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