Show that for all $\theta \in ] - \pi ; \pi [$, the function $f$ defined by
$$\begin{aligned}
f : ] 0 ; + \infty [ & \longrightarrow \mathbf { C } \\
t & \longmapsto \frac { t ^ { x - 1 } } { 1 + t e ^ { \mathrm { i } \theta } }
\end{aligned}$$
is defined and integrable on $] 0 ; + \infty [$, where $x$ is a fixed element of $]0;1[$.