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Beliebt Rechnen >

integral of (cos(2x))/(sin^4(x))

Lösung

\int \frac{cos ( 2 x )}{sin ^{4} ( x )} d x

Lösung

- \frac{1}{3} cot^{3} (x) + cot (x) + C

Schritte zur Lösung

\int \frac{cos ( 2 x )}{sin ^{4} ( x )} d x

Umschreiben mit Hilfe von Trigonometrie-Identitäten

= \int \frac{cos ^{2} ( x ) - sin ^{2} ( x )}{sin ^{4} ( x )} d x

Multipliziere aus

\frac{cos ^{2} ( x ) - sin ^{2} ( x )}{sin ^{4} ( x )} : \frac{cos ^{2} ( x )}{sin ^{4} ( x )} - \frac{1}{sin ^{2} ( x )}

= \int \frac{cos ^{2} ( x )}{sin ^{4} ( x )} - \frac{1}{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{cos ^{2} ( x )}{sin ^{4} ( x )} d x - \int \frac{1}{sin ^{2} ( x )} d x

\int \frac{cos ^{2} ( x )}{sin ^{4} ( x )} d x = - \frac{cot ^{3} ( x )}{3}

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

= - \frac{cot ^{3} ( x )}{3} - (- cot (x))

Vereinfache

- \frac{cot ^{3} ( x )}{3} - (- cot (x)) : - \frac{1}{3} cot^{3} (x) + cot (x)

= - \frac{1}{3} cot^{3} (x) + cot (x)

Füge eine Konstante zur Lösung hinzu

= - \frac{1}{3} cot^{3} (x) + cot (x) + C

Graph

Beliebte Beispiele

integral of-3/(5tsqrt(25t^2-49))

\int - \frac{3}{5 t 25 t ^{2} - 49} d t

integral of 1/(x^2+6x+50)

\int \frac{1}{x ^{2} + 6 x + 50} d x

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

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

integral of 1/(sqrt(9x+4))

\int \frac{1}{9 x + 4} d x

integral of 1/(x^{sqrt(3))}

\int \frac{1}{x ^{3}} d x