$$$1 - \sin{\left(x \right)}$$$ 的積分

求$$$\int \left(1 - \sin{\left(x \right)}\right)\, dx$$$。

逐項積分：

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

配合 $$$c=1$$$，應用常數法則 $$$\int c\, dx = c x$$$：

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

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

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

因此，

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

加上積分常數：

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

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