On evaluation of the integral \( int _0^{\infty} x^{-a}(1 - \sin^b x/x^b) \, dx\)

Abstract

In the present paper we provide a closed-form evaluation of the integral

\[ int _0^{\infty} x^{-a} \left( 1 - \frac{\sin^b x}{x^b} \right) \, dx\]  where \[a \in (0,3) \]  and \[b\in \mathbb{N}_0\]