ABSTRACT
The table of integrals [40] contains a large variety of evaluations of the type
I =
A(x)R(sin x, cosx) dx (5.1.1)
where A is an algebraic function, R is rational and −∞ ≤ a < b ≤ ∞. We present a systematic discussion of two families of integrals of this type. This paper is part of a general program started in [63, 64, 65, 66] intended to provide proofs and context to the formulas in [40].
