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Beliebt Rechnen >

integral of t^2sin(4t)

Lösung

\int t^{2} sin (4 t) d t

Lösung

- \frac{1}{4} t^{2} cos (4 t) + \frac{1}{32} (4 t sin (4 t) + cos (4 t)) + C

Schritte zur Lösung

\int t^{2} sin (4 t) d t

Wende die partielle Integration an

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

\int - \frac{1}{2} t cos (4 t) d t = - \frac{1}{32} (4 t sin (4 t) + cos (4 t))

= - \frac{1}{4} t^{2} cos (4 t) - (- \frac{1}{32} (4 t sin (4 t) + cos (4 t)))

Vereinfache

= - \frac{1}{4} t^{2} cos (4 t) + \frac{1}{32} (4 t sin (4 t) + cos (4 t))

Füge eine Konstante zur Lösung hinzu

= - \frac{1}{4} t^{2} cos (4 t) + \frac{1}{32} (4 t sin (4 t) + cos (4 t)) + C

Graph

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