\[ \int \frac {e^{\frac {10 x^5-2 x^6}{81-432 x+864 x^2-768 x^3+256 x^4}} \left (-150 x^4+76 x^5-16 x^6\right )}{-243+1620 x-4320 x^2+5760 x^3-3840 x^4+1024 x^5} \, dx \]
Optimal antiderivative \[ {\mathrm e}^{\frac {2 x \left (5-x \right )}{\left (4-\frac {3}{x}\right )^{4}}} \]
command
Int[(E^((10*x^5 - 2*x^6)/(81 - 432*x + 864*x^2 - 768*x^3 + 256*x^4))*(-150*x^4 + 76*x^5 - 16*x^6))/(-243 + 1620*x - 4320*x^2 + 5760*x^3 - 3840*x^4 + 1024*x^5),x]
Rubi 4.17.3 under Mathematica 13.3.1 output
\[ \int \frac {\exp \left (\frac {10 x^5-2 x^6}{81-432 x+864 x^2-768 x^3+256 x^4}\right ) \left (-150 x^4+76 x^5-16 x^6\right )}{-243+1620 x-4320 x^2+5760 x^3-3840 x^4+1024 x^5} \, dx \]
Rubi 4.16.1 under Mathematica 13.3.1 output
\[ e^{\frac {2 (5-x) x^5}{(3-4 x)^4}} \]