Find an upperbound as a function of $x$ for $|f_n|$

Question

$$f_n(x)=\frac{\sin(x^n)}{x^n(1+x)}$$

I want to find an upperbound for the absolute value of $f_n(x)$ that is integrable over $[0,\infty [$

I'm stuck

Answer 1

Can you think of how you might bound $|sin(x^2)|$?

What is the range of values the $sin$ function can take?

Also consider that you are working with $ x\in [0,\infty)$, using this $x$ bound on $\frac{1}{1+x}$ will give you an upper bound for that part.