\[ \int \frac {e^{\frac {45+\left (25 x^2+10 x^3+x^4\right ) \log \left (\frac {19+x}{3}\right )}{x^2 \log \left (\frac {19+x}{3}\right )}} \left (-45 x+(-1710-90 x) \log \left (\frac {19+x}{3}\right )+\left (190 x^3+48 x^4+2 x^5\right ) \log ^2\left (\frac {19+x}{3}\right )\right )}{\left (19 x^3+x^4\right ) \log ^2\left (\frac {19+x}{3}\right )} \, dx \]
Optimal antiderivative \[ {\mathrm e}^{\left (5+x \right )^{2}+\frac {45}{x^{2} \ln \left (\frac {x}{3}+\frac {19}{3}\right )}} \]
command
Int[(E^((45 + (25*x^2 + 10*x^3 + x^4)*Log[(19 + x)/3])/(x^2*Log[(19 + x)/3]))*(-45*x + (-1710 - 90*x)*Log[(19 + x)/3] + (190*x^3 + 48*x^4 + 2*x^5)*Log[(19 + x)/3]^2))/((19*x^3 + x^4)*Log[(19 + x)/3]^2),x]
Rubi 4.17.3 under Mathematica 13.3.1 output
\[ \int \frac {\exp \left (\frac {45+\left (25 x^2+10 x^3+x^4\right ) \log \left (\frac {19+x}{3}\right )}{x^2 \log \left (\frac {19+x}{3}\right )}\right ) \left (-45 x+(-1710-90 x) \log \left (\frac {19+x}{3}\right )+\left (190 x^3+48 x^4+2 x^5\right ) \log ^2\left (\frac {19+x}{3}\right )\right )}{\left (19 x^3+x^4\right ) \log ^2\left (\frac {19+x}{3}\right )} \, dx \]
Rubi 4.16.1 under Mathematica 13.3.1 output
\[ e^{\frac {45}{x^2 \log \left (\frac {x+19}{3}\right )}+(x+5)^2} \]