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Help me with this simple integral.

  1. Aug 9, 2012 #1
    1. The problem statement, all variables and given/known data

    Find:

    2. Relevant equations

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

    3. The attempt at a solution

    I tried to use u substitution with u=1-x but it did work.
     
  2. jcsd
  3. Aug 9, 2012 #2
    bump :)


    im really sorry, im new here. Please excuse my actions.
    where can i find the rules to read them?
     
    Last edited: Aug 9, 2012
  4. Aug 9, 2012 #3

    LCKurtz

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    The moderators will likely slap your wrist for bumping within an hour of posting if they see it. I might try something like ##x=\sin^2\theta## and see what happens.
     
  5. Aug 9, 2012 #4

    tiny-tim

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    Hi XtremePhysX! :smile:

    Try integrating by parts, or a trig substitution. :wink:
     
  6. Aug 9, 2012 #5
    I found it =)

    I used x=sin^2theta

    and the answer is [tex] sin^{-1}\sqrt{x}-\frac{sin2(sin^{-1}\sqrt{x})}{2} [/tex]


    how do i simplify it now?
     
  7. Aug 9, 2012 #6

    tiny-tim

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    instead of using sin2θ, write it as 2sinθcosθ :smile:

    (but when you've done all that, start again and try it with integration by parts :wink:)
     
  8. Aug 9, 2012 #7
    [tex]sin^{-1}\sqrt{x}-\frac{2sin(sin^{-1}\sqrt{x})cos(sin^{-1}\sqrt{x})}{2}=sin^{-1}\sqrt{x}-\frac{2(\sqrt{x})cos(sin^{-1}\sqrt{x})}{2}=sin^{-1}\sqrt{x}-\frac{2(\sqrt{x})cos(\sqrt{1-x})}{2}[/tex]

    Is this right?
     
  9. Aug 9, 2012 #8

    LCKurtz

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    No. Call ##\theta = \arcsin({\sqrt x})##. You have ##\theta - \sin\theta \cos\theta## which is equal to ##\theta - \sqrt x \sqrt{1-\sin^2\theta}=\arcsin\sqrt x-\sqrt x \sqrt{1-x}##, which you can verify is correct by differentiating it.
     
  10. Aug 10, 2012 #9

    tiny-tim

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    (just got up :zzz:)

    in other words cos(sin-1√x) = √(1 - x)

    (because if y = sin-1√x, then √x = siny so x = sin2y so 1 - x = cos2y, so cosy = √(1 - x) :wink:)
     
  11. Aug 10, 2012 #10

    berkeman

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    I see you edited your post after the premature bump. Yes, please do not bump your post after just an hour -- the PF rules specify that you must wait at least 24 hours before making a single bump post.

    EDIT -- And the Rules link is at the top of every PF page.
     
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