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