\[ \int \frac {\left (2 e^x x^2+e^{\frac {5 e^{-x}}{x}} (-10-10 x) \log (18)\right ) \log \left (\frac {x+e^{\frac {5 e^{-x}}{x}} \log (18)}{\log (18)}\right )+\left (e^x x^2+e^{\frac {5 e^{-x}}{x}+x} x \log (18)\right ) \log ^2\left (\frac {x+e^{\frac {5 e^{-x}}{x}} \log (18)}{\log (18)}\right )}{2 e^x x^2+2 e^{\frac {5 e^{-x}}{x}+x} x \log (18)} \, dx \]
Optimal antiderivative \[ \frac {\ln \! \left ({\mathrm e}^{\frac {5 \,{\mathrm e}^{-x}}{x}}+\frac {x}{\ln \left (18\right )}\right )^{2} x}{2} \]
command
integrate(((x*ln(18)*exp(x)*exp(5/exp(x)/x)+exp(x)*x**2)*ln((ln(18)*exp(5/exp(x)/x)+x)/ln(18))**2+((-10*x-10)*ln(18)*exp(5/exp(x)/x)+2*exp(x)*x**2)*ln((ln(18)*exp(5/exp(x)/x)+x)/ln(18)))/(2*x*ln(18)*exp(x)*exp(5/exp(x)/x)+2*exp(x)*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
\[ \frac {x \log {\left (\frac {x + e^{\frac {5 e^{- x}}{x}} \log {\left (18 \right )}}{\log {\left (18 \right )}} \right )}^{2}}{2} \]