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

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

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

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