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Integraal van $$$\operatorname{csch}^{2}{\left(x \right)}$$$
Gerelateerde rekenmachine: Rekenmachine voor bepaalde en oneigenlijke integralen
Uw invoer
Bepaal $$$\int \operatorname{csch}^{2}{\left(x \right)}\, dx$$$.
Oplossing
De integraal van $$$\operatorname{csch}^{2}{\left(x \right)}$$$ is $$$\int{\operatorname{csch}^{2}{\left(x \right)} d x} = - \coth{\left(x \right)}$$$:
$${\color{red}{\int{\operatorname{csch}^{2}{\left(x \right)} d x}}} = {\color{red}{\left(- \coth{\left(x \right)}\right)}}$$
Dus,
$$\int{\operatorname{csch}^{2}{\left(x \right)} d x} = - \coth{\left(x \right)}$$
Voeg de integratieconstante toe:
$$\int{\operatorname{csch}^{2}{\left(x \right)} d x} = - \coth{\left(x \right)}+C$$
Antwoord
$$$\int \operatorname{csch}^{2}{\left(x \right)}\, dx = - \coth{\left(x \right)} + C$$$A