Difficult Integral used in solution to Laplace equation for flow

[Troy]

Hi. I am having trouble solving the attached integral.

. . . . .$\displaystyle \displaystyle f(t)\, =\, \int\,$$\displaystyle \dfrac{x\, -\, x(t)}{\left(x\, -\, x(t)\right)^2\, +\, \left(y\, -\, y(t)\right)^2}\, dt$

. . . . .\(\displaystyle \mbox{where }\, \dfrac{dx}{dt}\, =\, \cos(\theta)\, \mbox{ and }\, \dfrac{dy}{dt}\, =\, \sin(\theta)\)

Its a part of a larger integral used in the solution to the Laplace equation for flow. My understanding is that x and y are constants for the given integral bounds, and the solution should make use of the fact that X(t) and Y(t) are linear functions of t. Any help will be greatly appreciated.