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 n≥q≥1. 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.