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Beliebt Rechnen >

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

Lösung

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

Lösung

- cot (x) - tan (x) + C

Schritte zur Lösung

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

Umschreiben mit Hilfe von Trigonometrie-Identitäten

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

Multipliziere aus

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

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

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

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

= - cot (x) - tan (x)

Füge eine Konstante zur Lösung hinzu

= - cot (x) - tan (x) + C

Graph

Beliebte Beispiele

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

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

integral of 1/(x^2+2x+4)

\int \frac{1}{x ^{2} + 2 x + 4} d x

integral of (x+5)/(x^2-6x+13)

\int \frac{x + 5}{x ^{2} - 6 x + 13} d x

integral of (3x^4+3x^2+1)/(x^2+1)

\int \frac{3 x ^{4} + 3 x ^{2} + 1}{x ^{2} + 1} d x

integral of x/(sqrt(1+5x))

\int \frac{x}{1 + 5 x} d x