\[ \int \frac {e^{-x} \left (e^{10 e^{-x}} \left (-2 e^x-10 x\right )-e^{e^x+2 x} x^3+e^{5 e^{-x}} \left (4 e^x+10 x\right )+e^x \left (-6-x^3\right )\right )}{x^3} \, dx \]
Optimal antiderivative \[ 2+\frac {\left (1-{\mathrm e}^{5 \,{\mathrm e}^{-x}}\right )^{2}+2}{x^{2}}-x -{\mathrm e}^{{\mathrm e}^{x}} \]
command
integrate((-x^3*exp(x)^2*exp(exp(x))+(-2*exp(x)-10*x)*exp(5/exp(x))^2+(4*exp(x)+10*x)*exp(5/exp(x))+(-x^3-6)*exp(x))/exp(x)/x^3,x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ -\frac {{\left (x^{3} e^{x} + x^{2} e^{\left (x + e^{x}\right )} - e^{\left (x + 10 \, e^{\left (-x\right )}\right )} + 2 \, e^{\left (x + 5 \, e^{\left (-x\right )}\right )} - 3 \, e^{x}\right )} e^{\left (-x\right )}}{x^{2}} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \int -\frac {{\left (x^{3} e^{\left (2 \, x + e^{x}\right )} + {\left (x^{3} + 6\right )} e^{x} + 2 \, {\left (5 \, x + e^{x}\right )} e^{\left (10 \, e^{\left (-x\right )}\right )} - 2 \, {\left (5 \, x + 2 \, e^{x}\right )} e^{\left (5 \, e^{\left (-x\right )}\right )}\right )} e^{\left (-x\right )}}{x^{3}}\,{d x} \]________________________________________________________________________________________