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

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

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

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

したがって、

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

積分定数を加える:

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

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