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Integrate[(a + b*x + c*x^2)^(-1 - n), x] ==
(2^(-2 - n)*(-b + Sqrt[b^2 - 4*a*c] - 2*c*x)* ((b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c])^ (1 + n)*(a + x*(b + c*x))^(-1 - n)* Hypergeometric2F1[-n, 1 + n, 1 - n, (-b + Sqrt[b^2 - 4*a*c] - 2*c*x)/ (2*Sqrt[b^2 - 4*a*c])])/(c*n)



                        2 -1 - n
Integrate[(a + b x + c x )      , x] == 

  -2 - n             2
(2       (-b + Sqrt[b  - 4 a c] - 2 c x) 
 
               2
     b + Sqrt[b  - 4 a c] + 2 c x 1 + n
    (----------------------------)      
                 2
           Sqrt[b  - 4 a c]
 
                     -1 - n
    (a + x (b + c x))       
 
    Hypergeometric2F1[-n, 1 + n, 1 - n, 
 
                2
     -b + Sqrt[b  - 4 a c] - 2 c x
     -----------------------------]) / (c n)
                  2
          2 Sqrt[b  - 4 a c]

Time to compute: 0.45 second

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