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Homework Help: Several Integrals

  1. Mar 25, 2008 #1
    1. The problem statement, all variables and given/known data
    [tex]\int[/tex][tex]\frac{xdx}{\sqrt{1-x}}[/tex]


    2. Relevant equations

    n/a

    3. The attempt at a solution
    I tried to multiple top and bottom by the conjugate:
    [tex]\int[/tex][tex]\frac{x\sqrt{1+x}dx}{\sqrt{1-x^{2}}}[/tex]

    I tried trig substitution and u-substitution, but nothing seems to work.

    I end up with -[tex]\int[/tex]cos[tex]\theta[/tex][tex]\sqrt{1+cos\theta}[/tex]

    Can anyone help me out on this? And show steps, please? Thanks so much!
     
  2. jcsd
  3. Mar 25, 2008 #2

    nicksauce

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    If you make a substitution u = 1-x (then x = 1-u), you now have the sum of two trivial integrals.
     
  4. Mar 25, 2008 #3
    thank you so much! oh, and sorry about the double post
     
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