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Beliebt Rechnen >

integral of t^2sin(3t)

Lösung

\int t^{2} sin (3 t) d t

Lösung

- \frac{1}{3} t^{2} cos (3 t) + \frac{2}{27} (3 t sin (3 t) + cos (3 t)) + C

Schritte zur Lösung

\int t^{2} sin (3 t) d t

Wende die partielle Integration an

= - \frac{1}{3} t^{2} cos (3 t) - \int - \frac{2}{3} t cos (3 t) d t

\int - \frac{2}{3} t cos (3 t) d t = - \frac{2}{27} (3 t sin (3 t) + cos (3 t))

= - \frac{1}{3} t^{2} cos (3 t) - (- \frac{2}{27} (3 t sin (3 t) + cos (3 t)))

Vereinfache

= - \frac{1}{3} t^{2} cos (3 t) + \frac{2}{27} (3 t sin (3 t) + cos (3 t))

Füge eine Konstante zur Lösung hinzu

= - \frac{1}{3} t^{2} cos (3 t) + \frac{2}{27} (3 t sin (3 t) + cos (3 t)) + C

Graph

Beliebte Beispiele

integral of e^xx^3

\int e^{x} x^{3} d x

integral from 3 to 6 of 1/(sqrt(3x+7))

\int_{3}^{6} \frac{1}{3 x + 7} d x

derivative of (3x^4(4x^3+4x))

\frac{d}{d x} ((3 x^{4}) (4 x^{3} + 4 x))

derivative f(x)=(7x^2-12x)e^x

d er i v a t i v e f (x) = (7 x^{2} - 12 x) e^{x}

fläche 3x^2,x^2+6

a re a 3 x^{2}, x^{2} + 6