Integraal van $$$r^{n}$$$ met betrekking tot $$$n$$$

De rekenmachine zal de integraal/primitieve van $$$r^{n}$$$ met betrekking tot $$$n$$$ bepalen, waarbij de stappen worden getoond.

Bepaal $$$\int r^{n}\, dn$$$.

Apply the exponential rule $$$\int{a^{n} d n} = \frac{a^{n}}{\ln{\left(a \right)}}$$$ with $$$a=r$$$:

$${\color{red}{\int{r^{n} d n}}} = {\color{red}{\frac{r^{n}}{\ln{\left(r \right)}}}}$$

Dus,

$$\int{r^{n} d n} = \frac{r^{n}}{\ln{\left(r \right)}}$$

Voeg de integratieconstante toe:

$$\int{r^{n} d n} = \frac{r^{n}}{\ln{\left(r \right)}}+C$$

$$$\int r^{n}\, dn = \frac{r^{n}}{\ln\left(r\right)} + C$$$A

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