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

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

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

           Sqrt[a + b x]
-2 ArcTanh[-------------]
              Sqrt[a]
-------------------------
         Sqrt[a]
Time to compute: 0.02 second
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