Let w = sqr(x)
x = w^2
dx = 2wdw
then your thing becomes.
integral [ (1/w) * 2w * sinw dw ]
the 2 w's cancel so your left with
integral [ 2 sin(w) dw ]
I think you can get the rest from there
I'm sorry to say but that wasn't right.
sine and cosine are functions, not constants. When you have sin(theta) that is not the same as sine * theta. If you have sin(theta)/theta, you cannot "reduce" the theta's and declare that sin(theta)/theta = sin
That doesn't make any sense.
In the future, I would recommend you do it the way smooth did, using substitution.