$$$3 \cos{\left(x \right)}$$$ 的積分

求$$$\int 3 \cos{\left(x \right)}\, dx$$$。

套用常數倍法則 $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$，使用 $$$c=3$$$ 與 $$$f{\left(x \right)} = \cos{\left(x \right)}$$$：

$${\color{red}{\int{3 \cos{\left(x \right)} d x}}} = {\color{red}{\left(3 \int{\cos{\left(x \right)} d x}\right)}}$$

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

$$3 {\color{red}{\int{\cos{\left(x \right)} d x}}} = 3 {\color{red}{\sin{\left(x \right)}}}$$

因此，

$$\int{3 \cos{\left(x \right)} d x} = 3 \sin{\left(x \right)}$$

加上積分常數：

$$\int{3 \cos{\left(x \right)} d x} = 3 \sin{\left(x \right)}+C$$

$$$\int 3 \cos{\left(x \right)}\, dx = 3 \sin{\left(x \right)} + C$$$A