How to integrate(anti-differentiate) 1/(x(2x-1)^1/2)

the question is in fraction. 2x-1 is under square root. Thanks.

integral 1/(x sqrt(-1+2 x)) dx
For the integrand 1/(x sqrt(2 x-1)), substitute u = 2 x-1 and du = 2 dx:
= integral 1/(sqrt(u) (u+1)) du
For the integrand 1/(sqrt(u) (u+1)), substitute s = sqrt(u) and ds = 1/(2 sqrt(u)) du:
= 2 integral 1/(s^2+1) ds
The integral of 1/(s^2+1) is tan^(-1)(s):
= 2 tan^(-1)(s)+constant
Substitute back for s = sqrt(u):
= 2 tan^(-1)(sqrt(u))+constant
Substitute back for u = 2 x-1:
= 2 tan^(-1)(sqrt(2 x-1))+constant

multiple top and bottom by (2x-1)^1/2 and you get (2x-1)^1/2 all divided by 2(x^2)-x

Use u substitution let u = 2x -1 and du = 2x dx.