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Beliebt Rechnen >

laplacetransform t^3e^{-2t}

Lösung

laplace transformation

t^{3} e^{- 2 t}

Lösung

\frac{6}{( s + 2 ) ^{4}}

Schritte zur Lösung

L {e^{- 2 t} t^{3}}

Wende Laplace-Transformationstabelle an:

L {t^{k} f (t)} = (- 1)^{k} \frac{d ^{k}}{d s ^{k}} (L {f (t)})

Für

t^{3} e^{- 2 t} : f (t) = e^{- 2 t}, k = 3

= (- 1)^{3} \frac{d ^{3}}{d s ^{3}} (L {e^{- 2 t}})

L {e^{- 2 t}} : \frac{1}{s + 2}

\frac{d ^{3}}{d s ^{3}} (\frac{1}{s + 2}) = - \frac{6}{( s + 2 ) ^{4}}

= (- 1)^{3} (- \frac{6}{( s + 2 ) ^{4}})

= \frac{6}{( s + 2 ) ^{4}}

Beliebte Beispiele

derivative of x*e^{-1/(x^2})

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

(e^{- 5 x})^{^{'}}

integral of (x+4)/x

\int \frac{x + 4}{x} d x

derivative of ax^3ln(x/4+bx^2(x-4))

\frac{d}{d x} (a x^{3} ln (\frac{x}{4}) + b x^{2} (x - 4))

derivative of (e^x/(4-2x))

\frac{d}{d x} (\frac{e ^{x}}{4 - 2 x})