I need your help in finding the Fourier Sine Transform of (x^(n-1))
See here. I don't know if the link I posted will get you the "Allow More Time" option, but you'll need to click that, if it doesn't give you the answer right away. You'll note the restrictions on n in the final result, as well as the restriction on s. Mathematica doesn't give an answer if those restrictions aren't met. I suspect the integral may not actually exist in that situation.