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(5*x - x*(1 + (a*x^2)/c)^(2/5)*Hypergeometric2F1[2/5, 1/2, 3/2, -((a*x^2)/c)])/(4*c*(c + a*x^2)^(2/5))

Integrate[(c + a*x^2)^(-7/5), x] ==
(5*x - x*(1 + (a*x^2)/c)^(2/5)*Hypergeometric2F1[2/5, 1/2, 3/2, -((a*x^2)/c)])/(4*c*(c + a*x^2)^(2/5)) 

                  2 -7/5
Integrate[(c + a x )    , x] == 

                 2
              a x  2/5
(5 x - x (1 + ----)    
               c
 
                                     2
                       2  1  3    a x
     Hypergeometric2F1[-, -, -, -(----)]) / 
                       5  2  2     c
 
               2 2/5
  (4 c (c + a x )   )
Time to compute: 0.07 second
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