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## Homework Statement

I have a question dealing with this integral: [tex]\int\frac{x}{\sqrt{x^2-4}}[/tex]. I did the trig substitution to check my other method of substitution and got two different answers: [tex]\sqrt{x^2-4}[/tex] and [tex]\sqrt{x^2-4}/2[/tex]. The latter is from trig substitution and the former from regular substitution.

## The Attempt at a Solution

Ok, here is my work for the trig substitution

x=2sec@

dx=2sec@tan@

(x^2-4) = 4tan^2@

I finally get the integral of sec^2@ which gives me tan@ and looking from the triangle I drew its answer is [tex]\sqrt{x^2-4}/2[/tex]. Why don't these two answers agree? Is there some rule suggesting not to use trig substitution or one way over the other?

Thank You