A direct computation of a certain family of integrals

Purpose: The authors propose a rather elementary method to compute a family of integrals on the half line, involving positive powers of sin x and negative powers of x, depending on the integer parameters (Formula presented.). Design/methodology/approach: Combinatorics, sine and cosine integral functions. Findings: The authors prove an explicit formula to evaluate sinc-type integrals. Originality/value: The proof is not present in the current literature, and it could be of interest for a large audience.