\[ \int \frac {d+e x}{\left (d^2-e^2 x^2\right )^{5/2}} \, dx \]
Optimal antiderivative \[ \frac {e x +d}{3 d e \left (-e^{2} x^{2}+d^{2}\right )^{\frac {3}{2}}}+\frac {2 x}{3 d^{3} \sqrt {-e^{2} x^{2}+d^{2}}} \]
command
integrate((e*x+d)/(-e^2*x^2+d^2)^(5/2),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \text {could not integrate} \]
Giac 1.7.0 via sagemath 9.3 output
\[ -\frac {\sqrt {-x^{2} e^{2} + d^{2}} {\left (x {\left (\frac {2 \, x^{2} e^{2}}{d^{3}} - \frac {3}{d}\right )} - e^{\left (-1\right )}\right )}}{3 \, {\left (x^{2} e^{2} - d^{2}\right )}^{2}} \]