integral of w^3sin(w)

Lösung

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

- w^{3} cos (w) + 3 (w^{2} sin (w) - 2 (- w cos (w) + sin (w))) + C

Schritte zur Lösung

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

Wende die partielle Integration an

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

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

= - w^{3} cos (w) - (- 3 (w^{2} sin (w) - 2 (- w cos (w) + sin (w))))

Vereinfache

= - w^{3} cos (w) + 3 (w^{2} sin (w) - 2 (- w cos (w) + sin (w)))

Füge eine Konstante zur Lösung hinzu

= - w^{3} cos (w) + 3 (w^{2} sin (w) - 2 (- w cos (w) + sin (w))) + C

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