Integraal van $$$5 e x$$$

Bepaal $$$\int 5 e x\, dx$$$.

Pas de constante-veelvoudregel $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$ toe met $$$c=5 e$$$ en $$$f{\left(x \right)} = x$$$:

$${\color{red}{\int{5 e x d x}}} = {\color{red}{\left(5 e \int{x d x}\right)}}$$

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

$$5 e {\color{red}{\int{x d x}}}=5 e {\color{red}{\frac{x^{1 + 1}}{1 + 1}}}=5 e {\color{red}{\left(\frac{x^{2}}{2}\right)}}$$

Dus,

$$\int{5 e x d x} = \frac{5 e x^{2}}{2}$$

Voeg de integratieconstante toe:

$$\int{5 e x d x} = \frac{5 e x^{2}}{2}+C$$

$$$\int 5 e x\, dx = \frac{5 e x^{2}}{2} + C$$$A