\frac {2}{x}\right )} \, dx \]
Optimal antiderivative \[ \frac {3 \ln \! \left (2+x +\frac {5}{x^{2}}-x^{2}\right )^{2}}{\ln \! \left (\frac {2}{x}\right )^{2} x^{2}} \]
command
integrate((((-6*x**4+6*x**3+12*x**2+30)*ln((-x**4+x**3+2*x**2+5)/x**2)**2+(12*x**4-6*x**3+60)*ln((-x**4+x**3+2*x**2+5)/x**2))*ln(2/x)+(6*x**4-6*x**3-12*x**2-30)*ln((-x**4+x**3+2*x**2+5)/x**2)**2)/(x**7-x**6-2*x**5-5*x**3)/ln(2/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
\[ \frac {3 \log {\left (\frac {- x^{4} + x^{3} + 2 x^{2} + 5}{x^{2}} \right )}^{2}}{x^{2} \log {\left (\frac {2}{x} \right )}^{2}} \]