I'm confused about how to solve big-oh notation problems using the definition and basic algebra. for example, a problem like this:
Prove that (x sin x + x log(2x + 4) + ((x^3 + 1)/(x^2 + 1)) is an element of big-oh(x log x).
hint:This will require both the algebraic properties of $O$ and its formal definition.
I'm thinking I can separate it into 3 parts and show each part is big-oh using limits(though I'm not sure that counts as an algebraic property) and the definition $(C,K)$?
I'd appreciate any help starting this out.