\[ \int \frac {-3 x-x^2+e^{5+x} \left (-9 x-3 x^2\right )+\left (3 x+2 x^2+e^{5+x} (9+6 x)\right ) \log \left (\frac {\log (5)}{3 e^{5+x}+x}\right )}{45 e^{5+x}+15 x} \, dx \]
Optimal antiderivative \[ 2+x \ln \left (\frac {\ln \left (5\right )}{3 \,{\mathrm e}^{5+x}+x}\right ) \left (\frac {1}{5}+\frac {x}{15}\right ) \]
command
Int[(-3*x - x^2 + E^(5 + x)*(-9*x - 3*x^2) + (3*x + 2*x^2 + E^(5 + x)*(9 + 6*x))*Log[Log[5]/(3*E^(5 + x) + x)])/(45*E^(5 + x) + 15*x),x]
Rubi 4.17.3 under Mathematica 13.3.1 output
\[ \frac {1}{15} x^2 \log \left (\frac {\log (5)}{x+3 e^{x+5}}\right )+\frac {1}{5} x \log \left (\frac {\log (5)}{x+3 e^{x+5}}\right ) \]
Rubi 4.16.1 under Mathematica 13.3.1 output
\[ \int \frac {-3 x-x^2+e^{5+x} \left (-9 x-3 x^2\right )+\left (3 x+2 x^2+e^{5+x} (9+6 x)\right ) \log \left (\frac {\log (5)}{3 e^{5+x}+x}\right )}{45 e^{5+x}+15 x} \, dx \]________________________________________________________________________________________