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Beliebt Rechnen >

integral of t^2sin(2t)

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die partielle Integration an

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

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

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

Vereinfache

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

limit as x approaches+pi/2 of tan(x)

x \to + \frac{π}{2} lim (tan (x))

y^{''}+y=7sin(2t)+5tcos(2t)

y^{^{''}} + y = 7 sin (2 t) + 5 t cos (2 t)

derivative y=arccos(4x)

d er i v a t i v e y = arccos (4 x)

limit as x approaches infinity of sqrt(x+1)

x \to \infty lim (x + 1)

derivative cos^2(x)

d er i v a t i v e cos^{2} (x)