Try integration by parts. You probably need to use parts twice to get the answer out. Alternatively, if you know about complex exponentials, try substituting them in, expanding and integrating directly.

Michael

PS. I'm assuming that this is sin x cos 3x not sin x cos³ x. If the latter is the case, of course you use the substitution u = cos x.

Thanks Michael for that tip. I'll do it by parts!

Alternatively, use some trig formulae.

sin(x + 3x) = sin(x)cos(3x) + cos(x)sin(3x)
sin(x - 3x) = sin(x)cos(3x) - cos(x)sin(3x)

Add these together and you get:

sin(x)cos(3x) = (sin 4x - sin 2x)/2

and from there it's straightforward.

Thank you again Michael.