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


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



             n
            x
Integrate[-------, x] == 
                2
          -a + x

                                                 2
   1 + n                      1 + n      1 + n  x
  x      Hypergeometric2F1[1, -----, 1 + -----, --]
                                2          2    a
-(-------------------------------------------------)
                      a (1 + n)

Time to compute: 0.04 second

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