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(x*(a*c*x^2)^(m/2))/(1 + m)

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

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

        2 m/2
x (a c x )
-------------
    1 + m
Time to compute: < 0.01 second
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