$$$4 \cos{\left(x \right)}$$$ 的积分

求$$$\int 4 \cos{\left(x \right)}\, dx$$$。

对 $$$c=4$$$ 和 $$$f{\left(x \right)} = \cos{\left(x \right)}$$$ 应用常数倍法则 $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$：

$${\color{red}{\int{4 \cos{\left(x \right)} d x}}} = {\color{red}{\left(4 \int{\cos{\left(x \right)} d x}\right)}}$$

余弦函数的积分为 $$$\int{\cos{\left(x \right)} d x} = \sin{\left(x \right)}$$$：

$$4 {\color{red}{\int{\cos{\left(x \right)} d x}}} = 4 {\color{red}{\sin{\left(x \right)}}}$$

因此，

$$\int{4 \cos{\left(x \right)} d x} = 4 \sin{\left(x \right)}$$

加上积分常数：

$$\int{4 \cos{\left(x \right)} d x} = 4 \sin{\left(x \right)}+C$$

$$$\int 4 \cos{\left(x \right)}\, dx = 4 \sin{\left(x \right)} + C$$$A