$$$\csc^{2}{\left(x \right)}$$$の積分

$$$\int \csc^{2}{\left(x \right)}\, dx$$$ を求めよ。

$$$\csc^{2}{\left(x \right)}$$$ の不定積分は $$$\int{\csc^{2}{\left(x \right)} d x} = - \cot{\left(x \right)}$$$ です:

$${\color{red}{\int{\csc^{2}{\left(x \right)} d x}}} = {\color{red}{\left(- \cot{\left(x \right)}\right)}}$$

したがって、

$$\int{\csc^{2}{\left(x \right)} d x} = - \cot{\left(x \right)}$$

積分定数を加える:

$$\int{\csc^{2}{\left(x \right)} d x} = - \cot{\left(x \right)}+C$$

$$$\int \csc^{2}{\left(x \right)}\, dx = - \cot{\left(x \right)} + C$$$A