1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Improper Integral

  1. Sep 24, 2012 #1
    1. The problem statement, all variables and given/known data
    [itex]\int \frac{dx}{\sqrt{x^2-4}}[/itex]

    2. Relevant equations

    3. The attempt at a solution

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

    and that [itex]-4sin\theta = dx[/itex]

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

    How do you account for this variation?
  2. jcsd
  3. Sep 24, 2012 #2


    Staff: Mentor

    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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook