\[ \int \frac {20 x^5+e^{15} \left (-800-640 x^2+2 x^5-20 x^6\right )+e^{30} \left (500 x+480 x^3+64 x^5+5 x^7\right )}{4 x^5-4 e^{15} x^6+e^{30} x^7} \, dx \]
Optimal antiderivative \[ \frac {4 \left (4+\frac {5}{x^{2}}\right )^{2}+x}{2 \,{\mathrm e}^{-15}-x}+5 x \]
command
integrate(((5*x^7+64*x^5+480*x^3+500*x)*exp(5)^6+(-20*x^6+2*x^5-640*x^2-800)*exp(5)^3+20*x^5)/(x^7*exp(5)^6-4*x^6*exp(5)^3+4*x^5),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ 5 \, x - \frac {25 \, e^{75} + 160 \, e^{45} + 256 \, e^{15} + 8}{4 \, {\left (x e^{15} - 2\right )}} + \frac {5 \, {\left (5 \, x^{3} e^{60} + 32 \, x^{3} e^{30} + 10 \, x^{2} e^{45} + 64 \, x^{2} e^{15} + 20 \, x e^{30} + 40 \, e^{15}\right )}}{4 \, x^{4}} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Exception raised: NotImplementedError} \]________________________________________________________________________________________