Formulaire important – Primitives

$$ \begin{array}{|c|c|} \hline \text { Fonction } f & \text { Primitive } F \\ \hline k \in \mathbb{R} & k x+C \\ \hline x^n, \; n \in \mathbb{R}\,\backslash \, \{-1\} & \frac{x^{n+1}}{n+1}+C \\ \hline \sin x & -\cos x+C \\ \hline \cos x & \sin x+C \\ \hline e^x & e^x+C \\ \hline \dfrac{1}{x} & \ln \lvert x \rvert + C \\ \hline e^{ax}, \; a\in \mathbb{R} & \dfrac{1}{a} e^{ax}+C \\ \hline \frac{1}{\sqrt{x}} & 2 \sqrt{x}+C \\ \hline u^{\prime}(x) u^n(x),\, n \in \mathbb{R}^{\ast} \; \backslash \; \{-1\} & \frac{u^{n+1}(x)}{n+1}+C \\ \hline \frac{u^{\prime}(x)}{\sqrt{u(x)}} & 2 \sqrt{u(x)}+C \\ \hline \frac{u^{\prime}(x)}{u(x)} & \ln |u(x)|+C \\ \hline u^{\prime}(x) e^{u(x)} & e^{u(x)}+C \\ \hline u^{\prime}(x) \cos (u(x)) & \sin (u(x))+C \\ \hline u^{\prime}(x) \sin (u(x)) & -\cos (u(x))+C \\ \hline \end{array} $$