Here is the problem.
Where has the integral come from?
Read this: Elliptic Integral of the First Kind -- from Wolfram MathWorld
The original problem is
In electrostatics, a charge distribution over a curve induces an electric potential in
The charge distribution is given by the charge density , and the induced electric potential at
is given by
where denotes the distance between and .
Consider a uniform charge density on the set
Find the potential at points on the x-axis, |x|>1.
And by using the parametrization and
I got the previous integral.
And how could the integral in the link you gave solve this integral?
I thought that might be the case. These sorts of integrals often occur in those contexts. You need to re-arrange your integral to recognise the elliptic-integral form you have. Evaluate your integral here: http://www.wolframalpha.com/ to see where you need to head.