Integration with U-Substitution

Question

Integral of [x/sqrt(x+1)] dx

I'm getting confused with how to deal with the x when I find the derivative of (x+1) because they don't match.

Answer 1

let
u^2 = x+1
x = u^2-1
2u du = dx

and we have

∫ (u^2-1)/u * 2u du
= 2∫u^2-1 du

and that's a cinch, right?