Exploring Explicit Definite Integral Formulae with Trigonometric and Hyperbolic Functions

Abstract

Making use of integration by parts and variable replacement methods, we derive some interesting explicit definite integral formulae involving trigonometric or hyperbolic functions, whose results are expressed in terms of Catalan’s constant, Dirichlet’s beta function, and Riemann’s zeta function, as well as π in the denominator.

Keywords

• integral
• Catalan’s constant
• Dirichlet’s beta function
• Riemann’s zeta function