\[ \int \frac {e^{-4 x^2} \left (e^{4 x^2} \log ^2(x)+e^{\frac {e^{-4 x^2} x}{\log (x)}} \left (31+5 x+\left (-31-5 x+248 x^2+40 x^3\right ) \log (x)-5 e^{4 x^2} \log ^2(x)\right )\right )}{\log ^2(x)} \, dx \]
Optimal antiderivative \[ x +{\mathrm e}^{\frac {x \,{\mathrm e}^{-4 x^{2}}}{\ln \left (x \right )}} \left (-31-5 x \right ) \]
command
integrate(((-5*exp(4*x**2)*ln(x)**2+(40*x**3+248*x**2-5*x-31)*ln(x)+5*x+31)*exp(x/exp(4*x**2)/ln(x))+exp(4*x**2)*ln(x)**2)/exp(4*x**2)/ln(x)**2,x)
Sympy 1.10.1 under Python 3.10.4 output
\[ \text {Exception raised: SystemError} \]
Sympy 1.8 under Python 3.8.8 output
\[ x + \left (- 5 x - 31\right ) e^{\frac {x e^{- 4 x^{2}}}{\log {\left (x \right )}}} \]