Question

How do you find the integral of `cos^4 x sin(2x) dx`?

Answer 1

Recall that `sin(2x) = 2sinxcosx`

Explanation:

`int cos^4xsin(2x) dx = int cos^4x (2sinxcosx) dx`

`= 2int cos^5x sinx dx`

Now use substitution.

Let `u = cosx`, and finish the substitution to get

`2int cos^5x sinx dx = -cos^6x/3+C`