Variable mass problem (integration help)

Homework Statement

I've pretty much solved it, but i'm unsure of my final integration

A uniform chain of length L and density /rho(kg/m) is initially stationary on a horizontal, frictionless table, with part of the chain (length yo) hanging over the edge. How much time passes before the entire chain has left the table?

Homework Equations

arccosh(x) = log(sqrt(x2-1)+x)

The Attempt at a Solution

I don't think i need to put all the work i've done.

my integral

$$\int \sqrt{(y^{2}-y^{2}_{o})g/l}^{-1/2}$$

$$arccosh( \sqrt{l/g}*y/y_{o})$$

or

$$\sqrt{l/g}*log(2(\sqrt{y^{2}-y^{2}_{o}}+y))$$

yet on wolfram and other websites they say that l/g should not be square rooted. Yet i don't see why.

thanks