\[ \int \frac {e^4 (-4-2 x)-11 x^2-8 e^{15} x^2-e^{20} x^2-8 x^3-x^4+e^8 (4+2 x)+e^5 \left (-4 e^4+4 e^8-28 x^2-8 x^3\right )+e^{10} \left (-e^4+e^8-23 x^2-2 x^3\right )}{16 x^2+8 e^{15} x^2+e^{20} x^2+8 x^3+x^4+e^{10} \left (24 x^2+2 x^3\right )+e^5 \left (32 x^2+8 x^3\right )} \, dx \]
Optimal antiderivative \[ \frac {x +\frac {{\mathrm e}^{4}-{\mathrm e}^{8}-x}{x}}{\left ({\mathrm e}^{5}+2\right )^{2}+x}-x \]
command
integrate((-x^2*exp(5)^4-8*x^2*exp(5)^3+(exp(4)^2-exp(4)-2*x^3-23*x^2)*exp(5)^2+(4*exp(4)^2-4*exp(4)-8*x^3-28*x^2)*exp(5)+(2*x+4)*exp(4)^2+(-2*x-4)*exp(4)-x^4-8*x^3-11*x^2)/(x^2*exp(5)^4+8*x^2*exp(5)^3+(2*x^3+24*x^2)*exp(5)^2+(8*x^3+32*x^2)*exp(5)+x^4+8*x^3+16*x^2),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ -x - \frac {x e^{10} + 4 \, x e^{5} + 5 \, x + e^{8} - e^{4}}{x^{2} + x e^{10} + 4 \, x e^{5} + 4 \, x} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Exception raised: NotImplementedError} \]________________________________________________________________________________________