\[ \int \frac {e^{\frac {1}{5} x^2 \log (x) \log \left (\log \left (-\frac {x}{20+5 x}\right )\right )} \left (4 x \log (x)+\left (\left (4 x+x^2\right ) \log \left (-\frac {x}{20+5 x}\right )+\left (8 x+2 x^2\right ) \log (x) \log \left (-\frac {x}{20+5 x}\right )\right ) \log \left (\log \left (-\frac {x}{20+5 x}\right )\right )\right )}{(20+5 x) \log \left (-\frac {x}{20+5 x}\right )} \, dx \]
Optimal antiderivative \[ {\mathrm e}^{\frac {x^{2} \ln \left (\ln \left (\frac {x}{-5 x -20}\right )\right ) \ln \left (x \right )}{5}} \]
command
integrate((((2*x**2+8*x)*ln(-x/(20+5*x))*ln(x)+(x**2+4*x)*ln(-x/(20+5*x)))*ln(ln(-x/(20+5*x)))+4*x*ln(x))*exp(1/5*x**2*ln(x)*ln(ln(-x/(20+5*x))))/(20+5*x)/ln(-x/(20+5*x)),x)
Sympy 1.10.1 under Python 3.10.4 output
\[ e^{\frac {x^{2} \log {\left (x \right )} \log {\left (\log {\left (- \frac {x}{5 x + 20} \right )} \right )}}{5}} \]
Sympy 1.8 under Python 3.8.8 output
\[ \text {Timed out} \]________________________________________________________________________________________