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