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