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(-2*(b + 2*c*x)*(b^2 - 8*b*c*x - 4*c*(3*a + 2*c*x^2)))/(3*(b^2 - 4*a*c)^2*(a + x*(b + c*x))^(3/2))


Integrate[(a + b*x + c*x^2)^(-5/2), x] ==
(-2*(b + 2*c*x)*(b^2 - 8*b*c*x - 4*c*(3*a + 2*c*x^2)))/(3*(b^2 - 4*a*c)^2* (a + x*(b + c*x))^(3/2))



                        2 -5/2
Integrate[(a + b x + c x )    , x] == 

                 2                             2
-2 (b + 2 c x) (b  - 8 b c x - 4 c (3 a + 2 c x ))
--------------------------------------------------
           2         2                  3/2
       3 (b  - 4 a c)  (a + x (b + c x))

Time to compute: 0.13 second

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