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(2*Sqrt[c]*(b + 2*c*x)*Sqrt[a + x*(b + c*x)] - (b^2 - 4*a*c)*Log[b + 2*c*x + 2*Sqrt[c]*Sqrt[a + x*(b + c*x)]])/(8*c^(3/2))


Integrate[Sqrt[a + b*x + c*x^2], x] ==
(2*Sqrt[c]*(b + 2*c*x)*Sqrt[a + x*(b + c*x)] - (b^2 - 4*a*c)*Log[b + 2*c*x + 2*Sqrt[c]* Sqrt[a + x*(b + c*x)]])/(8*c^(3/2))



                            2
Integrate[Sqrt[a + b x + c x ], x] == 

(2 Sqrt[c] (b + 2 c x) Sqrt[a + x (b + c x)] - 
 
      2
    (b  - 4 a c) Log[b + 2 c x + 
 
                                               3/2
       2 Sqrt[c] Sqrt[a + x (b + c x)]]) / (8 c   )

Time to compute: 0.17 second

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