\[ \int \frac {e \left (32 x+8 x^2-50 x^5\right )}{768+768 x+960 x^2+384 x^3+2592 x^4+1200 x^5+1200 x^6+1875 x^8} \, dx \]
Optimal antiderivative \[ \frac {{\mathrm e}}{21+\frac {3 \left (4+x \right )^{2}}{x^{2}}+75 x^{2}} \]
command
Int[(E*(32*x + 8*x^2 - 50*x^5))/(768 + 768*x + 960*x^2 + 384*x^3 + 2592*x^4 + 1200*x^5 + 1200*x^6 + 1875*x^8),x]
Rubi 4.17.3 under Mathematica 13.3.1 output
\[ \int \frac {e \left (32 x+8 x^2-50 x^5\right )}{768+768 x+960 x^2+384 x^3+2592 x^4+1200 x^5+1200 x^6+1875 x^8} \, dx \]
Rubi 4.16.1 under Mathematica 13.3.1 output
\[ \frac {e x^2}{3 \left (25 x^4+8 x^2+8 x+16\right )} \]