Integrating Derivatives of Trig Functions

Indeed, using the fantastic qualities of the 6 trigonometric functions, we can generate various kinds of beautiful integrals. $$\\$$ $\int \cos x \, dx = \sin x + C$

$\int \sin x \, dx = -\cos x + C$

$\int \sec^{2} x \, dx = \tan x + C$

$\int \csc^{2} x \, dx = -\cot x + C$

$\int \sec x \tan x \, dx = \sec x + C$

$\int \csc x \cot x \, dx = -\csc x + C$ $$\\$$ The 6 integrals above are just using the derivatives of the 6 trigonometric functions. Notice that only the integrals of $\sin x$ and $\cos x$ are here, leaving the other four trigonometric functions. Then what about their integrals? How many of all the 6 trigonometric functions have indefinite integrals that are compositions of the basic functions we covered already (e.g. logarithmic, exponential, absolute value, polynomial, factorial, trigonometric etc.)?