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

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

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

                   2
-ArcCot[Sqrt[-1 + x ]]
Time to compute: 0.01 second
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