\[ \int \frac {180 x^3-120 x^4 \log (3)+e^{2 x} \left (200 x-600 x^2+200 x^3 \log (3)\right )+e^x \left (360 x^2-120 x^3-180 x^4+\left (-200 x^3+60 x^4+60 x^5\right ) \log (3)\right )+\left (-60 x^2+180 x^3-60 x^4 \log (3)+e^x \left (-200 x+700 x^2-300 x^3+\left (-200 x^3+100 x^4\right ) \log (3)\right )\right ) \log \left (1-3 x+x^2 \log (3)\right )}{9 x^2-27 x^3+9 x^4 \log (3)+e^{2 x} \left (25-75 x+25 x^2 \log (3)\right )+e^x \left (30 x-90 x^2+30 x^3 \log (3)\right )} \, dx \]
Optimal antiderivative \[ \frac {4 \left ({\mathrm e}^{x}-\ln \! \left (x \left (x \ln \! \left (3\right )-3\right )+1\right )\right ) x}{\frac {{\mathrm e}^{x}}{x}+\frac {3}{5}} \]
command
Integrate[(180*x^3 - 120*x^4*Log[3] + E^(2*x)*(200*x - 600*x^2 + 200*x^3*Log[3]) + E^x*(360*x^2 - 120*x^3 - 180*x^4 + (-200*x^3 + 60*x^4 + 60*x^5)*Log[3]) + (-60*x^2 + 180*x^3 - 60*x^4*Log[3] + E^x*(-200*x + 700*x^2 - 300*x^3 + (-200*x^3 + 100*x^4)*Log[3]))*Log[1 - 3*x + x^2*Log[3]])/(9*x^2 - 27*x^3 + 9*x^4*Log[3] + E^(2*x)*(25 - 75*x + 25*x^2*Log[3]) + E^x*(30*x - 90*x^2 + 30*x^3*Log[3])),x]
Mathematica 13.1 output
\[ \int \frac {180 x^3-120 x^4 \log (3)+e^{2 x} \left (200 x-600 x^2+200 x^3 \log (3)\right )+e^x \left (360 x^2-120 x^3-180 x^4+\left (-200 x^3+60 x^4+60 x^5\right ) \log (3)\right )+\left (-60 x^2+180 x^3-60 x^4 \log (3)+e^x \left (-200 x+700 x^2-300 x^3+\left (-200 x^3+100 x^4\right ) \log (3)\right )\right ) \log \left (1-3 x+x^2 \log (3)\right )}{9 x^2-27 x^3+9 x^4 \log (3)+e^{2 x} \left (25-75 x+25 x^2 \log (3)\right )+e^x \left (30 x-90 x^2+30 x^3 \log (3)\right )} \, dx \]
Mathematica 12.3 output
\[ \frac {4 x^2 \left (5-15 x+x^2 \log (243)\right ) \left (e^x-\log \left (1-3 x+x^2 \log (3)\right )\right )}{\left (5 e^x+3 x\right ) \left (1-3 x+x^2 \log (3)\right )} \]