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(2*(a + b*x)^(1 + n/2)*(-2*a + b*(2 + n)*x))/(b^2*(2 + n)*(4 + n))

Integrate[x*(a + b*x)^(n/2), x] ==
(2*(a + b*x)^(1 + n/2)*(-2*a + b*(2 + n)*x))/ (b^2*(2 + n)*(4 + n)) 

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

           1 + n/2
2 (a + b x)        (-2 a + b (2 + n) x)
---------------------------------------
           2
          b  (2 + n) (4 + n)
Time to compute: 0.04 second
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