Optimal antiderivative \[ \frac {\arctanh \left (\sin \left (2 a x \right )\right )}{2 a} \]
command
integrate(sec(2*a*x),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \frac {\log \left ({\left | \frac {1}{\sin \left (2 \, a x\right )} + \sin \left (2 \, a x\right ) + 2 \right |}\right ) - \log \left ({\left | \frac {1}{\sin \left (2 \, a x\right )} + \sin \left (2 \, a x\right ) - 2 \right |}\right )}{8 \, a} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Exception raised: NotImplementedError} \]________________________________________________________________________________________