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(c + a*x^2)^(3/2 + m)/(3*a + 2*a*m)

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

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

        2 3/2 + m
(c + a x )
-----------------
   3 a + 2 a m
Time to compute: 0.03 second
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