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-((x^(1 - m)*Sqrt[a + b*x]*Hypergeometric2F1[-1/2, 1 - m, 2 - m, -((b*x)/a)])/((-1 + m)*Sqrt[(a + b*x)/a]))


Integrate[Sqrt[a + b*x]/x^m, x] ==
-((x^(1 - m)*Sqrt[a + b*x]*Hypergeometric2F1[-1/2, 1 - m, 2 - m, -((b*x)/a)])/ ((-1 + m)*Sqrt[(a + b*x)/a]))



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

    1 - m
-((x      Sqrt[a + b x] 
 
                          1                   b x
      Hypergeometric2F1[-(-), 1 - m, 2 - m, -(---)])\
                          2                    a
 
                      a + b x
     / ((-1 + m) Sqrt[-------]))
                         a

Time to compute: 0.05 second

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