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Integrate Sqrt[x^2-a]

  1. Dec 4, 2008 #1
    Could someone show me how to integrate this. Bear in mind 'a' could be positive or negative thus i don't think we can use sqrt(a) in our answer...
  2. jcsd
  3. Dec 4, 2008 #2


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    Well if a>0, then you can have sqrt(a) in your answer...

    But for a<0 => -a>0 meaning that your integrand will become sqrt{x^2+b} where b=-a
  4. Dec 4, 2008 #3
    Shouldn't matter if it's positive or negative, the integral is still the same, imaginary or not.
  5. Dec 4, 2008 #4


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    use trig substitutions, sec or tan depending on whether a is positive or negative.
  6. Dec 5, 2008 #5

    only problem is say if I use the substitution Let x = sqrt(a)Secy the integrated result has a tany in it
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