Let $f:[0,\infty)\to\mathbb{R}$ be continuous and $\lim\_{x\to\infty}f(x)=L$. Show that
$$\int\_0^{\infty}\frac{f(ax)-f(bx)}{x}dx=[f(0)-L]\ln\frac{b}{a}$$
where $0<a<b$.

I don't even know how to start.