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-(Sqrt[a + b*x]/(a*x)) + (b*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])/a^(3/2)

Integrate[1/(x^2*Sqrt[a + b*x]), x] ==
-(Sqrt[a + b*x]/(a*x)) + (b*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])/a^(3/2) 

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

                             Sqrt[a + b x]
                   b ArcTanh[-------------]
  Sqrt[a + b x]                 Sqrt[a]
-(-------------) + ------------------------
       a x                    3/2
                             a
Time to compute: 0.05 second
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