$$$\frac{1}{\sec{\left(x \right)}}$$$の積分

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

被積分関数を余弦で表せ:

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

余弦の積分は$$$\int{\cos{\left(x \right)} d x} = \sin{\left(x \right)}$$$:

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

したがって、

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

積分定数を加える:

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

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