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(-2*ArcTanh[Sqrt[c + a*x^n]/Sqrt[c]])/(Sqrt[c]*n)

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

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

                       n
           Sqrt[c + a x ]
-2 ArcTanh[--------------]
              Sqrt[c]
--------------------------
        Sqrt[c] n
Time to compute: 0.03 second
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