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(x*(3 + 2*x^2))/(3*(1 + x^2)^(3/2))


Integrate[(1 + x^2)^(-5/2), x] ==
(x*(3 + 2*x^2))/(3*(1 + x^2)^(3/2))



                2 -5/2
Integrate[(1 + x )    , x] == 

          2
x (3 + 2 x )
-------------
        2 3/2
3 (1 + x )

Time to compute: 0.02 second

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