\[ \int \frac {\sqrt {c d^2+2 c d e x+c e^2 x^2}}{(d+e x)^6} \, dx \]
Optimal antiderivative \[ -\frac {c^{2}}{4 e \left (e x +d \right ) \left (c \,e^{2} x^{2}+2 c d e x +c \,d^{2}\right )^{\frac {3}{2}}} \]
command
integrate((c*e^2*x^2+2*c*d*e*x+c*d^2)^(1/2)/(e*x+d)^6,x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ -\frac {\sqrt {c} e^{\left (-1\right )} \mathrm {sgn}\left (x e + d\right )}{4 \, {\left (x e + d\right )}^{4}} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Exception raised: NotImplementedError} \]________________________________________________________________________________________