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

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

被積分関数を余弦で表せ:

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

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

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

したがって、

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

積分定数を加える:

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

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