\[ \int \frac {\left (c d^2+2 c d e x+c e^2 x^2\right )^{5/2}}{(d+e x)^8} \, dx \]
Optimal antiderivative \[ -\frac {c^{3}}{2 e \left (e x +d \right ) \sqrt {c \,e^{2} x^{2}+2 c d e x +c \,d^{2}}} \]
command
integrate((c*e^2*x^2+2*c*d*e*x+c*d^2)^(5/2)/(e*x+d)^8,x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ -\frac {c^{\frac {5}{2}} e^{\left (-1\right )} \mathrm {sgn}\left (x e + d\right )}{2 \, {\left (x e + d\right )}^{2}} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Exception raised: NotImplementedError} \]________________________________________________________________________________________