I have some problems proving that some functions are integrable. For example, if $f$ is a measurable function on $[0,\infty)$, let
$F(s) = \int_o^{\infty}\frac{f(x)}{(1+sx)^2} dx$.
How can I show that if $f(x)/x$ is integrable, then $F(s)$ is finite for almost every $s$ and that $F$ is integrable on $[0,\infty)$?
Thanks!