Give the simplified tilde notation of each of the following formulas, and give the order of growth of each.

n $($n $1)($n $2)/24$

$($n $2)($lg n$)($lg n $+2)$

n $(4$n $+1)$ n$^2$

n $($n$^2+1)/2+$ n lg n

lg $(($n $1)($n$^2)($n $2))^3$