28.5 Problem number 669

\[ \int \frac {\cos (3 x)}{\sqrt {4-\sin ^2(3 x)}} \, dx \]

Optimal antiderivative \[ \frac {\arcsin \! \left (\frac {\sin \left (3 x \right )}{2}\right )}{3} \]

command

integrate(cos(3*x)/(4-sin(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

\[ \frac {1}{3} \, \arcsin \left (\frac {1}{2} \, \sin \left (3 \, x\right )\right ) \]