Find a limit of an integral $\lim_{n \to \infty} \int_0^{\infty} \frac{1}{1+x^n}$
It seems quite easy, but the problem is that I cannot find a dominating function when $x>1$

Let
$$
g(x) = \begin{cases}
1 &: 0\leq x\leq 1 \\
\frac{1}{1+x^2} &: x > 1
\end{cases}
$$
For $n\geq 3$, each integrand is dominated by $g$.
