Integrate (cosx)^3

In order to integrate (cosx)^3, there is no given rule (by-parts, 'try' method, chain rule) which we can follow. We would need to split it into (cosx)^2 and cosx. Then use the identity: (sinx)^2 + (cosx)^2 = 1. The function we are now integrating should look like this: (1-(sinx)^2)(cosx). Expand the brackets. Once the brackets have been expanded, cosx can be integrated to give sinx. Then we can use the 'try' method to integrate cosx(sinx)^2.