Solving an Improper Integral Homework Equation

[Bashyboy]

Homework Statement

\int \frac{dx}{\sqrt{x^2-4}}

Homework Equations

The Attempt at a Solution

I tried trig-substitution, by realizing that cot\theta = \frac{4}{\sqrt{x^2-4}}

and that -4sin\theta = dx

My answer, though, found after the substitution and integration, is very different from the books: mine is - \frac{\sqrt{x^2-4}}{x}, theirs is ln|x+\sqrt{x^2-4}|

How do you account for this variation?

 

[Mark44]

Homework Statement

\int \frac{dx}{\sqrt{x^2-4}}

Homework Equations

The Attempt at a Solution

I tried trig-substitution, by realizing that cot\theta = \frac{4}{\sqrt{x^2-4}}

and that -4sin\theta = dx

You have mistakes in your substitution. One of the legs in your triangle should be 2, not 4. Also, your equation for dx is incorrect.

My answer, though, found after the substitution and integration, is very different from the books: mine is - \frac{\sqrt{x^2-4}}{x}, theirs is ln|x+\sqrt{x^2-4}|

How do you account for this variation?