\[ \int \frac {-e^{1+x} x^2+2 e^{10+e^2+e^{8-x^2}-x^2} x^3+\left (2 e^{2+e^2+e^{8-x^2}} x+2 e^{1+x} x\right ) \log \left (e^{2+e^2+e^{8-x^2}}+e^{1+x}\right )}{\left (e^{2+e^2+e^{8-x^2}}+e^{1+x}\right ) \log ^2\left (e^{2+e^2+e^{8-x^2}}+e^{1+x}\right )} \, dx \]
Optimal antiderivative \[ \frac {x^{2}}{\ln \left ({\mathrm e}^{{\mathrm e}^{-x^{2}+8}+{\mathrm e}^{2}+2}+{\mathrm e}^{1+x}\right )} \]
command
integrate(((2*x*exp(exp(-x^2+8)+exp(2)+2)+2*x*exp(1+x))*log(exp(exp(-x^2+8)+exp(2)+2)+exp(1+x))+2*x^3*exp(-x^2+8)*exp(exp(-x^2+8)+exp(2)+2)-x^2*exp(1+x))/(exp(exp(-x^2+8)+exp(2)+2)+exp(1+x))/log(exp(exp(-x^2+8)+exp(2)+2)+exp(1+x))^2,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 \[ \int \frac {2 \, x^{3} e^{\left (-x^{2} + e^{2} + e^{\left (-x^{2} + 8\right )} + 10\right )} - x^{2} e^{\left (x + 1\right )} + 2 \, {\left (x e^{\left (x + 1\right )} + x e^{\left (e^{2} + e^{\left (-x^{2} + 8\right )} + 2\right )}\right )} \log \left (e^{\left (x + 1\right )} + e^{\left (e^{2} + e^{\left (-x^{2} + 8\right )} + 2\right )}\right )}{{\left (e^{\left (x + 1\right )} + e^{\left (e^{2} + e^{\left (-x^{2} + 8\right )} + 2\right )}\right )} \log \left (e^{\left (x + 1\right )} + e^{\left (e^{2} + e^{\left (-x^{2} + 8\right )} + 2\right )}\right )^{2}}\,{d x} \]_______________________________________________________