# Need help with integration

1. Oct 17, 2009

### staceybiomed

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. Oct 18, 2009

### staceybiomed

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? :-(

3. Oct 18, 2009

### LCKurtz

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.