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Beliebt Rechnen >

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

Lösung

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

Lösung

11 x + 12 cos (x) - sin (2 x) + C

Schritte zur Lösung

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

Multipliziere aus

(3 - 2 sin (x))^{2} : 9 - 12 sin (x) + 4 sin^{2} (x)

= \int 9 - 12 sin (x) + 4 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 9 d x - \int 12 sin (x) d x + \int 4 sin^{2} (x) d x

\int 9 d x = 9 x

\int 12 sin (x) d x = - 12 cos (x)

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

= 9 x - (- 12 cos (x)) + 2 x - sin (2 x)

Vereinfache

= 11 x + 12 cos (x) - sin (2 x)

Füge eine Konstante zur Lösung hinzu

= 11 x + 12 cos (x) - sin (2 x) + C

Graph

Beliebte Beispiele

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\int \frac{6 x ^{4} + 2 x ^{2} + 4 x + 15}{x ^{2} + 3} d x

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\int ln (y + 3) d y