Integraal van $$$e r^{3}$$$

Bepaal $$$\int e r^{3}\, dr$$$.

Pas de constante-veelvoudregel $$$\int c f{\left(r \right)}\, dr = c \int f{\left(r \right)}\, dr$$$ toe met $$$c=e$$$ en $$$f{\left(r \right)} = r^{3}$$$:

$${\color{red}{\int{e r^{3} d r}}} = {\color{red}{e \int{r^{3} d r}}}$$

Pas de machtsregel $$$\int r^{n}\, dr = \frac{r^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ toe met $$$n=3$$$:

$$e {\color{red}{\int{r^{3} d r}}}=e {\color{red}{\frac{r^{1 + 3}}{1 + 3}}}=e {\color{red}{\left(\frac{r^{4}}{4}\right)}}$$

Dus,

$$\int{e r^{3} d r} = \frac{e r^{4}}{4}$$

Voeg de integratieconstante toe:

$$\int{e r^{3} d r} = \frac{e r^{4}}{4}+C$$

$$$\int e r^{3}\, dr = \frac{e r^{4}}{4} + C$$$A