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Integraal van $$$- \sec^{2}{\left(x \right)}$$$
Gerelateerde rekenmachine: Rekenmachine voor bepaalde en oneigenlijke integralen
Uw invoer
Bepaal $$$\int \left(- \sec^{2}{\left(x \right)}\right)\, dx$$$.
Oplossing
Pas de constante-veelvoudregel $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$ toe met $$$c=-1$$$ en $$$f{\left(x \right)} = \sec^{2}{\left(x \right)}$$$:
$${\color{red}{\int{\left(- \sec^{2}{\left(x \right)}\right)d x}}} = {\color{red}{\left(- \int{\sec^{2}{\left(x \right)} d x}\right)}}$$
De integraal van $$$\sec^{2}{\left(x \right)}$$$ is $$$\int{\sec^{2}{\left(x \right)} d x} = \tan{\left(x \right)}$$$:
$$- {\color{red}{\int{\sec^{2}{\left(x \right)} d x}}} = - {\color{red}{\tan{\left(x \right)}}}$$
Dus,
$$\int{\left(- \sec^{2}{\left(x \right)}\right)d x} = - \tan{\left(x \right)}$$
Voeg de integratieconstante toe:
$$\int{\left(- \sec^{2}{\left(x \right)}\right)d x} = - \tan{\left(x \right)}+C$$
Antwoord
$$$\int \left(- \sec^{2}{\left(x \right)}\right)\, dx = - \tan{\left(x \right)} + C$$$A