A note on an integral by Grigorii Mikhailovich Fichtenholz

TL;DR

This paper derives a definite integral involving logarithmic, power, and polynomial functions expressed through the Lerch function, providing a useful reference table for researchers.

Contribution

It introduces a new integral expression involving the Lerch function and compiles a reference table for practical use.

Findings

Derived a new integral involving logarithmic and polynomial functions

Expressed the integral in terms of the Lerch function

Provided a reference table of integrals for researchers

Abstract

In this manuscript, the author derived a definite integral involving the logarithmic function, function of powers and polynomials in terms of the Lerch function. A summary of the results is produced in the form of a table of definite integrals for easy referencing by readers.