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Beliebt Rechnen >

integral of cos(3x-2pi)cos(x+pi)

Lösung

\int cos (3 x - 2 π) cos (x + π) d x

Lösung

- cos (3 x - 2 π) sin (x) - \frac{3}{2} (- \frac{1}{4} sin (4 x) + \frac{1}{2} sin (2 x)) + C

Schritte zur Lösung

\int cos (3 x - 2 π) cos (x + π) d x

Wende die partielle Integration an

= - cos (3 x - 2 π) sin (x) - \int 3 sin (3 x) sin (x) d x

\int 3 sin (3 x) sin (x) d x = \frac{3}{2} (- \frac{1}{4} sin (4 x) + \frac{1}{2} sin (2 x))

= - cos (3 x - 2 π) sin (x) - \frac{3}{2} (- \frac{1}{4} sin (4 x) + \frac{1}{2} sin (2 x))

Füge eine Konstante zur Lösung hinzu

= - cos (3 x - 2 π) sin (x) - \frac{3}{2} (- \frac{1}{4} sin (4 x) + \frac{1}{2} sin (2 x)) + C

Graph

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