$$$\frac{\cos{\left(\theta \right)}}{1312}$$$の積分

$$$\int \frac{\cos{\left(\theta \right)}}{1312}\, d\theta$$$ を求めよ。

定数倍の法則 $$$\int c f{\left(\theta \right)}\, d\theta = c \int f{\left(\theta \right)}\, d\theta$$$ を、$$$c=\frac{1}{1312}$$$ と $$$f{\left(\theta \right)} = \cos{\left(\theta \right)}$$$ に対して適用する:

$${\color{red}{\int{\frac{\cos{\left(\theta \right)}}{1312} d \theta}}} = {\color{red}{\left(\frac{\int{\cos{\left(\theta \right)} d \theta}}{1312}\right)}}$$

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

$$\frac{{\color{red}{\int{\cos{\left(\theta \right)} d \theta}}}}{1312} = \frac{{\color{red}{\sin{\left(\theta \right)}}}}{1312}$$

したがって、

$$\int{\frac{\cos{\left(\theta \right)}}{1312} d \theta} = \frac{\sin{\left(\theta \right)}}{1312}$$

積分定数を加える:

$$\int{\frac{\cos{\left(\theta \right)}}{1312} d \theta} = \frac{\sin{\left(\theta \right)}}{1312}+C$$

$$$\int \frac{\cos{\left(\theta \right)}}{1312}\, d\theta = \frac{\sin{\left(\theta \right)}}{1312} + C$$$A