A short note on a definite integral of a general form

TL;DR

This paper derives interesting definite integrals involving special functions such as Malmsten logarithm forms, reciprocal logarithm forms, and Kölbig type integrals, expanding the understanding of their properties.

Contribution

It introduces new integral formulas involving special functions, providing explicit evaluations and expanding the mathematical toolkit for such integrals.

Findings

Derived new integral formulas involving special functions

Expressed integrals in terms of known special functions

Enhanced understanding of Kölbig and related integrals

Abstract

In this note we derive some interesting definite integrals involving Malmsten logarithm forms, reciprocal logarithm forms and K\"{o}lbig type integrals in terms of special functions.