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



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

           2                                    2
        b x  m                    1     3    b x
(x (1 + ----)  (Hypergeometric2F1[-, m, -, -(----)] - 
         a                        2     2     a
 
                                          2
                        1         3    b x
      Hypergeometric2F1[-, 1 + m, -, -(----)])) / 
                        2         2     a
 
             2 m
  (b (a + b x ) )

Time to compute: 0.07 second

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