Note: This only works when \(x\) is measured in radians. We are now going to look at more complex trigonometric functions where we will use the general rule: \(\int {\cos (ax + b)dx = \frac{1}{a}} ...

Remember that integration is the inverse procedure to differentiation. So, if you can do trigonometric differentiation, you can do trig integration.

James M. Dickey, Three Multidimensional-integral Identities with Bayesian Applications, The Annals of Mathematical Statistics, Vol. 39, No. 5 (Oct., 1968), pp. 1615-1628 ...