\[ \int \frac {-15+29 x+4 x^2-4 x^3+\left (-3+7 x-2 x^2\right ) \log (5)+e^{2 x^2} \left (-25 x+55 x^2-128 x^3+12 x^4+8 x^5+\left (-5 x+12 x^2-28 x^3+8 x^4\right ) \log (5)\right )+\left (25 x+5 x^2+5 x \log (5)\right ) \log \left (5 x+x^2+x \log (5)\right )}{45 x-21 x^2-x^3+x^4+\left (9 x-6 x^2+x^3\right ) \log (5)} \, dx \]
Optimal antiderivative \[ \frac {\left (-1+2 x \right ) \left (\ln \! \left (x \left (x +\ln \! \left (5\right )+5\right )\right )-{\mathrm e}^{2 x^{2}}\right )}{-x +3} \]
command
Int[(-15 + 29*x + 4*x^2 - 4*x^3 + (-3 + 7*x - 2*x^2)*Log[5] + E^(2*x^2)*(-25*x + 55*x^2 - 128*x^3 + 12*x^4 + 8*x^5 + (-5*x + 12*x^2 - 28*x^3 + 8*x^4)*Log[5]) + (25*x + 5*x^2 + 5*x*Log[5])*Log[5*x + x^2 + x*Log[5]])/(45*x - 21*x^2 - x^3 + x^4 + (9*x - 6*x^2 + x^3)*Log[5]),x]
Rubi 4.17.3 under Mathematica 13.3.1 output
\[ \int \frac {-15+29 x+4 x^2-4 x^3+\left (-3+7 x-2 x^2\right ) \log (5)+e^{2 x^2} \left (-25 x+55 x^2-128 x^3+12 x^4+8 x^5+\left (-5 x+12 x^2-28 x^3+8 x^4\right ) \log (5)\right )+\left (25 x+5 x^2+5 x \log (5)\right ) \log \left (5 x+x^2+x \log (5)\right )}{45 x-21 x^2-x^3+x^4+\left (9 x-6 x^2+x^3\right ) \log (5)} \, dx \]
Rubi 4.16.1 under Mathematica 13.3.1 output
\[ \text {output too large to display} \]