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

Lösung

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

\frac{1}{5} tan (5 t) + \frac{1}{5} sec (5 t) + C

Schritte zur Lösung

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

Multipliziere aus

sec (5 t) (sec (5 t) + tan (5 t)) : sec^{2} (5 t) + sec (5 t) tan (5 t)

= \int sec^{2} (5 t) + sec (5 t) tan (5 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 sec^{2} (5 t) d t + \int sec (5 t) tan (5 t) d t

\int sec^{2} (5 t) d t = \frac{1}{5} tan (5 t)

\int sec (5 t) tan (5 t) d t = \frac{1}{5} sec (5 t)

= \frac{1}{5} tan (5 t) + \frac{1}{5} sec (5 t)

Füge eine Konstante zur Lösung hinzu

= \frac{1}{5} tan (5 t) + \frac{1}{5} sec (5 t) + C

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