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