\[ \int \frac {36-e^{3 x} x+12 \log (2)+\log ^2(2)+e^{2 x} (1-12 x-2 x \log (2))+e^x \left (12-32 x+(2-12 x) \log (2)-x \log ^2(2)\right )+\left (72+2 e^{2 x}+24 \log (2)+2 \log ^2(2)+e^x (24+4 \log (2))\right ) \log (x)}{36 x+e^{2 x} x+12 x \log (2)+x \log ^2(2)+e^x (12 x+2 x \log (2))} \, dx \]
Optimal antiderivative \[ \ln \! \left (2 x \right )-{\mathrm e}^{x}-\frac {4}{6+\ln \! \left (2\right )+{\mathrm e}^{x}}+\ln \! \left (x \right )^{2} \]
command
Integrate[(36 - E^(3*x)*x + 12*Log[2] + Log[2]^2 + E^(2*x)*(1 - 12*x - 2*x*Log[2]) + E^x*(12 - 32*x + (2 - 12*x)*Log[2] - x*Log[2]^2) + (72 + 2*E^(2*x) + 24*Log[2] + 2*Log[2]^2 + E^x*(24 + 4*Log[2]))*Log[x])/(36*x + E^(2*x)*x + 12*x*Log[2] + x*Log[2]^2 + E^x*(12*x + 2*x*Log[2])),x]
Mathematica 13.1 output
\[ \int \frac {36-e^{3 x} x+12 \log (2)+\log ^2(2)+e^{2 x} (1-12 x-2 x \log (2))+e^x \left (12-32 x+(2-12 x) \log (2)-x \log ^2(2)\right )+\left (72+2 e^{2 x}+24 \log (2)+2 \log ^2(2)+e^x (24+4 \log (2))\right ) \log (x)}{36 x+e^{2 x} x+12 x \log (2)+x \log ^2(2)+e^x (12 x+2 x \log (2))} \, dx \]
Mathematica 12.3 output
\[ -e^x-\frac {24-2 \log ^3(2)+\log ^2(2) (-12+\log (4))+\log (16)-\log (2) \log (4096)+\log (4) \log (4096)}{(6+\log (2)) \left (6+e^x+\log (2)\right )}+\log (x)+\log ^2(x) \]