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Beliebt Rechnen >

integral of sec(x)(5sec(x)+9tan(x))

Lösung

\int sec (x) (5 sec (x) + 9 tan (x)) d x

Lösung

5 tan (x) + 9 sec (x) + C

Schritte zur Lösung

\int sec (x) (5 sec (x) + 9 tan (x)) d x

Umschreiben mit Hilfe von Trigonometrie-Identitäten

= \int \frac{5 + 9 sin ( x )}{cos ^{2} ( x )} d x

Multipliziere aus

\frac{5 + 9 sin ( x )}{cos ^{2} ( x )} : \frac{5}{cos ^{2} ( x )} + \frac{9 sin ( x )}{cos ^{2} ( x )}

= \int \frac{5}{cos ^{2} ( x )} + \frac{9 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 \frac{5}{cos ^{2} ( x )} d x + \int \frac{9 sin ( x )}{cos ^{2} ( x )} d x

\int \frac{5}{cos ^{2} ( x )} d x = 5 tan (x)

\int \frac{9 sin ( x )}{cos ^{2} ( x )} d x = 9 sec (x)

= 5 tan (x) + 9 sec (x)

Füge eine Konstante zur Lösung hinzu

= 5 tan (x) + 9 sec (x) + C

Graph

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