\[ \int e^{-e^{1+e^{32}-2 x+x^2+e^{16} (-2+2 x)}} \left (-3 x+e^{1+e^{32}-2 x+x^2+e^{16} (-2+2 x)} \left (-4 x^2+4 e^{16} x^2+4 x^3\right )+\left (2 x+e^{1+e^{32}-2 x+x^2+e^{16} (-2+2 x)} \left (2 x^2-2 e^{16} x^2-2 x^3\right )\right ) \log (x)\right ) \, dx \]
Optimal antiderivative \[ \left (\ln \! \left (x \right )-2\right ) x^{2} {\mathrm e}^{-{\mathrm e}^{\left ({\mathrm e}^{16}+x -1\right )^{2}}} \]
command
integrate((((-2*x^2*exp(16)-2*x^3+2*x^2)*exp(exp(16)^2+(-2+2*x)*exp(16)+x^2-2*x+1)+2*x)*log(x)+(4*x^2*exp(16)+4*x^3-4*x^2)*exp(exp(16)^2+(-2+2*x)*exp(16)+x^2-2*x+1)-3*x)/exp(exp(exp(16)^2+(-2+2*x)*exp(16)+x^2-2*x+1)),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
\[ {\left (x^{2} e^{\left (x^{2} + 2 \, x e^{16} - 2 \, x + e^{32} - 2 \, e^{16} - e^{\left (x^{2} + 2 \, x e^{16} - 2 \, x + e^{32} - 2 \, e^{16} + 1\right )} + 1\right )} \log \left (x\right ) - 2 \, x^{2} e^{\left (x^{2} + 2 \, x e^{16} - 2 \, x + e^{32} - 2 \, e^{16} - e^{\left (x^{2} + 2 \, x e^{16} - 2 \, x + e^{32} - 2 \, e^{16} + 1\right )} + 1\right )}\right )} e^{\left (-x^{2} - 2 \, x e^{16} + 2 \, x - e^{32} + 2 \, e^{16} - 1\right )} \]