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Derivative of an integral?

  1. Oct 8, 2009 #1
    1. The problem statement, all variables and given/known data
    Can someone help me take the derivative of the integral
    u(1/r)((d/dr)[(r)(dV/dr)])=P


    2. Relevant equations



    3. The attempt at a solution
    my attempt yields V=(Pr^2)/(2u)+C(1), which is not right. The actual answer is V=(Pr^2)/4u+C(1)ln(r)+C(2). I am having trouble finding out where the 4 and everything else comes from could someone please explain to me what is going on. Thank YOU
     
  2. jcsd
  3. Oct 8, 2009 #2
    When you first integrated, did you include your constant? If not, that might explain why you lacked the extra term upon the second integration.
     
  4. Oct 9, 2009 #3

    HallsofIvy

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    You want to find
    [tex]\frac{d}{dx}\int u(1/r)\frac{d\left(r\frac{dV}{dr}\right)}{dr}dr[/tex]?
    That, of course, is equal to
    [tex]u(1/r)\frac{d\left(r\frac{dV}{dr}\right)}{dr}[/tex]?

    Or do you mean the integral of that integral?
     
  5. Oct 9, 2009 #4

    LCKurtz

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