\begin{propriete}[Primitives et opérations sur les fonctions]
Soient $u$ et $v$ deux fonctions dérivables sur un intervalle $I$.

\vspace{.5mm}

\begin{ltableau}{\linewidth}{3}
 \hline
 \centering Fonction &
 \centering Une primitive & 
 \centering Domaine de validité\tabularnewline
 \hline
 	\centering $f = u' + v'$ &
 	\centering $F = u + v$ &
 	\centering $x \in I$\tabularnewline
 \hline
 	\centering $f = u'u^n, n \in \mathbb{N}$ &
 	\Strut[1.5]\BotStrut[2.5] \centering $F = \dfrac{1}{n+1}u^{n+1}$ &
 	\centering $x \in I$\tabularnewline
 \hline
 	\Strut[1.8]\BotStrut[2.5] \centering $f = \dfrac{u'}{u^n}, n \in \mathbb{N}, n \geqslant 2$ &
 	\centering $F = -\,\dfrac{1}{n-1}\dfrac{1}{u^{n-1}}$ &
 	\centering $x \in I$ tel que $u(x) \neq 0$\tabularnewline
 \hline
 	\Strut[1.8]\BotStrut[2.5] \centering $f = \dfrac{u'}{u}$ &
 	\centering $F = \ln(u)$ &
 	\centering $x \in I$ tel que $u(x) > 0$\tabularnewline
 \hline
 	\Strut[1.8]\BotStrut[3] \centering $f = \dfrac{u'}{\sqrt{u}}$ &
 	\centering $F = 2\sqrt{u}$ &
 	\centering $x \in I$ tel que $u(x) > 0$\tabularnewline
 \hline
 	\centering $f = u'\text{e}^u$ &
 	\centering $F = \text{e}^u$ &
 	\centering $x \in I$\tabularnewline
 \hline
\end{ltableau}
\end{propriete}

