\[ \int \frac {\left (20 x-4 x^2\right ) \log (-5+x) \log (x)+((-80+16 x) \log (-5+x)-16 x \log (x)) \log (\log (-5+x))+((80-16 x) \log (-5+x)+16 x \log (x)) \log (\log (x))}{\left (-5 x+x^2\right ) \log (-5+x) \log (x)} \, dx \]
Optimal antiderivative \[ -4 x -8 \ln \left (5\right )-8 \left (\ln \left (\ln \left (-5+x \right )\right )-\ln \left (\ln \left (x \right )\right )\right )^{2} \]
command
integrate(((16*x*ln(x)+(-16*x+80)*ln(-5+x))*ln(ln(x))+(-16*x*ln(x)+(16*x-80)*ln(-5+x))*ln(ln(-5+x))+(-4*x**2+20*x)*ln(-5+x)*ln(x))/(x**2-5*x)/ln(-5+x)/ln(x),x)
Sympy 1.10.1 under Python 3.10.4 output
\[ - 4 x - 8 \log {\left (\log {\left (x \right )} \right )}^{2} + 16 \log {\left (\log {\left (x \right )} \right )} \log {\left (\log {\left (x - 5 \right )} \right )} - 8 \log {\left (\log {\left (x - 5 \right )} \right )}^{2} \]
Sympy 1.8 under Python 3.8.8 output
\[ \text {Timed out} \]________________________________________________________________________________________