\[ \int \frac {e^{7 x+x^2+8 e^{7 x+x^2} x^3} \left (-96 x^2-224 x^3-64 x^4\right )}{e^{10}+e^{16 e^{7 x+x^2} x^3}+2 e^{5+8 e^{7 x+x^2} x^3}} \, dx \]
Optimal antiderivative \[ \frac {4}{{\mathrm e}^{8 \,{\mathrm e}^{\left (7+x \right ) x} x^{3}}+{\mathrm e}^{5}} \]
command
integrate((-64*x^4-224*x^3-96*x^2)*exp(x^2+7*x)*exp(8*x^3*exp(x^2+7*x))/(exp(8*x^3*exp(x^2+7*x))^2+2*exp(5)*exp(8*x^3*exp(x^2+7*x))+exp(5)^2),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \frac {4}{e^{5} + e^{\left (8 \, x^{3} e^{\left (x^{2} + 7 \, x\right )}\right )}} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Exception raised: NotImplementedError} \]________________________________________________________________________________________