integral of t^3sin(t)

Lösung

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

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

Schritte zur Lösung

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

Wende die partielle Integration an

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

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

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

Vereinfache

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

Füge eine Konstante zur Lösung hinzu

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

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