Analytic Logarithm Integrals on Curved Contours with Near-Machine Precision

Analytic expressions are developed for integrals over curvilinear domains where the integrands are the product of polynomial bases with natural logarithm kernels whose arguments are polynomial. These integrands occur directly in two-dimensional electrostatic integral equations and indirectly in two-dimensional electrodynamic integral equations with singularity extractions. The analytic results are validated in double precision using an arbitrary-precision math library, and near-machine precision accuracy is observed over a wide range of parameter inputs. Limitations of the analytic expressions are also presented.