de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral of (sin^2(θ))/(cos^2(θ))

Lösung

\int \frac{sin ^{2} ( θ )}{cos ^{2} ( θ )} d θ

Lösung

tan (θ) - θ + C

Schritte zur Lösung

\int \frac{sin ^{2} ( θ )}{cos ^{2} ( θ )} d θ

Umschreiben mit Hilfe von Trigonometrie-Identitäten

= \int \frac{1 - cos ^{2} ( θ )}{cos ^{2} ( θ )} d θ

Multipliziere aus

\frac{1 - cos ^{2} ( θ )}{cos ^{2} ( θ )} : \frac{1}{cos ^{2} ( θ )} - 1

= \int \frac{1}{cos ^{2} ( θ )} - 1 d θ

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{1}{cos ^{2} ( θ )} d θ - \int 1 d θ

\int \frac{1}{cos ^{2} ( θ )} d θ = tan (θ)

\int 1 d θ = θ

= tan (θ) - θ

Füge eine Konstante zur Lösung hinzu

= tan (θ) - θ + C

Graph

Beliebte Beispiele

integral of (x-2)/(x^2+6x+13)

\int \frac{x - 2}{x ^{2} + 6 x + 13} d x

integral of (2x^2-1)/(1+x^2)

\int \frac{2 x ^{2} - 1}{1 + x ^{2}} d x

integral of (2x^2+1/3)

\int (2 x^{2} + \frac{1}{3}) d x

integral of (sqrt(x^2-5))/(x^2)

\int \frac{x ^{2} - 5}{x ^{2}} d x

integral of (sec(2θ)-csc(θ/2))

\int (sec (2 θ) - csc (\frac{θ}{2})) d θ