What is #int(cos(x))^4 dx#?
1 Answer
Explanation:
While initially appearing to be a really annoying integral, we can actually exploit trig identities to break this integral down into a series of simple integrals that we are more familiar with.
The identity we will be using is:
This lets us manipulate our equation as such:
We can now apply our rule again to eliminate the cos^2(2x) inside the parenthetical:
Now we actually have a fairly simple integration problem, we can distribute the integral into our parenthetical so that:
Each of these trig integrals is handled with the simple rule that
Thus,