integral of sec(t)(9sec(t)+7tan(t))

Lösung

\int sec (t) (9 sec (t) + 7 tan (t)) d t

9 tan (t) + 7 sec (t) + C

Schritte zur Lösung

\int sec (t) (9 sec (t) + 7 tan (t)) d t

Umschreiben mit Hilfe von Trigonometrie-Identitäten

= \int \frac{9 + 7 sin ( t )}{cos ^{2} ( t )} d t

Multipliziere aus

\frac{9 + 7 sin ( t )}{cos ^{2} ( t )} : \frac{9}{cos ^{2} ( t )} + \frac{7 sin ( t )}{cos ^{2} ( t )}

= \int \frac{9}{cos ^{2} ( t )} + \frac{7 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{9}{cos ^{2} ( t )} d t + \int \frac{7 sin ( t )}{cos ^{2} ( t )} d t

\int \frac{9}{cos ^{2} ( t )} d t = 9 tan (t)

\int \frac{7 sin ( t )}{cos ^{2} ( t )} d t = 7 sec (t)

= 9 tan (t) + 7 sec (t)

Füge eine Konstante zur Lösung hinzu

= 9 tan (t) + 7 sec (t) + C

in v erse l a pl a ce \frac{10}{s ^{2} + 2 s + 5}

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