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

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

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

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