September 9th, 2019, 01:41 PM  #1 
Newbie Joined: Sep 2019 From: india Posts: 1 Thanks: 0  Idea to solve this integration
I was trying to solve a differential equation that I defined to study the dynamics of a system. Meanwhile, I encounter integration. The integration is shown in the image below. I tried some solutions but I am failed to get a solution. In one solution, I took "x" common from the denominator terms and then apply a partial method to solve the equation. But that does not work. I request the members of this forum to give me at least an intuition to how can I solve this integration. Thanks a lot.

September 9th, 2019, 03:47 PM  #2 
Senior Member Joined: Sep 2016 From: USA Posts: 645 Thanks: 408 Math Focus: Dynamical systems, analytic function theory, numerics 
Its hard to tell some of your $u$'s from $x$'s. Is this the integral? \[ \int \frac{dx}{\sum\limits_{i = 0}^u \binom{u}{i} x^i (1x)^{ui}  ux} \] Assuming this is the case and that $u$ is an integer, then the denominator of your integral is actually just $1ux$ which makes the integral \[ \int \frac{dx}{1  ux} \] and I presume you can solve this easily. 

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