This is for my trig class. Thanks for the help!

Using a Product-to-Sum Identity:

6 sin(5x) cos(2x) = 3 [2 sin((7x+3x)/2) cos((7x-3x)/2)

= 3 sin(7x) + 3 sin(3x)

6 sin(5x) cos(2x) = 3 [2 sin((7x+3x)/2) cos((7x-3x)/2)

= 3 sin(7x) + 3 sin(3x)

The reason it's important to do this simplification is that it is MUCH easier to integrate 3 sin(7x) + 3 sin(3x) than the original expression. You'll do this in calculus.