I attempted the following problem: Integral of sin2xcos3xdx

and could not do it. After looking at the answer (typed below) Im kicking myself in the butt trying to figure out how they came up with this answer. What identities were used? Can someone help me?

The following is straight from the solutions manual:

Integral of sin2xcos3xdx

half the Integral of (sin5x-sinx)dx

Answer= -.1cos5x+.5cosx+C