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Stuck on the following integral

  1. Aug 25, 2006 #1
    Hi, I am kinda stuck on the following integral:


    [tex]\int\sqrt{\frac{1+x}{1-x}}dx[/tex]

    any hints?
     
  2. jcsd
  3. Aug 25, 2006 #2

    TD

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    If you let

    [tex]
    y^2 = \frac{{1 + x}}{{1 - x}} \Leftrightarrow x = \frac{{y^2 - 1}}{{y^2 + 1}}
    [/tex]

    The integral will become fraction of rationals, losing the square root.
     
  4. Aug 25, 2006 #3
    so are you saying to substitute that for x?
     
  5. Aug 25, 2006 #4
    or by making this substitution, the square root will be taken away
     
  6. Aug 25, 2006 #5
    Or you could do the trig substitution [tex]x = \sin\theta[/tex]
     
  7. Aug 25, 2006 #6

    TD

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    Yes, use that substitution to lose the square root.

    I already solved for x as well, which allows you to easily find dx in terms of dy by differentiating both sides.
     
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