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

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

Bepaal $$$\int n^{x}\, dx$$$.

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

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

Dus,

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

Voeg de integratieconstante toe:

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

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

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