To simplify the first integral answer isn't it just setting up a right triangle and figuring out what the values will be? I got and

So then the answer to that first integral would be right? To be honest I'm really lost on this entire problem after I got half way through the integral. How do I finish this problem up exactly? And when exactly do I change the limits on this? Assuming that I will have to at some point. I attached what wolfram got as an answer as well for the indefinite integral for a reference. I'm not reallly familiar with the reduction formula as I never learned that in calculus 2. Perhaps I also went too far in the integral above after looking at wolfram's work, though I'm not too sure again. Any help appreciated.

*Only put "Supposedly" in title because I wasn't completely sure if integration by parts is in this problem or not. But after submitting it seems more likely that it is.