\[ \int \frac {1}{5} e^{-6+\frac {4 e^{2 x} x+e^{3+x} \left (20 x+4 x^2\right )+e^6 \left (25 x+10 x^2+x^3\right )}{5 e^6}} \left (e^{2 x} (8+16 x)+e^6 \left (50+40 x+6 x^2\right )+e^{3+x} \left (40+56 x+8 x^2\right )\right ) \, dx \]
Optimal antiderivative \[ 2 \,{\mathrm e}^{\frac {x \left (5+2 \,{\mathrm e}^{x} {\mathrm e}^{-3}+x \right )^{2}}{5}} \]
command
integrate(1/5*((16*x+8)*exp(x)^2+(8*x^2+56*x+40)*exp(3)*exp(x)+(6*x^2+40*x+50)*exp(3)^2)*exp(1/5*(4*x*exp(x)^2+(4*x^2+20*x)*exp(3)*exp(x)+(x^3+10*x^2+25*x)*exp(3)^2)/exp(3)^2)/exp(3)^2,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
\[ 2 \, e^{\left (\frac {1}{5} \, x^{3} + \frac {4}{5} \, x^{2} e^{\left (x - 3\right )} + 2 \, x^{2} + \frac {4}{5} \, x e^{\left (2 \, x - 6\right )} + 4 \, x e^{\left (x - 3\right )} + 5 \, x\right )} \]