# On integrals involving quotients of hyperbolic functions

## TL;DR

This paper evaluates integrals of hyperbolic function quotients over [0,∞) using hypergeometric methods, providing new results and confirming some entries in classical integral tables.

## Contribution

It introduces a hypergeometric approach to evaluate integrals involving hyperbolic functions, yielding new formulas and verifying existing ones.

## Key findings

- Derived new integral formulas involving hyperbolic functions
- Confirmed several entries in Gradshteyn and Rhyzik's integral table
- Demonstrated the effectiveness of hypergeometric methods for such integrals

## Abstract

We evaluate some integrals over $[0,\infty)$ of quotients of powers of the hyperbolic functions $\sinh x$ and $\cosh x$ using a hypergeometric approach. Some of these results appear to be new but several verify the entries in the table of integrals of Gradshteyn and Rhyzik.