\[ \int \frac {\cos \left (a+\frac {b}{x^2}\right )}{x^3} \, dx \]
Optimal antiderivative \[ -\frac {\sin \left (a +\frac {b}{x^{2}}\right )}{2 b} \]
command
integrate(cos(a+b/x^2)/x^3,x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ -\frac {\sin \left (\frac {a x^{2} + b}{x^{2}}\right )}{2 \, b} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \int \frac {\cos \left (a + \frac {b}{x^{2}}\right )}{x^{3}}\,{d x} \]________________________________________________________________________________________