\[ \int \frac {12150-450 e^3+2025 x-27 x^3}{729 x^3+e^6 x^3+162 x^4+9 x^5+e^3 \left (-54 x^3-6 x^4\right )} \, dx \]
Optimal antiderivative \[ \frac {3 \left (5-x \right ) \left (5+x \right )}{x^{2} \left (\frac {{\mathrm e}^{3}}{3}-9-x \right )} \]
command
integrate((-450*exp(3)-27*x^3+2025*x+12150)/(x^3*exp(3)^2+(-6*x^4-54*x^3)*exp(3)+9*x^5+162*x^4+729*x^3),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \frac {9 \, {\left (e^{6} - 54 \, e^{3} + 504\right )}}{{\left (3 \, x - e^{3} + 27\right )} {\left (e^{6} - 54 \, e^{3} + 729\right )}} + \frac {225 \, {\left (3 \, x + e^{3} - 27\right )}}{x^{2} {\left (e^{6} - 54 \, e^{3} + 729\right )}} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Exception raised: NotImplementedError} \]________________________________________________________________________________________