I'm not totally sure how to do this problem. So far, I've done this:

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From here, I don't know how to calculate the integral. Is there a trig identity that simplifies the problem? Do I have to integral by parts or substitution? I plugged it into wolframalpa and got a solution but it didn't give me what I really wanted, the steps on how to solve the integral.

Am I even approaching the problem correctly? Thanks