I need your help in finding the Fourier Sine Transform of (x^(n-1))
Just to clarify:
$\displaystyle \mathcal{F}_{s}[x^{n-1}]:=\sqrt{\frac{2}{\pi}}\int_{0}^{\infty}x^{n-1}\sin(sx)\,dx.$
Correct? Or is it
$\displaystyle \mathcal{F}_{s}[x^{n-1}]:=\frac{\sqrt{2}}{\pi}\int_{0}^{\infty}x^{n-1}\sin(sx)\,dx?$
Assuming one of these forms is correct (I'm guessing the first), what thoughts have you had so far?
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.