Integral of $$$y \sin^{2}{\left(y \right)}$$$ with respect to $$$x$$$

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

Apply the constant rule $$$\int c\, dx = c x$$$ with $$$c=y \sin^{2}{\left(y \right)}$$$:

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

Therefore,

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

Add the constant of integration:

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

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