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^2(x)

Lösung

\int sec (x) \cdot tan^{2} (x) d x

Lösung

\frac{1}{2} sec (x) tan (x) - \frac{1}{2} ln ∣ tan (x) + sec (x) ∣ + C

Schritte zur Lösung

\int sec (x) tan^{2} (x) d x

Umschreiben mit Hilfe von Trigonometrie-Identitäten

= \int sec (x) (- 1 + sec^{2} (x)) d x

Multipliziere aus

sec (x) (- 1 + sec^{2} (x)) : - sec (x) + sec^{3} (x)

= \int - sec (x) + sec^{3} (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 sec (x) d x + \int sec^{3} (x) d x

\int sec (x) d x = ln ∣ tan (x) + sec (x) ∣

\int sec^{3} (x) d x = \frac{1}{2} sec (x) tan (x) + \frac{1}{2} ln ∣ tan (x) + sec (x) ∣

= - ln ∣ tan (x) + sec (x) ∣ + \frac{1}{2} sec (x) tan (x) + \frac{1}{2} ln ∣ tan (x) + sec (x) ∣

Vereinfache

- ln ∣ tan (x) + sec (x) ∣ + \frac{1}{2} sec (x) tan (x) + \frac{1}{2} ln ∣ tan (x) + sec (x) ∣ : \frac{1}{2} sec (x) tan (x) - \frac{1}{2} ln ∣ tan (x) + sec (x) ∣

= \frac{1}{2} sec (x) tan (x) - \frac{1}{2} ln ∣ tan (x) + sec (x) ∣

Füge eine Konstante zur Lösung hinzu

= \frac{1}{2} sec (x) tan (x) - \frac{1}{2} ln ∣ tan (x) + sec (x) ∣ + C

Graph

Beliebte Beispiele

derivative 3xe^{-2x}

d er i v a t i v e 3 x e^{- 2 x}

derivative G(r)=sqrt(r)+\sqrt[7]{r}

d er i v a t i v e G (r) = r + 7 r

derivative x*sqrt(x)

d er i v a t i v e x \cdot x

integral of sqrt(5+8x)

\int 5 + 8 x d x

3x-8ysqrt(x^2+1)(dy)/(dx)=0,y(0)=6

3 x - 8 y x^{2} + 1 \frac{d y}{d x} = 0, y (0) = 6