\[ \int \frac {e^{5 x} \left (-45 x+15 x^2+e^x \left (15 x^2-5 x^3\right )\right )+\left (36-24 x+e^x \left (-12 x+8 x^2\right )\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right )+\left (-36 x+12 x^2+e^x \left (-12 x+4 x^2\right )\right ) \log \left (\frac {1}{3} \left (-3 x+x^2\right )\right )}{9 x-3 x^2+e^x \left (-3 x^2+x^3\right )} \, dx \]
Optimal antiderivative \[ 4 \ln \! \left (\frac {1}{3} x^{2}-x \right ) \ln \! \left (x -3 \,{\mathrm e}^{-x}\right )-{\mathrm e}^{5 x} \]
command
integrate((((8*x^2-12*x)*exp(x)-24*x+36)*log((exp(x)*x-3)/exp(x))+((4*x^2-12*x)*exp(x)+12*x^2-36*x)*log(1/3*x^2-x)+((-5*x^3+15*x^2)*exp(x)+15*x^2-45*x)*exp(5*x))/((x^3-3*x^2)*exp(x)-3*x^2+9*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
\[ 4 \, x \log \left (3\right ) - 4 \, \log \left (3\right ) \log \left (x e^{x} - 3\right ) - 4 \, x \log \left (x - 3\right ) + 4 \, \log \left (x e^{x} - 3\right ) \log \left (x - 3\right ) - 4 \, x \log \left (x\right ) + 4 \, \log \left (x e^{x} - 3\right ) \log \left (x\right ) - e^{\left (5 \, x\right )} \]