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{\Large Tableau de dérivées et primitives calculées par {\itshape\color{frouge}\textbf{Maxima}}}\\[1cm]


\begin{tabular}{|c|c|c|}\hline
Fonctions & Dérivées & Primitives \\\hline
\(f(x)\) & \(f'(x)\) & \(\int f(x)\,\dd x\) \\\hline
\(x^3\) & \(3\,x^2\) & \(\frac{x^4}{4} + \lambda\) \\\hline
\(e^{a\,x}\) & \(a\,e^{a\,x}\) & \(\frac{e^{a\,x}}{a} + \lambda\) \\\hline
\(\log x\) & \(\frac{1}{x}\) & \(x\,\log x-x + \lambda\) \\\hline
\(\sin x\) & \(\cos x\) & \(-\cos x + \lambda\) \\\hline
\(\cos x\) & \(-\sin x\) & \(\sin x + \lambda\) \\\hline
\(\tan x\) & \(\sec ^2x\) & \(\log \sec x + \lambda\) \\\hline
\(\cot x\) & \(-\csc ^2x\) & \(\log \sin x + \lambda\) \\\hline
\(\arccos x\) & \(-\frac{1}{\sqrt{1-x^2}}\) & \(x\,\arccos x-\sqrt{1-x^2} + \lambda\) \\\hline
\(\arcsin x\) & \(\frac{1}{\sqrt{1-x^2}}\) & \(x\,\arcsin x+\sqrt{1-x^2} + \lambda\) \\\hline
\(\arctan x\) & \(\frac{1}{x^2+1}\) & \(x\,\arctan x-\frac{\log \left(x^2+1\right)}{2} + \lambda\) \\\hline
\(\frac{x}{\sqrt{1-x^2}}\) & \(-\frac{1}{\left(x-1\right)\,\left(x+1\right)\,\sqrt{1-x^2}}\) & \(-\sqrt{1-x^2} + \lambda\) \\\hline
\(\frac{\sin x}{\cos x+1}\) & \(\frac{1}{\cos x+1}\) & \(-\log \left(\cos x+1\right) + \lambda\) \\\hline
\(\frac{\cos x}{\sin x+1}\) & \(-\frac{1}{\sin x+1}\) & \(\log \left(\sin x+1\right) + \lambda\) \\\hline
\(\frac{1}{e^{x}+e^ {- x }}\) & \(-\frac{e^{x}-e^ {- x }}{\left(e^{x}+e^ {- x }\right)^2}\) & \(\arctan e^{x} + \lambda\) \\\hline
\(\frac{1}{e^{x}-e^ {- x }}\) & \(-\frac{e^{x}+e^ {- x }}{\left(e^{x}-e^ {- x }\right)^2}\) & \(\frac{\log \left(e^{x}-1\right)}{2}-\frac{\log \left(e^{x}+1\right)
 }{2} + \lambda\) \\\hline
\end{tabular}

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