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Beliebt Rechnen >

integral of cos^5(3x)sin(3x)

Lösung

\int cos^{5} (3 x) sin (3 x) d x

Lösung

- \frac{1}{18} cos^{6} (3 x) + C

Schritte zur Lösung

\int cos^{5} (3 x) sin (3 x) d x

Wende U-Substitution an

= \int - \frac{5 u}{15} d u

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - \frac{1}{15} \cdot \int 5 u d u

Wende die Potenzregel an

= - \frac{1}{15} \cdot \frac{5}{6} u^{\frac{6}{5}}

Setze in

u = cos^{5} (3 x)

ein

= - \frac{1}{15} \cdot \frac{5}{6} (cos^{5} (3 x))^{\frac{6}{5}}

Vereinfache

- \frac{1}{15} \cdot \frac{5}{6} (cos^{5} (3 x))^{\frac{6}{5}} : - \frac{1}{18} cos^{6} (3 x)

= - \frac{1}{18} cos^{6} (3 x)

Füge eine Konstante zur Lösung hinzu

= - \frac{1}{18} cos^{6} (3 x) + C

Graph

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