\[ \int \frac {1}{\left (a \cos ^4(x)\right )^{3/2}} \, dx \]
Optimal antiderivative \[ \frac {\cos \left (x \right ) \sin \left (x \right )}{a \sqrt {a \left (\cos ^{4}\left (x \right )\right )}}+\frac {2 \left (\sin ^{2}\left (x \right )\right ) \tan \left (x \right )}{3 a \sqrt {a \left (\cos ^{4}\left (x \right )\right )}}+\frac {\left (\sin ^{2}\left (x \right )\right ) \left (\tan ^{3}\left (x \right )\right )}{5 a \sqrt {a \left (\cos ^{4}\left (x \right )\right )}} \]
command
integrate(1/(a*cos(x)^4)^(3/2),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \frac {3 \, \tan \left (x\right )^{5} + 10 \, \tan \left (x\right )^{3} + 15 \, \tan \left (x\right )}{15 \, a^{\frac {3}{2}}} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Exception raised: TypeError} \]________________________________________________________________________________________