\[ \int \frac {432 x+216 e^3 x^2+e^6 \left (-18900+36 x^3\right )+e^9 \left (3150 x+2 x^4\right )}{216+108 e^3 x+18 e^6 x^2+e^9 x^3} \, dx \]
Optimal antiderivative \[ \left (x -\frac {3150}{\left (x +6 \,{\mathrm e}^{-3}\right )^{2}}\right ) x \]
command
integrate(((2*x^4+3150*x)*exp(3)^3+(36*x^3-18900)*exp(3)^2+216*x^2*exp(3)+432*x)/(x^3*exp(3)^3+18*x^2*exp(3)^2+108*x*exp(3)+216),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ x^{2} - \frac {3150 \, x e^{6}}{{\left (x e^{3} + 6\right )}^{2}} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \int \frac {2 \, {\left (108 \, x^{2} e^{3} + {\left (x^{4} + 1575 \, x\right )} e^{9} + 18 \, {\left (x^{3} - 525\right )} e^{6} + 216 \, x\right )}}{x^{3} e^{9} + 18 \, x^{2} e^{6} + 108 \, x e^{3} + 216}\,{d x} \]________________________________________________________________________________________