You didn't do it correctly. The substitution here is easy, it's the trig that gets to be a mess.
Try the substitution $x=3\sin(u)$ and be careful with the trig.
How is the integral (file attached) solved?
Correction: the integrand should be squared, as it equals x^2
I am aware of the pythagorian identities (cos^2x + sin^2x = 1, thus cos^2x = 1 - sin^2x). I have solved an integral with just a dx in the numerator but I have never solved an integral with an x^2 in the numerator. I don't what to do with it.
Sincere regards /