  The well known table of Gradshteyn and Ryzhik contains indefinite and
definite integrals of both elementary and special functions. We give proofs of
several entries containing integrands with some combination of hyperbolic and
trigonometric functions. In fact, we occasionally present an extension of such
entries or else give alternative evaluations. We develop connections with
special cases of special functions including the Hurwitz zeta function. Before
concluding we mention new integrals coming from the investigation of certain
elliptic functions.
