de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral of (3-cos(x))/(sin^2(x))

Lösung

\int \frac{3 - cos ( x )}{sin ^{2} ( x )} d x

Lösung

- 3 cot (x) + csc (x) + C

Schritte zur Lösung

\int \frac{3 - cos ( x )}{sin ^{2} ( x )} d x

Multipliziere aus

\frac{3 - cos ( x )}{sin ^{2} ( x )} : \frac{3}{sin ^{2} ( x )} - \frac{cos ( x )}{sin ^{2} ( x )}

= \int \frac{3}{sin ^{2} ( x )} - \frac{cos ( x )}{sin ^{2} ( 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 \frac{3}{sin ^{2} ( x )} d x - \int \frac{cos ( x )}{sin ^{2} ( x )} d x

\int \frac{3}{sin ^{2} ( x )} d x = - 3 cot (x)

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

= - 3 cot (x) - (- csc (x))

Vereinfache

= - 3 cot (x) + csc (x)

Füge eine Konstante zur Lösung hinzu

= - 3 cot (x) + csc (x) + C

Graph

Beliebte Beispiele

integral from-8 to 0 of 1/((x-8)^2)

\int_{- 8}^{0} \frac{1}{( x - 8 ) ^{2}} d x

(dy)/(dx)=((y^2+4))/(2xy)

\frac{d y}{d x} = \frac{( y ^{2} + 4 )}{2 x y}

(dy)/(dx)=(cos(8x))/(cos(4y))

\frac{d y}{d x} = \frac{cos ( 8 x )}{cos ( 4 y )}

inverselaplace (s+3)/(s+5)

in v erse l a pl a ce \frac{s + 3}{s + 5}

integral of e^{i7x}cos(3x)

\int e^{i 7 x} cos (3 x) d x