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Integrate[x/(a + b*x + c*x^2)^(3/2), x] ==
(4*a + 2*b*x)/((b^2 - 4*a*c)*Sqrt[a + x*(b + c*x)])

                   x
Integrate[-------------------, x] == 
                        2 3/2
          (a + b x + c x )

           4 a + 2 b x
----------------------------------
  2
(b  - 4 a c) Sqrt[a + x (b + c x)]