de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral of (1+cos(2x))/(sin^2(2x))

Lösung

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

Lösung

\frac{1}{2} (- cot (2 x) - csc (2 x)) + C

Schritte zur Lösung

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

Wende U-Substitution an

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

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

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

Multipliziere aus

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

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

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

\int \frac{1}{sin ^{2} ( u )} d u = - cot (u)

\int \frac{cos ( u )}{sin ^{2} ( u )} d u = - csc (u)

= \frac{1}{2} (- cot (u) - csc (u))

Setze in

u = 2 x

ein

= \frac{1}{2} (- cot (2 x) - csc (2 x))

Füge eine Konstante zur Lösung hinzu

= \frac{1}{2} (- cot (2 x) - csc (2 x)) + C

Graph

Beliebte Beispiele

(\partial)/(\partial y)(x+3y)

\frac{\partial}{\partial y} (x + 3 y)

steigung (-1.3)(3.5)

s l o p e (- 1.3) (3.5)

derivative g(x)=ln^3(x)

d er i v a t i v e g (x) = ln^{3} (x)

tangent y=(5x)/(2^x),\at x=2

t an g e n t y = \frac{5 x}{2 ^{x}}, at x = 2

(\partial)/(\partial y)(ln(x^2+3y))

\frac{\partial}{\partial y} (ln (x^{2} + 3 y))