\[ \int \frac {e^{162-36 x+2 x^2} \left (-17 x^2+180 x^3-20 x^4+e^x \left (-24 x+350 x^2-40 x^3\right )\right )+e^{162-36 x+2 x^2} \left (3 x^2-36 x^3+4 x^4+e^x \left (4 x-70 x^2+8 x^3\right )\right ) \log (x)}{-125+75 \log (x)-15 \log ^2(x)+\log ^3(x)} \, dx \]
Optimal antiderivative \[ \frac {x^{2} \left (2 \,{\mathrm e}^{x}+x \right ) {\mathrm e}^{2 \left (x -9\right )^{2}}}{\left (\ln \! \left (x \right )-5\right )^{2}} \]
command
Int[(E^(162 - 36*x + 2*x^2)*(-17*x^2 + 180*x^3 - 20*x^4 + E^x*(-24*x + 350*x^2 - 40*x^3)) + E^(162 - 36*x + 2*x^2)*(3*x^2 - 36*x^3 + 4*x^4 + E^x*(4*x - 70*x^2 + 8*x^3))*Log[x])/(-125 + 75*Log[x] - 15*Log[x]^2 + Log[x]^3),x]
Rubi 4.17.3 under Mathematica 13.3.1 output
\[ \int \frac {e^{162-36 x+2 x^2} \left (-17 x^2+180 x^3-20 x^4+e^x \left (-24 x+350 x^2-40 x^3\right )\right )+e^{162-36 x+2 x^2} \left (3 x^2-36 x^3+4 x^4+e^x \left (4 x-70 x^2+8 x^3\right )\right ) \log (x)}{-125+75 \log (x)-15 \log ^2(x)+\log ^3(x)} \, dx \]
Rubi 4.16.1 under Mathematica 13.3.1 output
\[ \frac {e^{2 (9-x)^2} x^2 \left (-5 x^2+x^2 \log (x)+45 x-9 x \log (x)\right )}{(9-x) (5-\log (x))^3}-\frac {2 e^{2 (9-x)^2+x} x \left (-20 x^2+4 x^2 \log (x)+175 x-35 x \log (x)\right )}{(1-4 (9-x)) (5-\log (x))^3} \]