$$$\frac{\cos{\left(x \right)}}{45}$$$の積分

$$$\int \frac{\cos{\left(x \right)}}{45}\, dx$$$ を求めよ。

定数倍の法則 $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$ を、$$$c=\frac{1}{45}$$$ と $$$f{\left(x \right)} = \cos{\left(x \right)}$$$ に対して適用する:

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

余弦の積分は$$$\int{\cos{\left(x \right)} d x} = \sin{\left(x \right)}$$$:

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

したがって、

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

積分定数を加える:

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

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