Stats chap 3 - primitives

$$x^{\alpha}$$

$$\frac{x^{\alpha+1}}{\alpha+1}$$

$$\frac{1}{x}$$

$$ln(\vert x\vert)$$

$$e^x$$

$$e^x$$

$$(ax+b)^{\alpha}$$

$$\frac{\left(ax+b\right)^{\alpha+1}}{\alpha\left(\alpha+1\right)}$$

$$\frac{1}{ax+b}$$

$$\frac{ln\left(\vert ax+b\vert\right)}{a}$$

$$e^{ax+b}$$

$$\frac{e^{ax+b}}{a}$$

Intégrale

\int f\left(x\right)\differentialD x=\left\lbrack F\left(x\right)\right\rbrack_{a}^{b}

$$\left\lbrack F\left(x\right)\right\rbrack_{a}^{b}$$

$$=F(b)-F(a)$$

Intégration par parties: $u\times v$

\int u^{\prime}\left(x\right)\cdot v\left(x\right)\differentialD x=\left\lbrack u\times v\right\rbrack_{a}^{b}-\int u\left(x\right)\times v^{\prime}\left(x\right)\differentialD x