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