How can I show the following function is integrable, given that $\displaystyle \phi \in L(\mathbb{R})$??

$\displaystyle \frac{2\phi (x)(\cos (h x)-1)}{i x}$, where $\displaystyle i=\sqrt{-1}$, and h is a fixed constant.

i.e. I want to show

$\displaystyle \int_{-\infty }^{\infty } |\frac{2\phi (x)(\cos (h x)-1)}{i x}| \, dx<\infty $

any ideas on how I might go about this??