\[ \int \frac {e^{-1+e^{\frac {1}{x}}-x} \left (-e^{\frac {1}{x}}-x^2\right )}{x^2} \, dx \]
Optimal antiderivative \[ \frac {{\mathrm e}^{\ln \left (x^{2}\right )+{\mathrm e}^{\frac {1}{x}}-x -1}}{x^{2}} \]
command
integrate((-exp(1/x)-x^2)*exp(log(x^2)+exp(1/x)-x-1)/x^4,x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \text {could not integrate} \]
Giac 1.7.0 via sagemath 9.3 output
\[ e^{\left (-x + e^{\frac {1}{x}} - 1\right )} \]