43.22 Problem number 2888

\[ \int \frac {1}{3} \left (-5+e^{-9-x+e^5 x-e^x x} \left (-3+3 e^5+e^x (-3-3 x)\right )\right ) \, dx \]

Optimal antiderivative \[ 1-\frac {5 x}{3}+{\mathrm e}^{x \left ({\mathrm e}^{5}-{\mathrm e}^{x}\right )-x -9} \]

command

integrate(1/3*((-3*x-3)*exp(x)+3*exp(5)-3)*exp(-exp(x)*x+x*exp(5)-x-9)-5/3,x, algorithm="giac")

Giac 1.9.0-11 via sagemath 9.6 output

\[ \text {could not integrate} \]

Giac 1.7.0 via sagemath 9.3 output

\[ -\frac {5}{3} \, x + e^{\left (x e^{5} - x e^{x} - x - 9\right )} \]