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

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

                1
Integrate[--------------, x] == 
                     m/2
          x (a + b x)

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