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