Find the antiderivative for each function when C equals $0.$ Do as many as you can mentally. Check your answers by differentiation.

a$.23cos23x$

b$.\frac{21}{2}cos(\frac{21x}{2})$

c$.cos(\frac{3x}{2})5cosx$

a$.$ The antiderivative of $23cos23x$ is $$

b$.$ The antiderivative of $\frac{21}{2}cos(\frac{21x}{2})$ is $.$

$($Type an exact answer, using $$ as needed.$)$

c$.$ The antiderivative of $cos(\frac{3x}{2})5cosx$ is $$

$($Type an exact answer, using $$ as needed.$)$