$$$\operatorname{sech}^{2}{\left(x \right)}$$$の積分

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

$$$\operatorname{sech}^{2}{\left(x \right)}$$$ の不定積分は $$$\int{\operatorname{sech}^{2}{\left(x \right)} d x} = \tanh{\left(x \right)}$$$ です:

$${\color{red}{\int{\operatorname{sech}^{2}{\left(x \right)} d x}}} = {\color{red}{\tanh{\left(x \right)}}}$$

したがって、

$$\int{\operatorname{sech}^{2}{\left(x \right)} d x} = \tanh{\left(x \right)}$$

積分定数を加える:

$$\int{\operatorname{sech}^{2}{\left(x \right)} d x} = \tanh{\left(x \right)}+C$$

$$$\int \operatorname{sech}^{2}{\left(x \right)}\, dx = \tanh{\left(x \right)} + C$$$A