|
|
|
|
|
|
|
|
|
|
|
|
Integral von $$$\sqrt{2} \tan{\left(x \right)} \sec{\left(x \right)}$$$
Verwandter Rechner: Rechner für bestimmte und uneigentliche Integrale
Ihre Eingabe
Bestimme $$$\int \sqrt{2} \tan{\left(x \right)} \sec{\left(x \right)}\, dx$$$.
Lösung
Wende die Konstantenfaktorregel $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$ mit $$$c=\sqrt{2}$$$ und $$$f{\left(x \right)} = \tan{\left(x \right)} \sec{\left(x \right)}$$$ an:
$${\color{red}{\int{\sqrt{2} \tan{\left(x \right)} \sec{\left(x \right)} d x}}} = {\color{red}{\sqrt{2} \int{\tan{\left(x \right)} \sec{\left(x \right)} d x}}}$$
Das Integral von $$$\tan{\left(x \right)} \sec{\left(x \right)}$$$ ist $$$\int{\tan{\left(x \right)} \sec{\left(x \right)} d x} = \sec{\left(x \right)}$$$:
$$\sqrt{2} {\color{red}{\int{\tan{\left(x \right)} \sec{\left(x \right)} d x}}} = \sqrt{2} {\color{red}{\sec{\left(x \right)}}}$$
Daher,
$$\int{\sqrt{2} \tan{\left(x \right)} \sec{\left(x \right)} d x} = \sqrt{2} \sec{\left(x \right)}$$
Fügen Sie die Integrationskonstante hinzu:
$$\int{\sqrt{2} \tan{\left(x \right)} \sec{\left(x \right)} d x} = \sqrt{2} \sec{\left(x \right)}+C$$
Antwort
$$$\int \sqrt{2} \tan{\left(x \right)} \sec{\left(x \right)}\, dx = \sqrt{2} \sec{\left(x \right)} + C$$$A