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