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(2*(a + b*x)^(n/2)*Hypergeometric2F1[-n/2, -n/2, 1 - n/2, -(a/(b*x))])/(n*(1 + a/(b*x))^(n/2))

Integrate[(a + b*x)^(n/2)/x, x] ==
(2*(a + b*x)^(n/2)*Hypergeometric2F1[-n/2, -n/2, 1 - n/2, -(a/(b*x))])/(n*(1 + a/(b*x))^(n/2)) 

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

            n/2                   -n  -n      n
(2 (a + b x)    Hypergeometric2F1[--, --, 1 - -, 
                                  2   2       2
 
        a                a  n/2
     -(---)]) / (n (1 + ---)   )
       b x              b x
Time to compute: 0.04 second
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