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) 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

integral of ((x-2))/((x^2-4x+3)^3)

\int \frac{( x - 2 )}{( x ^{2} - 4 x + 3 ) ^{3}} d x

inverselaplace (12)/s

in v erse l a pl a ce \frac{12}{s}

integral from 0 to 3 of x-1

\int_{0}^{3} x - 1 d x

taylor f(x)= 1/x

t a y l or f (x) = \frac{1}{x}

integral from-2 to 3 of (11)/(x^4)

\int_{- 2}^{3} \frac{11}{x ^{4}} d x