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Integrate[Sqrt[x]/(1 + x)^(7/2), x] ==
(2*x^(3/2)*(5 + 2*x))/(15*(1 + x)^(5/2))

           Sqrt[x]
Integrate[----------, x] == 
                 7/2
          (1 + x)

   3/2
2 x    (5 + 2 x)
----------------
           5/2
 15 (1 + x)