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(x^2*(30*a^2 + 40*a*b*x + 15*(b^2 + 2*a*c)*x^2 + 24*b*c*x^3 + 10*c^2*x^4))/60

Integrate[x*(a + b*x + c*x^2)^2, x] ==
(x^2*(30*a^2 + 40*a*b*x + 15*(b^2 + 2*a*c)*x^2 + 24*b*c*x^3 + 10*c^2*x^4))/60 

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

  2      2                   2           2
(x  (30 a  + 40 a b x + 15 (b  + 2 a c) x  + 
 
              3       2  4
      24 b c x  + 10 c  x )) / 60
Time to compute: 0.02 second
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