$$$\frac{\sin{\left(x \right)} \sec{\left(x \right)}}{\tan{\left(x \right)}}$$$の積分
関連する計算機: 定積分・広義積分計算機
入力内容
$$$\int \frac{\sin{\left(x \right)} \sec{\left(x \right)}}{\tan{\left(x \right)}}\, dx$$$ を求めよ。
解答
被積分関数を簡単化する:
$${\color{red}{\int{\frac{\sin{\left(x \right)} \sec{\left(x \right)}}{\tan{\left(x \right)}} d x}}} = {\color{red}{\int{1 d x}}}$$
$$$c=1$$$ に対して定数則 $$$\int c\, dx = c x$$$ を適用する:
$${\color{red}{\int{1 d x}}} = {\color{red}{x}}$$
したがって、
$$\int{\frac{\sin{\left(x \right)} \sec{\left(x \right)}}{\tan{\left(x \right)}} d x} = x$$
積分定数を加える:
$$\int{\frac{\sin{\left(x \right)} \sec{\left(x \right)}}{\tan{\left(x \right)}} d x} = x+C$$
解答
$$$\int \frac{\sin{\left(x \right)} \sec{\left(x \right)}}{\tan{\left(x \right)}}\, dx = x + C$$$A