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


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



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

           1 + E
a (c + b x)      (-c + b (1 + E) x)
-----------------------------------
          2             2
         b  (2 + 3 E + E )

Time to compute: 0.04 second

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