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Homework Help: Integral involving square root -need help

  1. Mar 21, 2009 #1
    1. The problem statement, all variables and given/known data

    integrate sqrt(1-x^-2/3)^1/2.

    2. Relevant equations

    3. The attempt at a solution

    The only thing I can think of is u substitution with u = 1 - x^-2/3. Obviously this cannot work because du differs by more than just a constant.

    I guess I need to somehow factor this equation but I do not know how. I think I can pull out an x^1/3 or something but I'm not sure. Any help would be appreciated.
  2. jcsd
  3. Mar 21, 2009 #2
    Whenever you see stuff like that in the square root, always think "Trig Substitution"!

    Hint: 1-sin(x)^2 = cos(x)^2.
  4. Mar 21, 2009 #3


    User Avatar
    Homework Helper

    Do you mean


    or do you mean (as you've written)
  5. Mar 21, 2009 #4
    the first one
  6. Mar 21, 2009 #5


    Staff: Mentor

    I'm not sure that trig substitution is the way to go in this problem. Trig substitution is a viable alternative for integrals that involve
    [tex]\sqrt{a^2 + x^2}[/tex]
    [tex]\sqrt{a^2 - x^2}[/tex]
    [tex]\sqrt{x^2 - a^2}[/tex]

    Maybe it can be made to work in the OP's problem, but I don't see it.
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