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Need help with integration

  1. Oct 17, 2009 #1
    1. The problem statement, all variables and given/known data
    Using the following equations,
    dX/dt = uX

    Derive the following equation:
    u0*t = (KS*YX/S + S0*YX/S + X0) * ln(X/X0) - (KS*YX/S)/(S0*YX/S + X0) * ln{(S0*YX/S + X0 - X)/(S0*YX/S)}

    2. Relevant equations
    u =u0*S/(KS + S)
    YX/S = (X - X0)/(S0 -S)


    3. The attempt at a solution
    Using the equation for YX/S, I solved for S and then plugged that and the equation for u into the equation for dx/dt. After some rearranging and use of common denominators, I have the following:

    u0*dt = (YX/S*KS + YX/S*S0 - X + X0)/{X*(YX/S - X + X0)} dx

    Integration of the left side is easy and results in u0*t but I'm still struggling with the left side.

    Can anybody please help? My calculus is a little rusty. I have to be able to show my work so using a integration calculator won't work. Thanks!
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Oct 18, 2009 #2
    I see that numerous people have viewed my post but nobody has replied. Does this mean that the problem is as difficult as I think it is? :-(
     
  4. Oct 18, 2009 #3

    LCKurtz

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    Science Advisor
    Homework Helper
    Gold Member

    I'm guessing the problem is stated so poorly nobody can figure out what the problem actually is. You give a simple DE with X in terms of t and the answer contains all kinds of other variables -- K, Y, S and "relevant equations" that don't seem to have anything to do with the original.
     
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