\[ \int \frac {2 e^{3+8 e^5} x}{e^9-15 e^6 x+75 e^3 x^2-125 x^3} \, dx \]
Optimal antiderivative \[ \frac {x^{2} {\mathrm e}^{8 \,{\mathrm e}^{5}}}{\left (5 x -{\mathrm e}^{3}\right )^{2}} \]
command
integrate(2*x*exp(3)*exp(4*exp(5))^2/(exp(3)^3-15*x*exp(3)^2+75*x^2*exp(3)-125*x^3),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \frac {{\left (10 \, x - e^{3}\right )} e^{\left (8 \, e^{5} + 3\right )}}{25 \, {\left (5 \, x - e^{3}\right )}^{2}} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \int -\frac {2 \, x e^{\left (8 \, e^{5} + 3\right )}}{125 \, x^{3} - 75 \, x^{2} e^{3} + 15 \, x e^{6} - e^{9}}\,{d x} \]________________________________________________________________________________________