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

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

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