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

[eddysd]

Trying to do an improper integral but for some reason am flummoxed by the integration of 1/sqrt(x-1).

 

[╔(σ_σ)╝]

Have you tried the substitution u^{2} = x-1?

 

[eddysd]

nope, thank-you!

 

[Char. Limit]

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.

 

[Mark44]

Have you tried the substitution u^{2} = x-1?

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.

 

[Char. Limit]

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

Indeed. u=x-1 is what I meant.