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