\[ \int \frac {e^{\frac {2}{3} \left (5 e^{9+6 x+x^2}-3 x-3 x^2 \log \left (e^2+2 x\right )\right )} \left (-6 e^2-12 x-12 x^2+e^{9+6 x+x^2} \left (120 x+40 x^2+e^2 (60+20 x)\right )+\left (-12 e^2 x-24 x^2\right ) \log \left (e^2+2 x\right )\right )}{3 e^2+6 x} \, dx \]
Optimal antiderivative \[ {\mathrm e}^{\frac {10 \,{\mathrm e}^{\left (3+x \right )^{2}}}{3}-2 x -2 x^{2} \ln \left ({\mathrm e}^{2}+2 x \right )} \]
command
integrate(((-12*exp(2)*x-24*x^2)*log(exp(2)+2*x)+((20*x+60)*exp(2)+40*x^2+120*x)*exp(x^2+6*x+9)-6*exp(2)-12*x^2-12*x)*exp(-x^2*log(exp(2)+2*x)+5/3*exp(x^2+6*x+9)-x)^2/(3*exp(2)+6*x),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
\[ e^{\left (-2 \, x^{2} \log \left (2 \, x + e^{2}\right ) - 2 \, x + \frac {10}{3} \, e^{\left (x^{2} + 6 \, x + 9\right )}\right )} \]