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Beliebt Rechnen >

integral of (sec(x)+tan(x))^2

Lösung

\int (sec (x) + tan (x))^{2} d x

Lösung

- x + 2 tan (x) + 2 sec (x) + C

Schritte zur Lösung

\int (sec (x) + tan (x))^{2} d x

Multipliziere aus

(sec (x) + tan (x))^{2} : sec^{2} (x) + 2 sec (x) tan (x) + tan^{2} (x)

= \int sec^{2} (x) + 2 sec (x) tan (x) + tan^{2} (x) d x

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int sec^{2} (x) d x + \int 2 sec (x) tan (x) d x + \int tan^{2} (x) d x

\int sec^{2} (x) d x = tan (x)

\int 2 sec (x) tan (x) d x = 2 sec (x)

\int tan^{2} (x) d x = - x + tan (x)

= tan (x) + 2 sec (x) - x + tan (x)

Vereinfache

= - x + 2 tan (x) + 2 sec (x)

Füge eine Konstante zur Lösung hinzu

= - x + 2 tan (x) + 2 sec (x) + C

Graph

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