\[ \int \frac {e^{-x} \left (e^{2 e^{-x} x} \left (2500 x^2-2500 x^3\right )+e^x \left (1250 e^5+300 x^2+4 x^3\right )+e^{e^{-x} x} \left (-7500 x^2-100 e^x x^2+7400 x^3+100 x^4\right )\right )}{625 x^2} \, dx \]
Optimal antiderivative \[ \frac {2 \left ({\mathrm e}^{x \,{\mathrm e}^{-x}}-3-\frac {x}{25}\right )^{2} x -2 \,{\mathrm e}^{5}}{x} \]
command
integrate(1/625*((-2500*x^3+2500*x^2)*exp(x/exp(x))^2+(-100*exp(x)*x^2+100*x^4+7400*x^3-7500*x^2)*exp(x/exp(x))+(1250*exp(5)+4*x^3+300*x^2)*exp(x))/exp(x)/x^2,x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \frac {2 \, {\left (x^{3} e^{\left (-x\right )} - 50 \, x^{2} e^{\left (x e^{\left (-x\right )} - x\right )} + 150 \, x^{2} e^{\left (-x\right )} + 625 \, x e^{\left (2 \, x e^{\left (-x\right )} - x\right )} - 3750 \, x e^{\left (x e^{\left (-x\right )} - x\right )} - 625 \, e^{\left (-x + 5\right )}\right )} e^{x}}{625 \, x} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \int -\frac {2 \, {\left (1250 \, {\left (x^{3} - x^{2}\right )} e^{\left (2 \, x e^{\left (-x\right )}\right )} - 50 \, {\left (x^{4} + 74 \, x^{3} - x^{2} e^{x} - 75 \, x^{2}\right )} e^{\left (x e^{\left (-x\right )}\right )} - {\left (2 \, x^{3} + 150 \, x^{2} + 625 \, e^{5}\right )} e^{x}\right )} e^{\left (-x\right )}}{625 \, x^{2}}\,{d x} \]________________________________________________________________________________________