Prove that this integral with exponent with whole part is convergent

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How can i prove that this integral is convergent?

$$ \int_{\vert\xi\vert\geq 1} \vert\xi\vert ^{-2\left[ \frac{n}{2}\right] -2} d\xi $$

I thought to use polar coordinates but i don't know how to work with $ \left[ \frac{n}{2}\right] $. Can anyone help me?