Improper Integrals Involving Powers of Inverse Trigonometric and Hyperbolic Functions

Abstract

Three classes of improper integrals involving higher powers of arctanh, arctan, and arcsin are examined using the recursive approach. Numerous explicit formulae are established, which evaluate these integrals in terms of π, ln2, the Riemann zeta function, and the Dirichlet beta function.

Keywords

• integration by parts
• trigonometric functions
• Fourier series
• Riemann zeta function
• Dirichlet beta function