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

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

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

                      2
Log[2 (x + Sqrt[-1 + x ])]
Time to compute: < 0.01 second
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