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$$$\cot{\left(x \right)} \csc{\left(x \right)}$$$の積分
関連する計算機: 定積分・広義積分計算機
入力内容
$$$\int \cot{\left(x \right)} \csc{\left(x \right)}\, dx$$$ を求めよ。
解答
$$$\cot{\left(x \right)} \csc{\left(x \right)}$$$ の不定積分は $$$\int{\cot{\left(x \right)} \csc{\left(x \right)} d x} = - \csc{\left(x \right)}$$$ です:
$${\color{red}{\int{\cot{\left(x \right)} \csc{\left(x \right)} d x}}} = {\color{red}{\left(- \csc{\left(x \right)}\right)}}$$
したがって、
$$\int{\cot{\left(x \right)} \csc{\left(x \right)} d x} = - \csc{\left(x \right)}$$
積分定数を加える:
$$\int{\cot{\left(x \right)} \csc{\left(x \right)} d x} = - \csc{\left(x \right)}+C$$
解答
$$$\int \cot{\left(x \right)} \csc{\left(x \right)}\, dx = - \csc{\left(x \right)} + C$$$A