100.50 Problem number 2020

\[ \int e^{-e-x} \left (e^{7+x}+e^{e^{-x} x} \left (e^{2+x}+e^e (1-x)+e^2 \left (x-x^2\right )\right )\right ) \, dx \]

Optimal antiderivative \[ \left (1+{\mathrm e}^{2} {\mathrm e}^{-{\mathrm e}} x \right ) \left ({\mathrm e}^{x \,{\mathrm e}^{-x}}+{\mathrm e}^{5}\right ) \]

command

integrate((((1-x)*exp(exp(1))+exp(1)^2*exp(x)+(-x^2+x)*exp(1)^2)*exp(x/exp(x))+exp(1)^2*exp(5)*exp(x))/exp(x)/exp(exp(1)),x, algorithm="giac")

Giac 1.9.0-11 via sagemath 9.6 output

\[ {\left (x e^{\left (x e^{\left (-x\right )} - x - e + 2\right )} + x e^{\left (-x - e + 7\right )} + e^{\left (x e^{\left (-x\right )} - x\right )}\right )} e^{x} \]

Giac 1.7.0 via sagemath 9.3 output

\[ \int -{\left ({\left ({\left (x^{2} - x\right )} e^{2} + {\left (x - 1\right )} e^{e} - e^{\left (x + 2\right )}\right )} e^{\left (x e^{\left (-x\right )}\right )} - e^{\left (x + 7\right )}\right )} e^{\left (-x - e\right )}\,{d x} \]________________________________________________________________________________________