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Confusing Integral!

  1. Sep 29, 2011 #1
    1. The problem statement, all variables and given/known data

    int[x/((L/2)+d-x)^2] * the integral of x over [(L over 2 + d - x) all squared]*


    2. Relevant equations
    Integral chart



    3. The attempt at a solution
    I have done this so many ways with so many different answers. Could somebody who is without a doubt sure of the answer please respond because this integral is driving me INSANE!
     
  2. jcsd
  3. Sep 29, 2011 #2
    You can't have x in the upper limit and as an integration dummy variable.
     
  4. Sep 29, 2011 #3
    Not following.
     
  5. Sep 29, 2011 #4
    Your dummy variable is x, your upper limit contains x.
     
  6. Sep 29, 2011 #5

    SammyS

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    Is this the integral?

    [itex]\displaystyle \int\frac{x}{((L/2)+d-x)^2}\ dx[/itex]
     
  7. Sep 29, 2011 #6
    Yes, that is the integral.
     
  8. Sep 29, 2011 #7

    SammyS

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    To simplify things, Let A = (L/2) + d .

    Your integral becomes: [itex]\displaystyle \int\frac{x}{(A-x)^2}\ dx[/itex]

    Notice the (A - x)2 = (x - A)2.

    Use the substitution: u = x - A .
     
  9. Sep 30, 2011 #8
    No, use the substitution:

    [tex]
    u = (x - A)^{2}
    [/tex]
     
  10. Sep 30, 2011 #9
    No unique substitution, but Sammy's substation is easier to work with
     
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