de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

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

Lösung

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

Lösung

sec (x) + x + C

Schritte zur Lösung

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

Umschreiben mit Hilfe von Trigonometrie-Identitäten

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

Multipliziere aus

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

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

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

\int 1 d x = x

= sec (x) + x

Füge eine Konstante zur Lösung hinzu

= sec (x) + x + C

Graph

Beliebte Beispiele

derivative of (4x^{ln(4x)})

\frac{d}{d x} ((4 x)^{l n (4 x)})

limit as x approaches 6 of 4/(x-6)

x \to 6 lim (\frac{4}{x - 6})

taylor 9ln(5-8x^2)

t a y l or 9 ln (5 - 8 x^{2})

integral of 3tcos(2t)

\int 3 t cos (2 t) d t

limit as x approaches 8 of (|8-x|)/(8-x)

x \to 8 lim (\frac{∣ 8 - x ∣}{8 - x})