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

  1. Dec 15, 2008 #1
    Anyone know how to integrate this?

  2. jcsd
  3. Dec 15, 2008 #2
    Yes. Start by factoring out 1/a, then make the trig substitution [tex]x = a \sec \theta[/tex]. After simplification, you will obtain an integral in terms of secant cubed, for which there is an entire http://en.wikipedia.org/wiki/Integral_of_secant_cubed" [Broken] devoted to explaining how to integrate that. Do so, back-substitute, and simplify. Or alternatively, simply look this up in your handy table of integrals, and find that the solution is:

    << complete solution deleted by berkeman >>
    Last edited by a moderator: May 3, 2017
  4. Dec 15, 2008 #3


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    [itex]y=\sqrt{x^2-a^2}[/itex] simplifies it a bit.
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