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Beliebt Rechnen >

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

Lösung

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

Lösung

- sin^{3} (x) cos (x) + \frac{3}{8} (x - \frac{1}{4} sin (4 x)) + C

Schritte zur Lösung

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

Wende die partielle Integration an

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

\int - 3 sin^{2} (x) cos^{2} (x) d x = - \frac{3}{8} (x - \frac{1}{4} sin (4 x))

= - sin^{3} (x) cos (x) - (- \frac{3}{8} (x - \frac{1}{4} sin (4 x)))

Vereinfache

= - sin^{3} (x) cos (x) + \frac{3}{8} (x - \frac{1}{4} sin (4 x))

Füge eine Konstante zur Lösung hinzu

= - sin^{3} (x) cos (x) + \frac{3}{8} (x - \frac{1}{4} sin (4 x)) + C

Graph

Beliebte Beispiele

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