Integraal van $$$e x^{29}$$$

Bepaal $$$\int e x^{29}\, dx$$$.

Pas de constante-veelvoudregel $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$ toe met $$$c=e$$$ en $$$f{\left(x \right)} = x^{29}$$$:

$${\color{red}{\int{e x^{29} d x}}} = {\color{red}{e \int{x^{29} d x}}}$$

Pas de machtsregel $$$\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ toe met $$$n=29$$$:

$$e {\color{red}{\int{x^{29} d x}}}=e {\color{red}{\frac{x^{1 + 29}}{1 + 29}}}=e {\color{red}{\left(\frac{x^{30}}{30}\right)}}$$

Dus,

$$\int{e x^{29} d x} = \frac{e x^{30}}{30}$$

Voeg de integratieconstante toe:

$$\int{e x^{29} d x} = \frac{e x^{30}}{30}+C$$

$$$\int e x^{29}\, dx = \frac{e x^{30}}{30} + C$$$A