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Beliebt Rechnen >

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

Lösung

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

Lösung

x - \frac{1}{2} ln ∣ sin (2 x) ∣ + C

Schritte zur Lösung

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

Multipliziere aus

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

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

\int 1 d x = x

\int \frac{cos ( 2 x )}{sin ( 2 x )} d x = \frac{1}{2} ln ∣ sin (2 x) ∣

= x - \frac{1}{2} ln ∣ sin (2 x) ∣

Füge eine Konstante zur Lösung hinzu

= x - \frac{1}{2} ln ∣ sin (2 x) ∣ + C

Graph

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