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((a + b*x)^(1 + p)*(2*a^2 - 2*a*b*(1 + p)*x + b^2*(2 + 3*p + p^2)*x^2))/(b^3*(3 + p)*(2 + 3*p + p^2))

Integrate[x^2*(a + b*x)^p, x] ==
((a + b*x)^(1 + p)*(2*a^2 - 2*a*b*(1 + p)*x + b^2*(2 + 3*p + p^2)*x^2))/ (b^3*(3 + p)*(2 + 3*p + p^2)) 

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

          1 + p     2
((a + b x)      (2 a  - 2 a b (1 + p) x + 
 
       2             2   2
      b  (2 + 3 p + p ) x )) / 
 
    3                     2
  (b  (3 + p) (2 + 3 p + p ))
Time to compute: 0.05 second
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