\[ \int \frac {e^{e^{-\frac {2 e^{-x}}{\log (x)}}-x-\frac {2 e^{-x}}{\log (x)}} \left (10-2 e^x+2 x+\left (10 x-2 e^x x+2 x^2\right ) \log (x)+e^{\frac {2 e^{-x}}{\log (x)}} \left (e^x x-e^{2 x} x\right ) \log ^2(x)\right )}{x \log ^2(x)} \, dx \]
Optimal antiderivative \[ {\mathrm e}^{{\mathrm e}^{-\frac {2 \,{\mathrm e}^{-x}}{\ln \left (x \right )}}} \left (x -{\mathrm e}^{x}+5\right ) \]
command
integrate(((-x*exp(x)**2+exp(x)*x)*ln(x)**2*exp(1/exp(x)/ln(x))**2+(-2*exp(x)*x+2*x**2+10*x)*ln(x)-2*exp(x)+2*x+10)*exp(1/exp(1/exp(x)/ln(x))**2)/x/exp(x)/ln(x)**2/exp(1/exp(x)/ln(x))**2,x)
Sympy 1.10.1 under Python 3.10.4 output
\[ \text {Timed out} \]
Sympy 1.8 under Python 3.8.8 output
\[ \left (x e^{- x} - 1 + 5 e^{- x}\right ) e^{x} e^{e^{- \frac {2 e^{- x}}{\log {\left (x \right )}}}} \]