\[ \int \frac {-150000 e^{10} x^2+390625 x^3}{4096 e^{30}-96000 e^{20} x+750000 e^{10} x^2-1953125 x^3} \, dx \]
Optimal antiderivative \[ -\frac {5 x}{\left (\frac {16 \,{\mathrm e}^{10}}{25 x}-5\right )^{2}} \]
command
integrate((-150000*x^2*exp(5)^2+390625*x^3)/(4096*exp(5)^6-96000*x*exp(5)^4+750000*x^2*exp(5)^2-1953125*x^3),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ -\frac {1}{5} \, x - \frac {256 \, {\left (375 \, x e^{20} - 32 \, e^{30}\right )}}{625 \, {\left (125 \, x - 16 \, e^{10}\right )}^{2}} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \int -\frac {3125 \, {\left (125 \, x^{3} - 48 \, x^{2} e^{10}\right )}}{1953125 \, x^{3} - 750000 \, x^{2} e^{10} + 96000 \, x e^{20} - 4096 \, e^{30}}\,{d x} \]________________________________________________________________________________________