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-ArcCot[Sqrt[-1 + x^4]]/2


Integrate[1/(x*Sqrt[-1 + x^4]), x] ==
-ArcCot[Sqrt[-1 + x^4]]/2



                 1
Integrate[---------------, x] == 
                       4
          x Sqrt[-1 + x ]

                   4
-ArcCot[Sqrt[-1 + x ]]
----------------------
          2

Time to compute: 0.05 second

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