\[ \int \frac {135 x+40 x^6+15 x^7+e^4 \left (40 x^4+15 x^5\right )+e^2 \left (90+80 x^5+30 x^6\right )}{e^4 x^3+2 e^2 x^4+x^5} \, dx \]
Optimal antiderivative \[ 5 x^{2} \left (4+x \right )-\frac {45}{x^{2} \left (x +{\mathrm e}^{2}\right )}-20 \]
command
integrate(((15*x^5+40*x^4)*exp(2)^2+(30*x^6+80*x^5+90)*exp(2)+15*x^7+40*x^6+135*x)/(x^3*exp(2)^2+2*x^4*exp(2)+x^5),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ 5 \, x^{3} + 20 \, x^{2} - \frac {45 \, e^{\left (-4\right )}}{x + e^{2}} + \frac {45 \, {\left (x - e^{2}\right )} e^{\left (-4\right )}}{x^{2}} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Exception raised: NotImplementedError} \]________________________________________________________________________________________