Derivation of some definite integrals

TL;DR

This paper derives numerous definite integrals from well-known tables using contour integration, providing explicit evaluations and special cases involving fundamental constants.

Contribution

It introduces a contour integration method to derive and evaluate integrals listed in classical tables, including special cases with fundamental constants.

Findings

Derived integrals from Prudnikov, Gradshteyn, and Ryzhik tables.

Evaluated special cases involving fundamental constants.

Provided explicit contour integration derivations.

Abstract

In this work derivations of definite integrals listed in Prudnikov volume I, Gradshteyn and Ryzhik and a few other tables are produced. Special cases of these integrals in terms of fundamental constants are also evaluated. The method used in these derivations is contour integration.