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Beliebt Rechnen >

integral of sec(t)(5sec(t)+4tan(t))

Lösung

\int sec (t) (5 sec (t) + 4 tan (t)) d t

Lösung

5 tan (t) + 4 sec (t) + C

Schritte zur Lösung

\int sec (t) (5 sec (t) + 4 tan (t)) d t

Umschreiben mit Hilfe von Trigonometrie-Identitäten

= \int \frac{5 + 4 sin ( t )}{cos ^{2} ( t )} d t

Multipliziere aus

\frac{5 + 4 sin ( t )}{cos ^{2} ( t )} : \frac{5}{cos ^{2} ( t )} + \frac{4 sin ( t )}{cos ^{2} ( t )}

= \int \frac{5}{cos ^{2} ( t )} + \frac{4 sin ( t )}{cos ^{2} ( t )} d t

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} ( t )} d t + \int \frac{4 sin ( t )}{cos ^{2} ( t )} d t

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

\int \frac{4 sin ( t )}{cos ^{2} ( t )} d t = 4 sec (t)

= 5 tan (t) + 4 sec (t)

Füge eine Konstante zur Lösung hinzu

= 5 tan (t) + 4 sec (t) + C

Graph

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