Integraal van $$$2 x y$$$ met betrekking tot $$$x$$$

Bepaal $$$\int 2 x y\, dx$$$.

Pas de constante-veelvoudregel $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$ toe met $$$c=2 y$$$ en $$$f{\left(x \right)} = x$$$:

$${\color{red}{\int{2 x y d x}}} = {\color{red}{\left(2 y \int{x d x}\right)}}$$

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

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

Dus,

$$\int{2 x y d x} = x^{2} y$$

Voeg de integratieconstante toe:

$$\int{2 x y d x} = x^{2} y+C$$

$$$\int 2 x y\, dx = x^{2} y + C$$$A