\[ \int \frac {-700+e^{\frac {1}{25} \left (-125+145 x-16 x^2+25 x \log (3 x)\right )} \left (25-170 x+32 x^2-25 x \log (3 x)\right )}{19600-1400 e^{\frac {1}{25} \left (-125+145 x-16 x^2+25 x \log (3 x)\right )}+25 e^{\frac {2}{25} \left (-125+145 x-16 x^2+25 x \log (3 x)\right )}} \, dx \]
Optimal antiderivative \[ \frac {x}{{\mathrm e}^{x +4+x \ln \left (3 x \right )-\left (\frac {4 x}{5}-3\right )^{2}}-28} \]
command
Integrate[(-700 + E^((-125 + 145*x - 16*x^2 + 25*x*Log[3*x])/25)*(25 - 170*x + 32*x^2 - 25*x*Log[3*x]))/(19600 - 1400*E^((-125 + 145*x - 16*x^2 + 25*x*Log[3*x])/25) + 25*E^((2*(-125 + 145*x - 16*x^2 + 25*x*Log[3*x]))/25)),x]
Mathematica 13.1 output
\[ \int \frac {-700+e^{\frac {1}{25} \left (-125+145 x-16 x^2+25 x \log (3 x)\right )} \left (25-170 x+32 x^2-25 x \log (3 x)\right )}{19600-1400 e^{\frac {1}{25} \left (-125+145 x-16 x^2+25 x \log (3 x)\right )}+25 e^{\frac {2}{25} \left (-125+145 x-16 x^2+25 x \log (3 x)\right )}} \, dx \]
Mathematica 12.3 output
\[ -\frac {e^{5+\frac {16 x^2}{25}} x}{28 e^{5+\frac {16 x^2}{25}}-3^x e^{29 x/5} x^x} \]