Module
Primitives des fonctions usuelles
- Domaine
- Analyse
- Prérequis
- Primitives et intégrales
Primitives des fonctions usuelles
Tableau Primitives des fonctions usuelles
| \(f(x)\) | \(F(x)\) | sur \(I\) |
|---|---|---|
| \(k,\,k\in\mathbb{R}\) | \(kx+C\) | \(I=\mathbb{R}\) |
| \(x^a,\,a\notin\{-1,0\}\) | \(\dfrac{x^{a+1}}{a+1}+C\) | \(I=\mathbb{R}\) si \(a\in\mathbb{N}^*\) ; \(I=]-\infty,0[\) ou \(I=]0,+\infty[\) si \(a\in\mathbb{Z}_{-}^{*}\setminus\{-1\}\) ; \(I=]0,+\infty[\) si \(a\in\mathbb{R}\setminus\mathbb{Z}\) |
| \(\dfrac{1}{x^2}\) | \(-\dfrac{1}{x}+C\) | \(I=]-\infty,0[\) ou \(I=]0,+\infty[\) |
| \(\dfrac{1}{\sqrt{x}}\) | \(2\sqrt{x}+C\) | \(I=]0,+\infty[\) |
| \(\dfrac{1}{x}\) | \(\ln\lvert x\rvert+C\) | \(I=]-\infty,0[\) ou \(I=]0,+\infty[\) |
| \(e^x\) | \(e^x+C\) | \(I=\mathbb{R}\) |
| \(e^{ax+b},\,(a,b)\in\mathbb{R}^*\times\mathbb{R}\) | \(\dfrac{1}{a}e^{ax+b}+C\) | \(I=\mathbb{R}\) |
| \(\sin x\) | \(-\cos x+C\) | \(I=\mathbb{R}\) |
| \(\cos x\) | \(\sin x+C\) | \(I=\mathbb{R}\) |
| \(\sin(ax+b),\,(a,b)\in\mathbb{R}^*\times\mathbb{R}\) | \(-\dfrac{1}{a}\cos(ax+b)+C\) | \(I=\mathbb{R}\) |
| \(\cos(ax+b),\,(a,b)\in\mathbb{R}^*\times\mathbb{R}\) | \(\dfrac{1}{a}\sin(ax+b)+C\) | \(I=\mathbb{R}\) |
| \(\dfrac{1}{\cos^2 x}=1+\tan^2 x\) | \(\tan x+C\) | \(I=] -\dfrac{\pi}{2}+k\pi,\dfrac{\pi}{2}+k\pi[,\,k\in\mathbb{Z}\) |