\[ \int \frac {-3 e^3 x^2+3 x^3+e^{-2-2 x} \left (-18 e^3+18 x\right )+e^{-1-x} \left (-15 e^3 x+12 x^2-3 x^3\right )+\left (e^{-2-2 x} \left (-18+18 e^3\right )-3 x^2+3 e^3 x^2+e^{-1-x} \left (-12 x+15 e^3 x+3 x^2\right )\right ) \log (x)+\left (18 e^{-2-2 x}+15 e^{-1-x} x+3 x^2+\left (-18 e^{-2-2 x}-15 e^{-1-x} x-3 x^2\right ) \log (x)\right ) \log \left (\frac {3 e^{-1-x} x+x^2}{2 e^{-1-x}+x}\right )}{6 e^{4-2 x} x^2+5 e^{5-x} x^3+e^6 x^4+\left (-12 e^{1-2 x} x^2-10 e^{2-x} x^3-2 e^3 x^4\right ) \log \left (\frac {3 e^{-1-x} x+x^2}{2 e^{-1-x}+x}\right )+\left (6 e^{-2-2 x} x^2+5 e^{-1-x} x^3+x^4\right ) \log ^2\left (\frac {3 e^{-1-x} x+x^2}{2 e^{-1-x}+x}\right )} \, dx \]
Optimal antiderivative \[ \frac {3 \ln \left (x \right )-3 x}{\left (\ln \left (\frac {x}{2+x \,{\mathrm e}^{1+x}}+x \right )-{\mathrm e}^{3}\right ) x} \]
command
integrate((((-18*exp(-1-x)^2-15*x*exp(-1-x)-3*x^2)*log(x)+18*exp(-1-x)^2+15*x*exp(-1-x)+3*x^2)*log((3*x*exp(-1-x)+x^2)/(2*exp(-1-x)+x))+((18*exp(3)-18)*exp(-1-x)^2+(15*x*exp(3)+3*x^2-12*x)*exp(-1-x)+3*x^2*exp(3)-3*x^2)*log(x)+(-18*exp(3)+18*x)*exp(-1-x)^2+(-15*x*exp(3)-3*x^3+12*x^2)*exp(-1-x)-3*x^2*exp(3)+3*x^3)/((6*x^2*exp(-1-x)^2+5*x^3*exp(-1-x)+x^4)*log((3*x*exp(-1-x)+x^2)/(2*exp(-1-x)+x))^2+(-12*x^2*exp(3)*exp(-1-x)^2-10*x^3*exp(3)*exp(-1-x)-2*x^4*exp(3))*log((3*x*exp(-1-x)+x^2)/(2*exp(-1-x)+x))+6*x^2*exp(3)^2*exp(-1-x)^2+5*x^3*exp(3)^2*exp(-1-x)+x^4*exp(3)^2),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \text {output too large to display} \]
Giac 1.7.0 via sagemath 9.3 output \[ \text {Timed out} \]_______________________________________________________