Integration: Trigonometric substitution
The problem i am stuck on is: find the integral of (x^2)/(sqrt(9-x^2))
I have managed to complete the problem to the second to last step where i get (9 theta)/2-9/4 sin(2 theta),
since i substituted at the beginning x=3sin(theta) i can rearrange for theta and get the first part = 9/2sin^-1(x/3).
What I am struggling with is to complete the 9/4sin(2theta) by putting this back in terms of x.
The answer i am looking for is 1/2 x sqrt(9-x^2) so if someone could explain how to get 9/4 sin(2 theta) to 1/2 x sqrt(9-x^2) that be be extremely helpful.