I want to establish a Big-O estimate for the following:
$(n! + 2^{n+3})(111n^3 + 15\log(n^{201} +1))$
Would the following be correct?
$n! = O(n^{n})$
$2^{n+3}=O(2^{n+3})$
$111n^{3}=O(n^{3})$
$15\log(n^{201} +1)= O(15\log n^{201})$
Therefore the dominant term appears to derive from $(n!)\cdot(111n^{3})$ which would give us $O(n^{n+3})$. Would this be correct?