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September 9th, 2019, 01:41 PM   #1
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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.
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September 9th, 2019, 03:47 PM   #2
SDK
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Its hard to tell some of your $u$'s from $x$'s. Is this the integral?
\[ \int \frac{dx}{\sum\limits_{i = 0}^u \binom{u}{i} x^i (1-x)^{u-i} - ux} \]
Assuming this is the case and that $u$ is an integer, then the denominator of your integral is actually just $1-ux$ which makes the integral
\[ \int \frac{dx}{1 - ux} \]
and I presume you can solve this easily.
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