I tried integrating by parts but I couldn't solve it. Please help by writing how to do it. I have a test in two days and I need to know how to solve this before then and it takes forever if I have to ask for one step at a time when there might be several questions.

You can just factor out the constants like 3 and pi. And it doesn't sound like you done integration by parts before. There are some examples here: http://en.wikipedia.org/wiki/Integration_by_parts Start from u=x and dv=sin(x)^2*cos(x)dx. Try to figure out what v is by integrating dv.