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



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

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

Time to compute: 0.17 second

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