\[ \int \frac {\left (c d^2+2 c d e x+c e^2 x^2\right )^{5/2}}{d+e x} \, dx \]
Optimal antiderivative \[ \frac {\left (c \,e^{2} x^{2}+2 c d e x +c \,d^{2}\right )^{\frac {5}{2}}}{5 e} \]
command
integrate((c*e^2*x^2+2*c*d*e*x+c*d^2)^(5/2)/(e*x+d),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \frac {1}{5} \, {\left (c^{2} x^{5} e^{4} + 5 \, c^{2} d x^{4} e^{3} + 10 \, c^{2} d^{2} x^{3} e^{2} + 10 \, c^{2} d^{3} x^{2} e + 5 \, c^{2} d^{4} x\right )} \sqrt {c} \mathrm {sgn}\left (x e + d\right ) \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Exception raised: NotImplementedError} \]________________________________________________________________________________________