\[ \int \frac {-16-32 x-16 x^2+e^{2 x+e^{2 x} \left (3 e^{\frac {2 x}{2+2 x}} x+6 e^{\frac {x}{2+2 x}} x^2+3 x^3\right )} \left (-108 x^2-288 x^3-252 x^4-72 x^5+e^{\frac {2 x}{2+2 x}} \left (-36-180 x-180 x^2-72 x^3\right )+e^{\frac {x}{2+2 x}} \left (-144 x-468 x^2-432 x^3-144 x^4\right )\right )}{16 x^2+32 x^3+16 x^4+e^{2 e^{2 x} \left (3 e^{\frac {2 x}{2+2 x}} x+6 e^{\frac {x}{2+2 x}} x^2+3 x^3\right )} \left (9+18 x+9 x^2\right )+e^{e^{2 x} \left (3 e^{\frac {2 x}{2+2 x}} x+6 e^{\frac {x}{2+2 x}} x^2+3 x^3\right )} \left (24 x+48 x^2+24 x^3\right )} \, dx \]
Optimal antiderivative \[ \frac {4}{4 x +3 \,{\mathrm e}^{3 \,{\mathrm e}^{2 x} \left (x +{\mathrm e}^{\frac {x}{2 x +2}}\right )^{2} x}} \]
command
integrate((((-72*x^3-180*x^2-180*x-36)*exp(x/(2+2*x))^2+(-144*x^4-432*x^3-468*x^2-144*x)*exp(x/(2+2*x))-72*x^5-252*x^4-288*x^3-108*x^2)*exp(x)^2*exp((3*x*exp(x/(2+2*x))^2+6*x^2*exp(x/(2+2*x))+3*x^3)*exp(x)^2)-16*x^2-32*x-16)/((9*x^2+18*x+9)*exp((3*x*exp(x/(2+2*x))^2+6*x^2*exp(x/(2+2*x))+3*x^3)*exp(x)^2)^2+(24*x^3+48*x^2+24*x)*exp((3*x*exp(x/(2+2*x))^2+6*x^2*exp(x/(2+2*x))+3*x^3)*exp(x)^2)+16*x^4+32*x^3+16*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 \[ \text {Timed out} \]_______________________________________________________