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Calc 1 integration substitution and Implicit diff!

I need some help with 2 and 8.

2) I see that U = sqrt(x-1) and then du=1/(2sqrt(x-1)) but how do I get an integer to sub in for xdx? Usually in our past problems we would have like xdx and u=x^2 so du = 2x and the fraction is 1/2. I guess I'm just not seeing it so some further good instruction would be nice.

8.I have the answer key that my prof gave me and I can't get the answer. I keep coming up with:

y=ln(x^2+y^2)

y'=1/(x^2+y^2) * 2x +2yy'

y'-2yy' = 2x/(x^2+y^2)

but the answer key says:

y'=2x/(x^2+y^2-2y)

I don't see how you get the -2y in the denominator..