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

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

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

                                  2
Log[2 (a x + Sqrt[a] Sqrt[-b + a x ])]
--------------------------------------
               Sqrt[a]
Time to compute: 0.04 second
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