Integralen av $$$\tan{\left(\theta \right)} \sec{\left(\theta \right)}$$$
Relaterad kalkylator: Kalkylator för bestämda och oegentliga integraler
Din inmatning
Bestäm $$$\int \tan{\left(\theta \right)} \sec{\left(\theta \right)}\, d\theta$$$.
Lösning
Integralen av $$$\tan{\left(\theta \right)} \sec{\left(\theta \right)}$$$ är $$$\int{\tan{\left(\theta \right)} \sec{\left(\theta \right)} d \theta} = \sec{\left(\theta \right)}$$$:
$${\color{red}{\int{\tan{\left(\theta \right)} \sec{\left(\theta \right)} d \theta}}} = {\color{red}{\sec{\left(\theta \right)}}}$$
Alltså,
$$\int{\tan{\left(\theta \right)} \sec{\left(\theta \right)} d \theta} = \sec{\left(\theta \right)}$$
Lägg till integrationskonstanten:
$$\int{\tan{\left(\theta \right)} \sec{\left(\theta \right)} d \theta} = \sec{\left(\theta \right)}+C$$
Svar
$$$\int \tan{\left(\theta \right)} \sec{\left(\theta \right)}\, d\theta = \sec{\left(\theta \right)} + C$$$A