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

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

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

         1 + p
(a + b x)      (-a + b (1 + p) x)
---------------------------------
        2
       b  (1 + p) (2 + p)
Time to compute: 0.03 second
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