\[ \int \frac {384 x+128 e^{32} x+256 x^2}{9+e^{64}+24 x+16 x^2+e^{32} (6+8 x)} \, dx \]
Optimal antiderivative \[ \frac {16 x^{2}}{\frac {3}{4}+\frac {{\mathrm e}^{32}}{4}+x} \]
command
integrate((128*x*exp(16)^2+256*x^2+384*x)/(exp(16)^4+(8*x+6)*exp(16)^2+16*x^2+24*x+9),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ 16 \, x + \frac {4 \, {\left (e^{64} + 6 \, e^{32} + 9\right )}}{4 \, x + e^{32} + 3} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Exception raised: NotImplementedError} \]________________________________________________________________________________________