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


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



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

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

Time to compute: 0.02 second

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