44.17 Problem number 1043

\[ \int e^{x+e^{90+10 e^2} x+2 e^{45+5 e^2} x \log \left (e^{-x} x\right )+x \log ^2\left (e^{-x} x\right )} \left (1+e^{90+10 e^2}+e^{45+5 e^2} (2-2 x)+\left (2+2 e^{45+5 e^2}-2 x\right ) \log \left (e^{-x} x\right )+\log ^2\left (e^{-x} x\right )\right ) \, dx \]

Optimal antiderivative \[ {\mathrm e}^{x \left (\ln \left (x \,{\mathrm e}^{-x}\right )+{\mathrm e}^{5 \,{\mathrm e}^{2}+45}\right )^{2}+x} \]

command

integrate((ln(x/exp(x))**2+(2*exp(5*exp(1)**2+45)-2*x+2)*ln(x/exp(x))+exp(5*exp(1)**2+45)**2+(2-2*x)*exp(5*exp(1)**2+45)+1)*exp(x*ln(x/exp(x))**2+2*x*exp(5*exp(1)**2+45)*ln(x/exp(x))+x*exp(5*exp(1)**2+45)**2+x),x)

Sympy 1.10.1 under Python 3.10.4 output

\[ \text {Exception raised: SystemError} \]

Sympy 1.8 under Python 3.8.8 output

\[ e^{x \log {\left (x e^{- x} \right )}^{2} + 2 x e^{5 e^{2} + 45} \log {\left (x e^{- x} \right )} + x + x e^{10 e^{2} + 90}} \]