$$$\frac{1}{\csc{\left(x \right)}}$$$ 的積分

求$$$\int \frac{1}{\csc{\left(x \right)}}\, dx$$$。

用正弦表示被積函數:

$${\color{red}{\int{\frac{1}{\csc{\left(x \right)}} d x}}} = {\color{red}{\int{\sin{\left(x \right)} d x}}}$$

正弦函數的積分為 $$$\int{\sin{\left(x \right)} d x} = - \cos{\left(x \right)}$$$：

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

因此，

$$\int{\frac{1}{\csc{\left(x \right)}} d x} = - \cos{\left(x \right)}$$

加上積分常數：

$$\int{\frac{1}{\csc{\left(x \right)}} d x} = - \cos{\left(x \right)}+C$$

$$$\int \frac{1}{\csc{\left(x \right)}}\, dx = - \cos{\left(x \right)} + C$$$A