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



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

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

Time to compute: 0.13 second

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