Definite Integrals Involving Combinations of Powers and Logarithmic Functions of Complicated Arguments Expressed in Terms of the Hurwitz Zeta Function

Abstract

In this manuscript, the authors derive closed formula for definite integrals of combinations of powers and logarithmic functions of complicated arguments and express these integrals in terms of the Hurwitz zeta functions. These derivations are then expressed in terms of fundamental constants, elementary, and special functions. A summary of the results is produced in the form of a table of definite integrals for easy referencing by readers.