Hey everyone. This is my first post. I just need help with this problem in Calculus II. The problem states: Integrate the trigonometric integral: Integral of sin ^ 2 (5x) * cos (2x) dx. I wasn't sure how to approach it. Thanks for any help. BTW, this is what I have so far:

I've moved it around a little using trig identities:

Integral of (1 - cos ^ 2 (5x)) cos (2x) dx

= Integral of (cos (2x) - cos ^ 2 (5x) * cos (2x)) dx

= [1/2 * sin (2x)] - Integral of (cos ^ 2 (5x) * cos (2x)) dx