How Can the Integral of 1/sqrt(x^2 - 1) Be Expressed Using Ln?

[rado5]

Homework Statement

$$\int$$dx/$$\sqrt{}x^2 -1$$
I actually know that the answer is arccosh(x) but I want to prove it in form of Ln(x+$$\sqrt{}x^2 -1$$)

Homework Equations

The Attempt at a Solution

I have tried many times such as u=x²-1 and u=x²

 

[rocomath]

Did you mean ...

$$\int\frac{dx}{\sqrt{x^2-1}}$$

 

[rado5]

Yes I mean

LaTeX Code: \\int\\frac{dx}{\\sqrt{x^2-1}}

 

[Defennder]

Use a trigo substitution here.

 

[rado5]

Thank you now I got it x=sect