Integral of $$$\frac{\sin{\left(x \right)}}{34}$$$

Find $$$\int \frac{\sin{\left(x \right)}}{34}\, dx$$$.

Apply the constant multiple rule $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$ with $$$c=\frac{1}{34}$$$ and $$$f{\left(x \right)} = \sin{\left(x \right)}$$$:

$${\color{red}{\int{\frac{\sin{\left(x \right)}}{34} d x}}} = {\color{red}{\left(\frac{\int{\sin{\left(x \right)} d x}}{34}\right)}}$$

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

$$\frac{{\color{red}{\int{\sin{\left(x \right)} d x}}}}{34} = \frac{{\color{red}{\left(- \cos{\left(x \right)}\right)}}}{34}$$

Therefore,

$$\int{\frac{\sin{\left(x \right)}}{34} d x} = - \frac{\cos{\left(x \right)}}{34}$$

Add the constant of integration:

$$\int{\frac{\sin{\left(x \right)}}{34} d x} = - \frac{\cos{\left(x \right)}}{34}+C$$

$$$\int \frac{\sin{\left(x \right)}}{34}\, dx = - \frac{\cos{\left(x \right)}}{34} + C$$$A