\[ \int \frac {12 x^8-8 x^9-12 x^{10}+e^{10} \left (6 x^3-4 x^4-6 x^5\right )+\left (12 x^8-4 x^9-4 x^{10}+e^{10} \left (-24 x^3+8 x^4+8 x^5\right )\right ) \log \left (3 x-x^2-x^3\right )}{\left (e^{24} \left (-3+x+x^2\right )+e^{14} \left (-12 x^5+4 x^6+4 x^7\right )+e^4 \left (-12 x^{10}+4 x^{11}+4 x^{12}\right )\right ) \log ^2\left (3 x-x^2-x^3\right )} \, dx \]
Optimal antiderivative \[ \frac {2 \,{\mathrm e}^{-4}}{\left (\frac {{\mathrm e}^{10}}{x^{4}}+2 x \right ) \ln \left (x \left (-x^{2}-x +3\right )\right )} \]
command
integrate((((8*x^5+8*x^4-24*x^3)*exp(5)^2-4*x^10-4*x^9+12*x^8)*log(-x^3-x^2+3*x)+(-6*x^5-4*x^4+6*x^3)*exp(5)^2-12*x^10-8*x^9+12*x^8)/((x^2+x-3)*exp(4)*exp(5)^4+(4*x^7+4*x^6-12*x^5)*exp(4)*exp(5)^2+(4*x^12+4*x^11-12*x^10)*exp(4))/log(-x^3-x^2+3*x)^2,x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \frac {2 \, x^{4}}{2 \, x^{5} e^{4} \log \left (-x^{3} - x^{2} + 3 \, x\right ) + e^{14} \log \left (-x^{3} - x^{2} + 3 \, x\right )} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Timed out} \]________________________________________________________________________________________