# U-substitution - Where does the dx go?

HorseBox
I'm having serious trouble with the concept of u-substitution. Using this as an example
int 2x(x2−1)4
I make u = x2−1
first thing I don't get is why du/dx = 2x is rearranged to du = 2xdx. Second thing I don't get is where the dx dissappears to. In this method is 2xdx just being represented as du? The part that confuses me is how you can represent something in an integrand as the derivative of another term in the integrand. I'm completely lost there.

$$\int f(g(x))g'(x)dx = \int f(u) du$$
this is the substitution formula, the $$dx$$ part is adjusted by $$g'(x)dx$$
to act as $$du$$