\[ \int \frac {20 x+129 x^2+50 x^3+5 x^4+\left (60+730 x+171 x^2-20 x^3-5 x^4\right ) \log (x)+\left (-60-387 x-150 x^2-15 x^3\right ) \log \left (\frac {4 x+25 x^2+5 x^3}{75+15 x}\right )}{\left (20 x+129 x^2+50 x^3+5 x^4\right ) \log ^2(x)} \, dx \]
Optimal antiderivative \[ \frac {3 \ln \! \left (\frac {\left (x +\frac {4}{25+5 x}\right ) x}{3}\right )-x -\ln \! \left (x \right )}{\ln \! \left (x \right )} \]
command
integrate(((-15*x**3-150*x**2-387*x-60)*ln((5*x**3+25*x**2+4*x)/(15*x+75))+(-5*x**4-20*x**3+171*x**2+730*x+60)*ln(x)+5*x**4+50*x**3+129*x**2+20*x)/(5*x**4+50*x**3+129*x**2+20*x)/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
\[ - \frac {x}{\log {\left (x \right )}} + \frac {3 \log {\left (\frac {5 x^{3} + 25 x^{2} + 4 x}{15 x + 75} \right )}}{\log {\left (x \right )}} \]