I’m currently operating with the following integral:

∫u′(t)(1−u(t))2dt

But I notice that

ddtu(t)1−u(t)=u′(t)(1−u(t))2

and

ddt11−u(t)=u′(t)(1−u(t))2

It seems that both solutions are possible, but that seems to contradict the uniqueness of Riemann’s Integral.

So the questions are:

Which one of them is the correct integral?- If both are correct, why the solution is not unique?
- The pole at u(t)=1 has something to say?

**Answer**

It is not really a contradiction, since difference of the two functions is constant:

11−u(t)−u(t)1−u(t)=1−u(t)1−u(t)=1.

(Derivative of a constant function is zero. Primitive function is determined uniquely up to a constant.)

**Attribution***Source : Link , Question Author : Dargor , Answer Author : Martin Sleziak*