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

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

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

         -2 (b + 2 c x)
---------------------------------
  2                            2
(b  - 4 a c) Sqrt[a + b x + c x ]
Time to compute: 0.06 second
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