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Integrate 1/(x^2-a^2)

  1. Mar 31, 2012 #1
    1. The problem statement, all variables and given/known data

    [itex]\int \frac{dx}{x^2-a^2}[/itex]

    2. Relevant equations

    3. The attempt at a solution

    I've reached the answer, [itex]\frac{1}{2a} ln |\frac{x-a}{x+a}| + C[/itex] , using partial fractions, but my professor asks for the work using substitution. Now I know how to do this when there's a radical in the denominator, but would this also be a substitution [itex]x=asec(\theta)[/itex]?
  2. jcsd
  3. Mar 31, 2012 #2


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    Try [itex]x=a\cosh u[/itex]
  4. Mar 31, 2012 #3


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    Hello qw3x. Welcome to PF !

    [itex]x=asec(\theta)[/itex] should work fine. I think that leads to integrating csc(θ) .
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