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Beliebt Rechnen >

integral of (sin^2(2x)+sin(2x))

Lösung

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

Lösung

\frac{1}{2} (x - \frac{1}{4} sin (4 x)) - \frac{1}{2} cos (2 x) + C

Schritte zur Lösung

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

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

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

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

Füge eine Konstante zur Lösung hinzu

= \frac{1}{2} (x - \frac{1}{4} sin (4 x)) - \frac{1}{2} cos (2 x) + C

Graph

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