\[ \int \frac {960+480 x+2520 x^2+360 e^3 x^2}{400-320 x-16 x^2-248 x^3+116 x^4+28 x^5+49 x^6+e^6 x^6+e^3 \left (-40 x^3+16 x^4+4 x^5+14 x^6\right )} \, dx \]
Optimal antiderivative \[ \frac {12}{\left (\frac {2}{x}-\frac {\left (7+{\mathrm e}^{3}\right ) x^{2}}{10}-\frac {4}{5}-\frac {x}{5}\right ) x} \]
command
integrate((360*x^2*exp(3)+2520*x^2+480*x+960)/(x^6*exp(3)^2+(14*x^6+4*x^5+16*x^4-40*x^3)*exp(3)+49*x^6+28*x^5+116*x^4-248*x^3-16*x^2-320*x+400),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ -\frac {120}{x^{3} e^{3} + 7 \, x^{3} + 2 \, x^{2} + 8 \, x - 20} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \int \frac {120 \, {\left (3 \, x^{2} e^{3} + 21 \, x^{2} + 4 \, x + 8\right )}}{x^{6} e^{6} + 49 \, x^{6} + 28 \, x^{5} + 116 \, x^{4} - 248 \, x^{3} - 16 \, x^{2} + 2 \, {\left (7 \, x^{6} + 2 \, x^{5} + 8 \, x^{4} - 20 \, x^{3}\right )} e^{3} - 320 \, x + 400}\,{d x} \]________________________________________________________________________________________