Primitives

$x \mapsto a$

$\color{black}{x \mapsto ax + b}$

$\color{black}{\rm I= \mathbb R}$, $\color{black}{(a~;b) \in \mathbb R^2}$

$\color{black}{x \mapsto x^n}$

$\color{black}{\displaystyle x \mapsto \frac{x^{n+1}}{n + 1} + c}$

$\color{black}{n \in \mathbb Z\backslash\{-1\}}$, $\color{black}{c\in \mathbb R}$

Si $\color{black}{n < 0}$, $\color{black}{\rm I = \mathbb R}$

Si $\color{black}{n < 0}$, $\color{black}{\rm I = ] -\infty~; 0[}$ ou $\color{black}{]0~; +\infty[}$

$\color{black}{x \mapsto \cos(x)}$

$\color{black}{x \mapsto \sin(x) +c}$

$\color{black}{\rm I = \mathbb R}$, $\color{black}{c \in \mathbb R}$

$\color{black}{x \mapsto \cos}$
$\color{black}{(ax + b)}$

$\color{black}{\displaystyle x \mapsto \frac{1}{a}\sin}$
$\color{black}{(ax + b) + c}$

$\color{black}{\rm I = \mathbb R}$, $\color{black}{(a~;b~c)\in \mathbb R^3}$, $\color{black}{a \neq 0}$

$\color{black}{x \mapsto \sin(x)}$

$\color{black}{x \mapsto - \cos(x) + c}$

$\color{black}{\rm I = \mathbb R}$, $\color{black}{c \in \mathbb R}$

$\color{black}{x \mapsto \sin}$

$\color{black}{(ax + b)}$

$\color{black}{\displaystyle x \mapsto -\frac{1}{a}\cos}$

$\color{black}{(ax + b) + c}$

$\color{black}{\rm I = \mathbb R}$, $\color{black}{(a~;b~c)\in \mathbb R^3}$, $\color{black}{a \neq 0}$

$\color{black}{\displaystyle x \mapsto \frac{1}{x}}$

$\color{black}{x \mapsto \ln(x) + c}$

$\color{black}{\rm I = ]0~;+\infty[}$, $\color{black}{c \in \mathbb R}$

$\color{black}{x \mapsto \mathrm e^x}$

$\color{black}{x \mapsto \mathrm e^x + c}$

$\color{black}{\rm I = \mathbb R}$, $\color{black}{c \in \mathbb R}$

$\color{black}{u' \times u^n}$

$\color{black}{\displaystyle \frac{u^{n+1}}{n+1} + \rm C}$

$\color{black}{n \in \mathbb N}$ ou si $\color{black}{n \in \mathbb Z^- \backslash\{-1\}}$, $\color{black}{u(x) \neq 0}$

$\color{black}{u' \times \mathrm e^u}$

$\color{black}{\mathrm e^u+ \mathrm C}$

$\color{black}{\displaystyle \frac{u'}{u}}$

$\color{black}{\ln(u)+ \mathrm C}$

Intervalle tel que $\color{black}{u(x) > 0}$