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