A conjecture of Richard Hall (Q1191744)

In this paper the author determines the behaviour of the integral \[ \int^ \infty{\sin\mu x\over (\log(bx+c)+\sin x)^ a}dx \] where \(a\) and \(b\) are positive constants, and \(c\) and \(\mu\) are real numbers. A conjecture of Hall which states that \[ \int^ \infty{\sin\mu x\over \log x+x^{-1/m}\sin x}dx \] would be convergent if \(x^{-1/m}\) were replaced by 1 for all real \(\mu\) except odd integers, has incidently been proved to be correct.