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

Lösung

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

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

Schritte zur Lösung

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

Wende die partielle Integration an

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

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

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

Vereinfache

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

Füge eine Konstante zur Lösung hinzu

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

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