\[ \int x^{35+609 x+2650 x^2+625 x^3+e^2 (4+x)} \left (72+1218 x+5300 x^2+1250 x^3+e^2 (8+2 x)+\left (1218 x+2 e^2 x+10600 x^2+3750 x^3\right ) \log (x)\right ) \, dx \]
Optimal antiderivative \[ 2 \,{\mathrm e}^{\left (\left (3+25 x \right )^{2}+{\mathrm e}^{2}\right ) \left (4+x \right ) \ln \left (x \right )} \]
command
integrate(((2*exp(2)*x+3750*x^3+10600*x^2+1218*x)*log(x)+(2*x+8)*exp(2)+1250*x^3+5300*x^2+1218*x+72)*exp(((4+x)*exp(2)+625*x^3+2650*x^2+609*x+36)*log(x))/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
\[ 2 \, e^{\left (625 \, x^{3} \log \left (x\right ) + 2650 \, x^{2} \log \left (x\right ) + x e^{2} \log \left (x\right ) + 609 \, x \log \left (x\right ) + 4 \, e^{2} \log \left (x\right ) + 36 \, \log \left (x\right )\right )} \]