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


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



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

             Sqrt[b]
  ArcTan[---------------]
                      2
         Sqrt[-b + a x ]
-(-----------------------)
          Sqrt[b]

Time to compute: 0.04 second

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