\[ \int \frac {1}{3} e^{\frac {1}{3} \left (e^{31/5} x^2+e^{\frac {6}{5}+x} x^2\right )} \left (2 e^{31/5} x+e^{\frac {6}{5}+x} \left (2 x+x^2\right )\right ) \, dx \]
Optimal antiderivative \[ {\mathrm e}^{\frac {\left ({\mathrm e}^{5}+{\mathrm e}^{x}\right ) {\mathrm e}^{\frac {6}{5}} x^{2}}{3}} \]
command
integrate(1/3*((x^2+2*x)*exp(3/5)^2*exp(x)+2*x*exp(3/5)^2*exp(5/2)^2)*exp(1/3*x^2*exp(3/5)^2*exp(x)+1/3*x^2*exp(3/5)^2*exp(5/2)^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
\[ e^{\left (\frac {1}{3} \, x^{2} e^{\frac {31}{5}} + \frac {1}{3} \, x^{2} e^{\left (x + \frac {6}{5}\right )}\right )} \]