Trig Integrals Containing Sines and Cosines, Secants and Tangents, or Cosecants and Cotangents

By Mark Ryan

In this article on trig integrals, you integrate powers of the six trigonometric functions and products or quotients of different trig functions. To use the techniques covered in the article, you must either have an integrand that contains just one of the six trig functions or a certain pairing of trig functions.

If the integrand has two trig functions, the two must be one of these three pairs: sine with cosine, secant with tangent, or cosecant with cotangent. If you have an integrand containing something other than one of these three pairs, you can easily convert the problem into one of these pairs by using trig identities. The basic idea with most of the trig integrals discussed is to organize the integrand so that you can make a handy u-substitution and then integrate with the reverse power rule.

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