Integral of $$$\frac{\cos{\left(x \right)}}{45}$$$

Find $$$\int \frac{\cos{\left(x \right)}}{45}\, dx$$$.

Apply the constant multiple rule $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$ with $$$c=\frac{1}{45}$$$ and $$$f{\left(x \right)} = \cos{\left(x \right)}$$$:

$${\color{red}{\int{\frac{\cos{\left(x \right)}}{45} d x}}} = {\color{red}{\left(\frac{\int{\cos{\left(x \right)} d x}}{45}\right)}}$$

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

$$\frac{{\color{red}{\int{\cos{\left(x \right)} d x}}}}{45} = \frac{{\color{red}{\sin{\left(x \right)}}}}{45}$$

Therefore,

$$\int{\frac{\cos{\left(x \right)}}{45} d x} = \frac{\sin{\left(x \right)}}{45}$$

Add the constant of integration:

$$\int{\frac{\cos{\left(x \right)}}{45} d x} = \frac{\sin{\left(x \right)}}{45}+C$$

$$$\int \frac{\cos{\left(x \right)}}{45}\, dx = \frac{\sin{\left(x \right)}}{45} + C$$$A