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

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Homework Help Overview

The discussion revolves around the integral of the function 1/sqrt(x^2 - 1), with the original poster expressing a desire to prove that it can be represented in the form of ln(x + sqrt(x^2 - 1)).

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • The original poster attempts various substitutions, including u = x^2 - 1 and u = x^2, to explore the integral. Some participants suggest using trigonometric substitution as a potential approach.

Discussion Status

The discussion is active, with participants providing suggestions and clarifications. There is acknowledgment of the integral's form, and some guidance has been offered regarding substitution methods.

Contextual Notes

The original poster is seeking to express the integral in a specific logarithmic form, indicating a focus on proving a particular relationship rather than simply solving the integral.

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Homework Statement



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

Homework Equations


The Attempt at a Solution


I have tried many times such as u=x2-1 and u=x2
 
Last edited:
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Did you mean ...

[tex]\int\frac{dx}{\sqrt{x^2-1}}[/tex]
 


Yes I mean

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


Use a trigo substitution here.
 


Thank you now I got it x=sect
 

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