  Cable-like bodies play a key role in many interdisciplinary systems but are
hard to simulate. Asymptotic theories, called slender-body theories, are
effective but apply in specific regimes and can be hard to extend beyond
leading order. In this letter we develop an exact slender-body-like theory for
the surface traction of cable-like bodies in viscous flow. This theory
expresses the traction as a series of solutions to a well-behaved
one-dimensional Fredholm integral equation of the second kind. This process can
be simply generalised to other systems.
