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Beliebt Rechnen >

laplacetransform (t+6)^3

Lösung

laplace transformation

(t + 6)^{3}

Lösung

\frac{6}{s ^{4}} + \frac{36}{s ^{3}} + \frac{108}{s ^{2}} + \frac{216}{s}

Schritte zur Lösung

L {(t + 6)^{3}}

Schreibe

(t + 6)^{3}

um:

t^{3} + 18 t^{2} + 108 t + 216

= L {t^{3} + 18 t^{2} + 108 t + 216}

Verwende die lineare Eigenschaft der Laplace-Transformation:

Für Funktionen

f (t), g (t)

und Konstanten

a, b : L {a \cdot f (t) + b \cdot g (t)} = a \cdot L {f (t)} + b \cdot L {g (t)}

= L {t^{3}} + 18 L {t^{2}} + 108 L {t} + L {216}

L {t^{3}} : \frac{6}{s ^{4}}

L {t^{2}} : \frac{2}{s ^{3}}

L {t} : \frac{1}{s ^{2}}

L {216} : \frac{216}{s}

= \frac{6}{s ^{4}} + 18 \cdot \frac{2}{s ^{3}} + 108 \cdot \frac{1}{s ^{2}} + \frac{216}{s}

Fasse

\frac{6}{s ^{4}} + 18 \frac{2}{s ^{3}} + 108 \frac{1}{s ^{2}} + \frac{216}{s}

zusammen:

\frac{6}{s ^{4}} + \frac{36}{s ^{3}} + \frac{108}{s ^{2}} + \frac{216}{s}

= \frac{6}{s ^{4}} + \frac{36}{s ^{3}} + \frac{108}{s ^{2}} + \frac{216}{s}

Beliebte Beispiele

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h \to 0 lim (- \frac{5 h}{x ( x + h )})

derivative (x^3)/7

d er i v a t i v e \frac{x ^{3}}{7}

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\int 3 x x + 2 d x

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\frac{\partial}{\partial y} (x^{4} y^{3} + 8 x^{2} y)

derivative of ((1-x^2)/(2-x))

\frac{d}{d x} (\frac{( 1 - x ^{2} )}{2 - x})