\[ \int \frac {16 x^2+e^x \left (8 x+8 x^2\right )+\left (6 x+e^{2 x} x+2 x^3+e^x \left (3+3 x^2\right )\right ) \log \left (3+e^x x+x^2\right )+\left (64 x+e^x (32+32 x)+\left (24+8 e^x x+8 x^2\right ) \log \left (3+e^x x+x^2\right )\right ) \log \left ((-1+\log (9)) \log \left (3+e^x x+x^2\right )\right )}{\left (3+e^x x+x^2\right ) \log \left (3+e^x x+x^2\right )} \, dx \]
Optimal antiderivative \[ {\mathrm e}^{x}+\left (4 \ln \! \left (\ln \! \left (3+\left (x +{\mathrm e}^{x}\right ) x \right ) \left (2 \ln \! \left (3\right )-1\right )\right )+x \right )^{2} \]
command
integrate((((8*exp(x)*x+8*x^2+24)*log(exp(x)*x+x^2+3)+(32*x+32)*exp(x)+64*x)*log((2*log(3)-1)*log(exp(x)*x+x^2+3))+(x*exp(x)^2+(3*x^2+3)*exp(x)+2*x^3+6*x)*log(exp(x)*x+x^2+3)+(8*x^2+8*x)*exp(x)+16*x^2)/(exp(x)*x+x^2+3)/log(exp(x)*x+x^2+3),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \text {Timed out} \]
Giac 1.7.0 via sagemath 9.3 output
\[ x^{2} + 8 \, x \log \left (2 \, \log \left (3\right ) - 1\right ) + 8 \, x \log \left (\log \left (x^{2} + x e^{x} + 3\right )\right ) + 32 \, \log \left (2 \, \log \left (3\right ) - 1\right ) \log \left (\log \left (x^{2} + x e^{x} + 3\right )\right ) + 16 \, \log \left (\log \left (x^{2} + x e^{x} + 3\right )\right )^{2} + e^{x} \]