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Show the integral of dx/(1-x^2/a^2)

  1. Jan 19, 2012 #1
    1. The problem statement, all variables and given/known data
    Hi, I am having a bit of trouble visualizing the process of the following integral:

    ∫dx/(1-x^2/a^2)

    The answer to this would be: atanh-1[itex]\frac{x}{a}[/itex]

    if someone could show me this, that would be greatly appreciated.

    Thanks
     
  2. jcsd
  3. Jan 19, 2012 #2
    Substitute x/a = tanh θ and use the identity 1 - (tanh θ)^2 = 1/(cosh θ)^2.
     
  4. Jan 19, 2012 #3
    thanks for the tip, I managed to solve the question.
     
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