\[ \int \frac {-9 x^3-18 x^4-15 x^5-4 x^6+e^4 \left (27 x^2+36 x^3+25 x^4+6 x^5\right )}{e^{12}-3 e^8 x+3 e^4 x^2-x^3} \, dx \]
Optimal antiderivative \[ \frac {x^{3} \left (3+x \right ) \left (x^{2}+2 x +3\right )}{\left (x -{\mathrm e}^{4}\right )^{2}} \]
command
integrate(((6*x^5+25*x^4+36*x^3+27*x^2)*exp(4)-4*x^6-15*x^5-18*x^4-9*x^3)/(exp(4)^3-3*x*exp(4)^2+3*x^2*exp(4)-x^3),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ x^{4} + 2 \, x^{3} e^{4} + 5 \, x^{3} + 3 \, x^{2} e^{8} + 10 \, x^{2} e^{4} + 9 \, x^{2} + 4 \, x e^{12} + 15 \, x e^{8} + 18 \, x e^{4} + 9 \, x + \frac {6 \, x e^{20} + 25 \, x e^{16} + 36 \, x e^{12} + 27 \, x e^{8} - 5 \, e^{24} - 20 \, e^{20} - 27 \, e^{16} - 18 \, e^{12}}{{\left (x - e^{4}\right )}^{2}} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \int \frac {4 \, x^{6} + 15 \, x^{5} + 18 \, x^{4} + 9 \, x^{3} - {\left (6 \, x^{5} + 25 \, x^{4} + 36 \, x^{3} + 27 \, x^{2}\right )} e^{4}}{x^{3} - 3 \, x^{2} e^{4} + 3 \, x e^{8} - e^{12}}\,{d x} \]________________________________________________________________________________________