\[ \int \frac {(80-20 x) \log \left (\frac {1}{3} e^{-16+8 x-x^2} \left (-1-15 e^{16-8 x+x^2}\right )\right )}{3+45 e^{16-8 x+x^2}} \, dx \]
Optimal antiderivative \[ \frac {5 \ln \! \left (-\frac {{\mathrm e}^{-\left (-x +4\right )^{2}}}{3}-5\right )^{2}}{3} \]
command
Int[((80 - 20*x)*Log[(E^(-16 + 8*x - x^2)*(-1 - 15*E^(16 - 8*x + x^2)))/3])/(3 + 45*E^(16 - 8*x + x^2)),x]
Rubi 4.17.3 under Mathematica 13.3.1 output
\[ \int \frac {(80-20 x) \log \left (\frac {1}{3} e^{-16+8 x-x^2} \left (-1-15 e^{16-8 x+x^2}\right )\right )}{3+45 e^{16-8 x+x^2}} \, dx \]
Rubi 4.16.1 under Mathematica 13.3.1 output
\[ \frac {5}{3} \log ^2\left (-\frac {1}{3} e^{-(4-x)^2}-5\right ) \]