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


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



                     1
Integrate[-----------------------, x] == 
          Sqrt[a + b x] (c + d x)

           Sqrt[d] Sqrt[a + b x]
-2 ArcTanh[---------------------]
            Sqrt[-(b c) + a d]
---------------------------------
   Sqrt[d] Sqrt[-(b c) + a d]

Time to compute: 0.06 second

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