I need to check whether or not $\displaystyle \frac{1}{x} \in {L}^p$

$\displaystyle \int_{0}^{1} \frac{1}{|x|^p} ~dx = \frac{1}{-p + 1} x^{-p + 1}|_{0}^1$

because this integral divergent, so $\displaystyle \frac{1}{x} \notin {L}^p$

is it correct??

thanks for any comment and suggestion