|
|
|
|
|
|
|
|
|
|
|
|
Integral of $$$\operatorname{sech}^{2}{\left(u \right)}$$$
Related calculator: Definite and Improper Integral Calculator
Your Input
Find $$$\int \operatorname{sech}^{2}{\left(u \right)}\, du$$$.
Solution
The integral of $$$\operatorname{sech}^{2}{\left(u \right)}$$$ is $$$\int{\operatorname{sech}^{2}{\left(u \right)} d u} = \tanh{\left(u \right)}$$$:
$${\color{red}{\int{\operatorname{sech}^{2}{\left(u \right)} d u}}} = {\color{red}{\tanh{\left(u \right)}}}$$
Therefore,
$$\int{\operatorname{sech}^{2}{\left(u \right)} d u} = \tanh{\left(u \right)}$$
Add the constant of integration:
$$\int{\operatorname{sech}^{2}{\left(u \right)} d u} = \tanh{\left(u \right)}+C$$
Answer
$$$\int \operatorname{sech}^{2}{\left(u \right)}\, du = \tanh{\left(u \right)} + C$$$A