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Integrate[1/(x*Sqrt[-a^2 + x^n]), x] ==
(2*ArcCot[a/Sqrt[-a^2 + x^n]])/(a*n)

                 1
Integrate[----------------, x] == 
                   2    n
          x Sqrt[-a  + x ]

               a
2 ArcCot[--------------]
                2    n
         Sqrt[-a  + x ]
------------------------
          a n