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Homework Help: Tricky Integral?

  1. Nov 8, 2009 #1
    Tricky Integral??

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

    So the problem is to integrate this:

    {(x^2) / sqrt[(x^2) - 9] } dx

    I cannot, for the life of me, solve this problem, and I know it's not that hard. I have tried using trig substitutions x = 3 cos(theta) and x = 3 sec(theta) but for some reason, maybe a math error, it doesn't work out. Can someone compute this for me and give steps?
  2. jcsd
  3. Nov 8, 2009 #2


    Staff: Mentor

    Re: Tricky Integral??

    Your trig substitution is set up wrong. Draw a right triangle with x as the hypotenuse and 3 as the base. The altitude will be sqrt(x^2 - 9). The substitution is sec(theta) = x/3. Using this substitution should get you to [itex]27\int sec^3(\theta) d\theta[/itex]. That one requires integration by parts once or twice, if I recall correctly.
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