Find the $α$ values $(α ∈ R)$ by which the integral below is convergent.
$\int^{+∞}_{-∞} |x|^{-α}arctan(\frac{x}{x^4+1})dx$
Since we know that the integral of an odd function from $-a$ to $a$ is always equal to zero, I thought that this specific integral converges for every $α$. Is this correct? I even tried to approximate this function to $\frac{1}{|x|^α}$, since we know that $-1≤arctan≤1$, so it results that the integral converges for $α>1$. Is it that easy, or am I missing something?