\[ \int \frac {14 e^4 x-324 x^4+27 x^6+10206 x^9+e^2 \left (-4+3 x^2-756 x^5\right )}{e^4-54 e^2 x^4+729 x^8} \, dx \]
Optimal antiderivative \[ \left (\frac {x}{27 x^{4}-{\mathrm e}^{2}}-7\right ) \left (-x^{2}+4\right ) \]
command
integrate((14*x*exp(1)^4+(-756*x^5+3*x^2-4)*exp(1)^2+10206*x^9+27*x^6-324*x^4)/(exp(1)^4-54*x^4*exp(1)^2+729*x^8),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ 7 \, x^{2} - \frac {x^{3} - 4 \, x}{27 \, x^{4} - e^{2}} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \int \frac {10206 \, x^{9} + 27 \, x^{6} - 324 \, x^{4} + 14 \, x e^{4} - {\left (756 \, x^{5} - 3 \, x^{2} + 4\right )} e^{2}}{729 \, x^{8} - 54 \, x^{4} e^{2} + e^{4}}\,{d x} \]________________________________________________________________________________________