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(Sqrt[1 - x^(-2)]*x*(Sqrt[-1 + x^2] + ArcTan[1/Sqrt[-1 + x^2]]))/Sqrt[-1 + x^2]


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



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

           -2                2
(Sqrt[1 - x  ] x (Sqrt[-1 + x ] + 
 
                   1                       2
      ArcTan[-------------])) / Sqrt[-1 + x ]
                        2
             Sqrt[-1 + x ]

Time to compute: 0.04 second

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