Solving Integral using substitution [More help needed]

I have been having a trouble with this problem:

X / (4X^2+1)^2 dx<-------This is an integral that I have to solve using substitution

This is what I did.

u=4x^2+1

u'=8x

du/8=dx

So then I went back to original problem and plugged that in and got.

1/8*(1/(1/3)u^3) I got that from taking the anti derivative of x^2

I plugged u back in and got

1/8 * 1/(1/3)(4x^2+1)^3

after i simplify i get:

1/ ((8/3)(64x^6+1))

I would appreciate it if someone could tell me where i messed up. Thanks!