Mastering the Integration of 1/sqrt(x-1): Tips and Tricks

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Homework Help Overview

The discussion revolves around the integration of the function 1/sqrt(x-1), specifically focusing on approaches to solve an improper integral involving this expression.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants explore different substitution methods for the integral, with one suggesting u² = x-1 and another proposing u = x+1. There is a discussion about the effectiveness and simplicity of these substitutions.

Discussion Status

Participants are actively engaging with various substitution techniques, with some expressing preference for one method over another. There is a recognition of the effectiveness of the suggested substitutions, but no consensus has been reached on a single approach.

Contextual Notes

There is a mention of a potential typo regarding the substitutions, indicating some confusion about the correct form. The nature of the integral as improper is acknowledged, but specific details about limits or convergence are not provided.

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Trying to do an improper integral but for some reason am flummoxed by the integration of 1/sqrt(x-1).
 
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Have you tried the substitution u^{2} = x-1?
 
nope, thank-you!
 
Why that substitution, I wonder? It seems to me that the substitution u=x+1 would be simpler... but I'm sure that, if I tried yours, it would work out just as easy.

Wait, I did. And it was quite easy. Thanks for the alternative substitution route, I actually like this one better.
 
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╔(σ_σ)╝ said:
Have you tried the substitution u^{2} = x-1?

Char. Limit said:
Why that substitution, I wonder? It seems to me that the substitution u=x+1 would be simpler... but I'm sure that, if I tried yours, it would work out just as easy.

Wait, I did. And it was quite easy. Thanks for the alternative substitution route, I actually like this one better.

Probably a typo, but u = x - 1 is a better choice than u = x + 1.
 
Mark44 said:
Probably a typo, but u = x - 1 is a better choice than u = x + 1.

Indeed. u=x-1 is what I meant.
 

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