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(2*(a + b*x)^(1 + n/2))/(2*b + b*n)

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

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

           1 + n/2
2 (a + b x)
------------------
    2 b + b n
Time to compute: 0.02 second
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