Asymptotic notation question (logarithms) I am working through some problems and I have come across one I do not understand. Could someone clarify why 
$$2x^3 + 3x^2\log(x) + 7x + 1$$
is  $O(x^3\log(x))$ for $x>0$? 
I guess I am missing some sort of knowledge to be able to answer this question :(

if f(x) = $2x^3 + 3x^2\log(x) + 7x + 1$, f(x) = $x^3$$(2 + \frac{3\log(x)}{x} + \frac{7}{x^2} + \frac{1}{x^3})$. Then if x approaches the infinity, ($\frac{3\log(x)}{x} + \frac{7}{x^2} + \frac{1}{x^3}$) is negligible comparing to $x^3$.
And, if $f(x)$ = $2x^3 + 3x^3\log(x) + 7x + 1$, f(x) = $x^3log(x)$$(\frac{2}{log(x)} + 3 + \frac{7}{x^2} + \frac{1}{x^3})$. Then if x approaches the infinity, ($3+ \frac{7}{x^2} + \frac{1}{x^3}$) is negligible comparing to $x^3log(x)$.
