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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

    Mark44

    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.
     
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