\[ \int \frac {e^x x \log (x)+e^x x^2 \log ^2(x)+e^{e^{3 e^{-x}}} \left (-3 e^{3 e^{-x}} x \log (x)+e^x x \log ^2(x)\right )+\left (-e^{e^{3 e^{-x}}+x}-e^x x\right ) \log \left (e^{e^{3 e^{-x}}}+x\right )}{e^{e^{3 e^{-x}}+x} x \log ^2(x)+e^x x^2 \log ^2(x)} \, dx \]
Optimal antiderivative \[ \frac {\ln \! \left ({\mathrm e}^{{\mathrm e}^{3 \,{\mathrm e}^{-x}}}+x \right )}{\ln \! \left (x \right )}+x \]
command
integrate(((-exp(x)*exp(exp(3/exp(x)))-exp(x)*x)*ln(exp(exp(3/exp(x)))+x)+(-3*x*ln(x)*exp(3/exp(x))+x*exp(x)*ln(x)**2)*exp(exp(3/exp(x)))+x**2*exp(x)*ln(x)**2+x*exp(x)*ln(x))/(x*exp(x)*ln(x)**2*exp(exp(3/exp(x)))+x**2*exp(x)*ln(x)**2),x)
Sympy 1.10.1 under Python 3.10.4 output
\[ \text {Exception raised: TypeError} \]
Sympy 1.8 under Python 3.8.8 output
\[ x + \frac {\log {\left (x + e^{e^{3 e^{- x}}} \right )}}{\log {\left (x \right )}} \]