Integraal van $$$\frac{e^{x}}{4}$$$

Bepaal $$$\int \frac{e^{x}}{4}\, dx$$$.

Pas de constante-veelvoudregel $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$ toe met $$$c=\frac{1}{4}$$$ en $$$f{\left(x \right)} = e^{x}$$$:

$${\color{red}{\int{\frac{e^{x}}{4} d x}}} = {\color{red}{\left(\frac{\int{e^{x} d x}}{4}\right)}}$$

De integraal van de exponentiële functie is $$$\int{e^{x} d x} = e^{x}$$$:

$$\frac{{\color{red}{\int{e^{x} d x}}}}{4} = \frac{{\color{red}{e^{x}}}}{4}$$

Dus,

$$\int{\frac{e^{x}}{4} d x} = \frac{e^{x}}{4}$$

Voeg de integratieconstante toe:

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

$$$\int \frac{e^{x}}{4}\, dx = \frac{e^{x}}{4} + C$$$A