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% ########################### MES PARAMETRES ##############################################################
\def\monnumero{ }
\def\madate{ Mars 2026 }
\def\maclasse{ T\textsuperscript{erm} Spé maths}
% ########################### MES PARAMETRES ##############################################################

% en-tête
\lhead{\footnotesize{\textsf{Lycée Schuman Perret\\ \madate}}} %gauche
\chead{\textsf{\textcolor{red}{\textbf{\textsc{SERIE D'EXERCICES SUR L'INTEGRATION}}}}} %centre
\rhead{\footnotesize{\textsf{\maclasse}}}%droit
%pied de page
\rfoot{\scriptsize{\textsf{Page~\thepage{}~sur~\pageref{LastPage}}}}
\lfoot{ {\scriptsize{\textsf{\textsc{Stéphane Le Méteil }}}}}


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\begin{document}
%\everymath{\displaystyle}
%\doublespacing



\exo 
\begin{multicols}{2}

\begin{align*}
	1.\ & \int_{0}^{1} (3x^2 + 2x + 1)\,dx \\
	2.\ & \int_{1}^{2} (5x^4 - 3x^2)\,dx \\
	3.\ & \int_{1}^{e} \left(\frac{1}{x} + 4x^3\right)\,dx \\
	4.\ & \int_{0}^{1} (7e^x - 2)\,dx \\
	5.\ & \int_{0}^{\pi} (6\cos x + 3x)\,dx \\
\end{align*}	
\begin{align*}	
	6.\ & \int_{0}^{1} (4\sin x - x^2)\,dx \\
	7.\ & \int_{1}^{2} \left(2x + \frac{3}{x^2}\right)\,dx \\
	8.\ & \int_{0}^{\ln 2} (8 - 5e^x)\,dx \\
	9.\ & \int_{0}^{\pi/2} (x^3 + 2\cos x)\,dx \\
	10.\ & \int_{1}^{3} \left(\frac{5}{x} - 4\sin x\right)\,dx
\end{align*}
\end{multicols}

\exo 
\begin{multicols}{2}

\begin{align*}
	1.\ & \int_{0}^{1} (2x)(x^2 + 1)^3\,dx \\
	2.\ & \int_{0}^{\pi/2} \cos x\,(\sin x)^4\,dx \\
	3.\ & \int_{1}^{2} \frac{2x}{x^2 + 1}\,dx \\
	4.\ & \int_{0}^{1} e^{x^2}\cdot 2x\,dx \\
	5.\ & \int_{0}^{\pi} \sin x\,(1 - \cos x)^2\,dx
\end{align*}

\begin{align*}
	1.\ & \int_{0}^{1} (2x+1)(x+3)\,dx \\
	2.\ & \int_{-1}^{2} (x-2)(3x+4)\,dx \\
	3.\ & \int_{0}^{2} (4x-1)(2x+5)\,dx \\
	4.\ & \int_{1}^{3} (x+1)(x-1)\,dx \\
	5.\ & \int_{0}^{1} (3x+2)(5x-1)\,dx
\end{align*}

\end{multicols}

\exo

\begin{align*}
	1.\ & \int_{0}^{1} \frac{2x+1}{x+1}\,dx \\
	2.\ & \int_{1}^{2} \frac{3x-1}{x+2}\,dx \\
	3.\ & \int_{0}^{2} \frac{4x+5}{2x+1}\,dx \\
	4.\ & \int_{1}^{3} \frac{x+3}{x-1}\,dx \\
	5.\ & \int_{0}^{1} \frac{5x-2}{3x+1}\,dx
\end{align*}

\end{document} 
