Integral of csc(x) and sec(x)

The integrals of sec(x) and csc(x) can usually be found in tables of integrals, and if all you are looking for is the answer, then here it is:

However, if you would like to know more, then here are the derivations for the integrals broken down step-by-step.  I tried to give as much detail as possible so it would be easy to read and comprehend.

Proof for integral of sec(x).

Proof for integral of csc(x).