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Math Help - Integration Problem

  1. #1
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    Integration Problem

    I'm having a lot of trouble with this question:

    \int \frac{1}{\sqrt{x^2-4x}} dx

    Can any math pros help me with it?
    Last edited by dragonic2020; January 19th 2009 at 11:47 AM.
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  2. #2
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    mr fantastic's Avatar
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    Quote Originally Posted by dragonic2020 View Post
    I'm having a lot of trouble with this question:

    \int \frac{1}{\sqrt{x^2-4x}} dx

    Can any math pros help me with it?
    = \int \frac{1}{\sqrt{(x - 2)^2 - 4}} \, dx = \frac{1}{2} \int \frac{1}{\sqrt{\frac{(x - 2)^2}{4} - 1}} \, dx .

    Now make either of the following substitutions:

    1. \cosh t = \frac{x - 2}{2} (the easy way), or

    2. \sec t = \frac{x - 2}{2} (the hard way).

    There are other fancy ways that will probably work but the above is the usual approach.
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  3. #3
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    Put x=\frac{4}{1-{{z}^{2}}} and you'll get an easy integral.
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