\[ \int \frac {6 x+3 x^2+e^4 \left (6 x+3 x^2\right )+\left (6 x+3 x^2\right ) \log (3)+\left (-170-414 x-241 x^2-53 x^3-4 x^4+e^4 \left (-170-244 x-82 x^2-8 x^3\right )+\left (-170-244 x-82 x^2-8 x^3\right ) \log (3)\right ) \log \left (\frac {17+4 x}{5+x}\right )}{\left (170 x+159 x^2+45 x^3+4 x^4\right ) \log \left (\frac {17+4 x}{5+x}\right )} \, dx \]
Optimal antiderivative \[ \left (1+{\mathrm e}^{4}+\ln \! \left (3\right )\right ) \ln \! \left (\frac {5 \ln \! \left (4-\frac {3}{5+x}\right )}{x \left (2+x \right )}\right )-x \]
command
Int[(6*x + 3*x^2 + E^4*(6*x + 3*x^2) + (6*x + 3*x^2)*Log[3] + (-170 - 414*x - 241*x^2 - 53*x^3 - 4*x^4 + E^4*(-170 - 244*x - 82*x^2 - 8*x^3) + (-170 - 244*x - 82*x^2 - 8*x^3)*Log[3])*Log[(17 + 4*x)/(5 + x)])/((170*x + 159*x^2 + 45*x^3 + 4*x^4)*Log[(17 + 4*x)/(5 + x)]),x]
Rubi 4.17.3 under Mathematica 13.3.1 output
\[ \int \frac {6 x+3 x^2+e^4 \left (6 x+3 x^2\right )+\left (6 x+3 x^2\right ) \log (3)+\left (-170-414 x-241 x^2-53 x^3-4 x^4+e^4 \left (-170-244 x-82 x^2-8 x^3\right )+\left (-170-244 x-82 x^2-8 x^3\right ) \log (3)\right ) \log \left (\frac {17+4 x}{5+x}\right )}{\left (170 x+159 x^2+45 x^3+4 x^4\right ) \log \left (\frac {17+4 x}{5+x}\right )} \, dx \]
Rubi 4.16.1 under Mathematica 13.3.1 output
\[ -x-\frac {1}{2} \left (2+2 e^4+\log (9)\right ) \log (x)-\frac {1}{2} \left (2+2 e^4+\log (9)\right ) \log (x+2)+\left (1+e^4+\log (3)\right ) \log \left (\log \left (\frac {4 x+17}{x+5}\right )\right ) \]