Integraal van $$$y \sin^{2}{\left(y \right)}$$$ met betrekking tot $$$x$$$

Bepaal $$$\int y \sin^{2}{\left(y \right)}\, dx$$$.

Pas de constantenregel $$$\int c\, dx = c x$$$ toe met $$$c=y \sin^{2}{\left(y \right)}$$$:

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

Dus,

$$\int{y \sin^{2}{\left(y \right)} d x} = x y \sin^{2}{\left(y \right)}$$

Voeg de integratieconstante toe:

$$\int{y \sin^{2}{\left(y \right)} d x} = x y \sin^{2}{\left(y \right)}+C$$

$$$\int y \sin^{2}{\left(y \right)}\, dx = x y \sin^{2}{\left(y \right)} + C$$$A