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Beliebt Rechnen >

integral of sec(x)(cos(x)+tan(x))

Lösung

\int sec (x) (cos (x) + tan (x)) d x

Lösung

x + sec (x) + C

Schritte zur Lösung

\int sec (x) (cos (x) + tan (x)) d x

Umschreiben mit Hilfe von Trigonometrie-Identitäten

= \int \frac{cos ^{2} ( x ) + sin ( x )}{cos ^{2} ( x )} d x

Multipliziere aus

\frac{cos ^{2} ( x ) + sin ( x )}{cos ^{2} ( x )} : 1 + \frac{sin ( x )}{cos ^{2} ( x )}

= \int 1 + \frac{sin ( x )}{cos ^{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 1 d x + \int \frac{sin ( x )}{cos ^{2} ( x )} d x

\int 1 d x = x

\int \frac{sin ( x )}{cos ^{2} ( x )} d x = sec (x)

= x + sec (x)

Füge eine Konstante zur Lösung hinzu

= x + sec (x) + C

Graph

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