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(x^(1 + m)*Sqrt[1 + x^2/a^2]*Hypergeometric2F1[1/2, (1 + m)/2, (3 + m)/2, -(x^2/a^2)])/((1 + m)*Sqrt[a^2 + x^2])

Integrate[x^m/Sqrt[a^2 + x^2], x] ==
(x^(1 + m)*Sqrt[1 + x^2/a^2]*Hypergeometric2F1[1/2, (1 + m)/2, (3 + m)/2, -(x^2/a^2)])/ ((1 + m)*Sqrt[a^2 + x^2]) 

                m
               x
Integrate[-------------, x] == 
                2    2
          Sqrt[a  + x ]

                  2
  1 + m          x                     1  1 + m
(x      Sqrt[1 + --] Hypergeometric2F1[-, -----, 
                  2                    2    2
                 a
 
               2
     3 + m    x                      2    2
     -----, -(--)]) / ((1 + m) Sqrt[a  + x ])
       2       2
              a
Time to compute: 0.07 second
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