Integral of $$$\sin{\left(x_{0} \right)}$$$

Find $$$\int \sin{\left(x_{0} \right)}\, dx_{0}$$$.

The integral of the sine is $$$\int{\sin{\left(x_{0} \right)} d x_{0}} = - \cos{\left(x_{0} \right)}$$$:

$${\color{red}{\int{\sin{\left(x_{0} \right)} d x_{0}}}} = {\color{red}{\left(- \cos{\left(x_{0} \right)}\right)}}$$

Therefore,

$$\int{\sin{\left(x_{0} \right)} d x_{0}} = - \cos{\left(x_{0} \right)}$$

Add the constant of integration:

$$\int{\sin{\left(x_{0} \right)} d x_{0}} = - \cos{\left(x_{0} \right)}+C$$

$$$\int \sin{\left(x_{0} \right)}\, dx_{0} = - \cos{\left(x_{0} \right)} + C$$$A