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-(Sqrt[2]*ArcTanh[Sqrt[2]*Sqrt[x]])

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

                  1
Integrate[------------------, x] == 
          Sqrt[x] (-1 + 2 x)

-(Sqrt[2] ArcTanh[Sqrt[2] Sqrt[x]])
Time to compute: 0.08 second
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