I have a problem with the integration in the following.
Given a function $f(x,y)$ and a region $R$ in the $x-y$ plane, \begin{equation} F(y)=\int_{l_0}^{L_0}\frac{1}{x}f(x,y)dx, \end{equation} where \begin{equation} f(x,y) = [1-\mathscr{H}(y-bx)] \left ( \frac{1}{bx} - \frac{1}{x} \right ) + [\mathscr{H}(y-bx)-\mathscr{H}(y-L_0)] \left ( \frac{1}{y} - \frac{1}{x} \right ), \end{equation} and $\mathscr{H}$ is the Heaviside function and $l_0 \ll y < L_0$.
The answer is \begin{equation} F(y) = \frac{-\ln{b}}{y} - \frac{1}{bL_0}. \end{equation}
I'm not sure whether to approach this. Any helps to get me started would be greatly appreciated.