Show that, for all $x \in \mathbb { R } _ { + } ^ { * }$, the function $\left\lvert\, \begin{array} { r l l } \mathbb { R } _ { + } ^ { * } & \rightarrow & \mathbb { R } \\ t & \mapsto & \left( \mathrm { e } ^ { t } - 1 \right) ^ { 2 } \end{array} \quad \frac { \mathrm { e } ^ { - t } } { t } \right.$ is integrable on $\left. ] 0 , x \right]$.