I worded my question poorly (my bad

). What I mean is this.

I get where we use completing the square to transform:

int 1/sqrt(x^2-3x+2) dx--> int 1/sqrt( (x-3/2)^2 - 1/4 )dx

From there we have u = x-3/2 and therefore du = dx

Plug in and we get int 1/ (u^2 - 1/4)^1/2 du

Now, we pull out or factor out the 1/4; But I am struggling with when we do that, how

int 1/ (u^2 - 1/4)^1/2 du becomes

Int[1/((1/4)(2u)^2 - 1/4)^{1/2}du]

(we pull out 1/4, so how does u^2 become 2u^2 ?

and then

2*Int[1/((2u)^2 - 1)^{1/2}du]

Sorry for bothering you guys so much!