  A method of deriving quadrature rules has been developed which gives nodes
and weights for a Gaussian-type rule which integrates functions of the form:
f(x,y,t) = a(x,y,t)/((x-t)^2+y^2) + b(x,y,t)/([(x-t)^2+y^2]^{1/2}) +
c(x,y,t)\log[(x-t)^2+y^2]^{1/2} + d(x,y,t), without having to explicitly
analyze the singularities of $f(x,y,t)$ or separate it into its components. The
method extends previous work on a similar technique for the evaluation of
Cauchy principal value or Hadamard finite part integrals, in the case when
$y\equiv0$. The method is tested by evaluating standard reference integrals and
its error is found to be comparable to machine precision in the best case.
