Integraal van $$$39 x^{21}$$$

Bepaal $$$\int 39 x^{21}\, dx$$$.

Pas de constante-veelvoudregel $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$ toe met $$$c=39$$$ en $$$f{\left(x \right)} = x^{21}$$$:

$${\color{red}{\int{39 x^{21} d x}}} = {\color{red}{\left(39 \int{x^{21} d x}\right)}}$$

Pas de machtsregel $$$\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ toe met $$$n=21$$$:

$$39 {\color{red}{\int{x^{21} d x}}}=39 {\color{red}{\frac{x^{1 + 21}}{1 + 21}}}=39 {\color{red}{\left(\frac{x^{22}}{22}\right)}}$$

Dus,

$$\int{39 x^{21} d x} = \frac{39 x^{22}}{22}$$

Voeg de integratieconstante toe:

$$\int{39 x^{21} d x} = \frac{39 x^{22}}{22}+C$$

$$$\int 39 x^{21}\, dx = \frac{39 x^{22}}{22} + C$$$A