How do I calculate $mathcal{L}^{-1}left[frac{s}{s^{alpha}(s^{2}+1)}right]$?

I was solving some problems of fractional calculus, and needed this intermediate result. How do I calculate $mathcal{L}^{-1}left[frac{s}{s^{alpha}(s^{2}+1)}right]$?