\[ \int \frac {\cos (5+3 x)}{\sqrt {3+\cos ^2(5+3 x)}} \, dx \]
Optimal antiderivative \[ \frac {\arcsin \! \left (\frac {\sin \left (5+3 x \right )}{2}\right )}{3} \]
command
integrate(cos(5+3*x)/(3+cos(5+3*x)^2)^(1/2),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
\[ \frac {1}{3} \, \arcsin \left (\frac {1}{2} \, \sin \left (3 \, x + 5\right )\right ) \]