\begin{exercice*}
Réduire chacune des expressions suivantes (on ne demande pas de les calculer) :
\begin{enumerate}
 \item $\displaystyle{\int_0^1} (\text{e}^{x^2}-1)\,\mathrm{d}x
 			+ \displaystyle{\int_0^1} \mathrm{d}x
 			+ \displaystyle{\int_1^2} \text{e}^{x^2}\,\mathrm{d}x$ \vspace{2mm}
 
 \item $\displaystyle{\int_4^6} \dfrac{1}{\ln(x)}\,\mathrm{d}x
 			+ \displaystyle{\int_{3}^4} \dfrac{1}{\ln(x)}\,\mathrm{d}x$ \vspace{2mm}
 
 \item $\displaystyle{\int_0^1} \dfrac{1}{1+x^2}\,\mathrm{d}x
 			- \displaystyle{\int_0^{-2}} \dfrac{1}{1+x^2}\,\mathrm{d}x$ \vspace{2mm}
 
 \item $\displaystyle{\int_0^{\frac{\pi}{2}}} \cos(t^2)\,\mathrm{d}t
 			+ \displaystyle{\int_{\frac{\pi}{2}}^{\pi}} \cos(u^2)\,\mathrm{d}u$ \vspace{2mm}
 
 \item $\displaystyle{\int_0^1} \dfrac{1}{1+\text{e}^x}\,\mathrm{d}x
 			- \displaystyle{\int_3^1} \mathrm{d}u
 			+ \displaystyle{\int_3^1} \dfrac{\text{e}^t}{1+\text{e}^t}\,\mathrm{d}t $ \vspace{2mm}
 
 \item $\displaystyle{\sum_{k=1}^{100} \int_k^{k+1}} \dfrac{1}{x}\,\mathrm{d}x$
\end{enumerate}
\begin{corrige}
\begin{colenumerate}{2}
 \item $\displaystyle{\int_0^2} \text{e}^{x^2} \mathrm{d}x$
 \item $\displaystyle{\int_3^6} \dfrac{1}{\ln(x)} \mathrm{d}x$
 \item $\displaystyle{\int_{-2}^1} \dfrac{1}{1+x^2} \mathrm{d}x$
 \item $\displaystyle{\int_0^{\pi}} \cos(t^2) \mathrm{d}t$
 \item $\displaystyle{\int_0^3} \dfrac{1}{1+\text{e}^x} \mathrm{d}x$
 \item $\displaystyle{\int_1^{101}} \dfrac{1}{x} \mathrm{d}x$
\end{colenumerate}
\end{corrige}
\end{exercice*}

