$$$\frac{1}{\sec{\left(x \right)}}$$$ 的积分

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

将被积函数用余弦表示:

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

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

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

因此，

$$\int{\frac{1}{\sec{\left(x \right)}} d x} = \sin{\left(x \right)}$$

加上积分常数：

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

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