Calculate the following antiderivatives:

(a) $\displaystyle\int \frac{4}{\cos^2 x} \, dx$ = $+ C$.

(b) $\displaystyle\int \sec x(\sec x + \tan x) \, dx$ = $+ C$.

(c) $\displaystyle\int \frac{\sin(2x)}{\cos x} \,dx$ = $+ C$.

Hint: For some of these problems, you will need to change the form of the integrand before finding an antiderivative.