I thought it would be fun to see if I could find the area of a circle with a radius of 5 by taking the integral of the positive form of a circle equation and multiplying it by two (since I believe the area of the bottom half is equal to the area of the upper half, or I should be able to take a definite integral from 0 to 5 and multiply it by 4). It turns out that integrating it was not as easy as I thought it would be.

I tried u-replacement, even though it looks like nothing will cancel.

I don't think there's anything I can do with this.

It looks like the equation fits one of the inverse trigonomic integrals, but it's not a fraction.

Next, I try to integrate by parts. I can't really think of anything else.

By the way, if there's something I should have seen here that would indicate to me that integrating by parts here will not work, let me know.

I don't think it helped. I could maybe integrate by parts again, but it would probably not make it any easier to solve. What could I do to solve this?