Have you tried trig substitution? let x = 3sin(s) and then substitute in... you should get an expression that you can integrate, after a few trig tricks of course.
The Attempt at a Solution
Have tried multiple methods but none seem to work for me!
You have a mistake at two places. The sin^2(s) should be (3 sin(s))^2 and the 3 needs to be a 9. Other than that, you're so-far good. After substituting, you should get an easy 3+2cos(s), which of course needs to be multiplied by dx. So while you're doing that, it might be a good idea to get dx in terms of ds.so...y=3+2*sqrt(1-(x^2/9))
then... y=y=3+2*sqrt(1-(sin^2(s)/3)) yes?
after that what should occur?