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Beliebt Rechnen >

integral of cos^2(x)-cos^4(x)

Lösung

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

Lösung

x cos^{2} (x) sin^{2} (x) - \frac{1}{2} (- \frac{1}{4} x cos (4 x) + \frac{1}{16} sin (4 x)) + C

Schritte zur Lösung

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

Wende die partielle Integration an

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

\int \frac{1}{2} x sin (4 x) d x = \frac{1}{2} (- \frac{1}{4} x cos (4 x) + \frac{1}{16} sin (4 x))

= x cos^{2} (x) sin^{2} (x) - \frac{1}{2} (- \frac{1}{4} x cos (4 x) + \frac{1}{16} sin (4 x))

Füge eine Konstante zur Lösung hinzu

= x cos^{2} (x) sin^{2} (x) - \frac{1}{2} (- \frac{1}{4} x cos (4 x) + \frac{1}{16} sin (4 x)) + C

Graph

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