\[ \int \frac {e^{-x+x^{\frac {e^3+4 x}{x}}} \left (x^2+x^{\frac {e^3+4 x}{x}} \left (-e^3-4 x+e^3 \log (x)\right )\right )}{x^2} \, dx \]
Optimal antiderivative \[ -{\mathrm e}^{{\mathrm e}^{\frac {\left ({\mathrm e}^{3}+4 x \right ) \ln \left (x \right )}{x}}-x} \]
command
integrate(((log(x)*exp(3)-exp(3)-4*x)*exp((exp(3)+4*x)*log(x)/x)+x^2)*exp(exp((exp(3)+4*x)*log(x)/x)-x)/x^2,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
\[ -e^{\left (x^{\frac {e^{3}}{x} + 4} - x\right )} \]