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Integral of (2-x^2)^{3/2} ?

  1. Nov 4, 2008 #1
    Integral of (2-x^2)^{3/2} ???

    1. The problem statement, all variables and given/known data

    I am doing an iterated integral and I am stuck at [tex]\int(2-x^2)^{3/2}dx[/tex]

    Should this be easy or did I mess up in a previous step? I think it should be easy...

    EDIT: by "easy" I am mean do I need a table? Or is it something that can be done with a substitution expediently?
  2. jcsd
  3. Nov 4, 2008 #2
    Re: Integral of (2-x^2)^{3/2} ???

    I don't think you can do that by substitution; I plugged it into mathematica just for the heck of it and it's

    [tex]\int(2-x^2)^{3/2}dx = -\frac{x\sqrt{2-x^2}(x^2-5)}{4}+\frac{3}{2}\tan^{-1}(\frac{x}{\sqrt{2}})[/tex]

    so make what you will of that. I'd just try going at it with different by parts or identities.
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