\[ \int \frac {d+e x}{\left (d^2-e^2 x^2\right )^{7/2}} \, dx \]
Optimal antiderivative \[ \frac {e x +d}{5 d e \left (-e^{2} x^{2}+d^{2}\right )^{\frac {5}{2}}}+\frac {4 x}{15 d^{3} \left (-e^{2} x^{2}+d^{2}\right )^{\frac {3}{2}}}+\frac {8 x}{15 d^{5} \sqrt {-e^{2} x^{2}+d^{2}}} \]
command
integrate((e*x+d)/(-e^2*x^2+d^2)^(7/2),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
\[ -\frac {\sqrt {-x^{2} e^{2} + d^{2}} {\left ({\left (4 \, x^{2} {\left (\frac {2 \, x^{2} e^{4}}{d^{5}} - \frac {5 \, e^{2}}{d^{3}}\right )} + \frac {15}{d}\right )} x + 3 \, e^{\left (-1\right )}\right )}}{15 \, {\left (x^{2} e^{2} - d^{2}\right )}^{3}} \]