  A non-local slender body approximation for slender flexible fibers in Stokes
flow can be derived, yielding an integral equation along the center lines of
the fibers that involves a slenderness parameter. The formulation contains a
so-called finite part singular integral, and can in the case of several fibers
or evaluation of the flow field require the evaluation of nearly singular
integrals.
  We introduce a numerical technique to accurately and efficiently evaluate the
finite part integral. This technique can be applied combined with any panel
based quadrature rule and will add no additional cost except for a small
precomputation of modified quadrature weights. We also show how a related
technique that was recently introduced can be applied for the evaluation of the
nearly singular integrals.
