Question

Question #43621

Answer 1

`intsin(4x)cos^2(4x)dx = - cos^3(4x)/12 + C`

Explanation:

By evaluating, I'm assuming you mean integration.

To begin, use substitution:
`u = cos(4x), du = -4sin(4x)dx or (du)/(-4sin(4x)) = dx`

Then proceed and we will get that the integral is now:
`-1/4intu^2du`
Notice that when we used substitution, we found that `(du)/(-4sin(4x)) = dx` and when we substituted `dx` with `(du)/(-4sin(4x))`, we can cancel out `sin(4x)`. This leaves us with the new integral above.

Then integrating that is a simple matter, so: `(-1/4)u^(2+1)/(2+1) + C` which is basically `-u^3/12`. Then we reverse our substitution, and we would get our answer: `-cos^3(4x)/12 + C`.