While you were at the Wolfram site, you should've asked for a solution to your integral and at least look to see if your substitution is correct!
Tricky for me at least:
I worked it out to this:
I got pretty close to the answer I know because when I asked Wolfram to differentiate this it gave me
Maybe I made a mistake reverting to x from theta? I was a bit confused about how to handle sin(2theta) even though I drew a diagram of the right triangle. That's why I wrote sin(arcsin...) which I'm not sure is correct? Any clarification is appreciated