How to prove the following $\Theta$notation If the following function is given: $f(n)=n^2+ n \ln(n)+1$. 
How do  you prove the $\Theta$ notation?
I assume that is must be $\Theta$($n^2$). 
But I'm not sure how to solve it.

It's clear that
$$n^2\le f(n),\quad \forall n\ge1$$
so
$$n^2=\mathcal O(f(n))$$
moreover we have
$$\ln n\le n,\quad \forall n\ge1$$
so
$$f(n)\le 3n^2 ,\quad \forall n\ge1$$
and then
$$f(n)=\mathcal O(n^2)$$
so we get
$$f(n)=\Theta(n^2)$$
