The function $h$ is defined on $\mathbb{R}$ by $$h(u) = u - [u] - 1/2$$ Is the application $u \longmapsto \dfrac{h(u)}{u+x}$ integrable on $\mathbb{R}_{+}$?
The function $h$ is defined on $\mathbb{R}$ by
$$h(u) = u - [u] - 1/2$$
Is the application $u \longmapsto \dfrac{h(u)}{u+x}$ integrable on $\mathbb{R}_{+}$?