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Beliebt Rechnen >

laplacetransform t^3e^t

Lösung

laplace transformation

t^{3} e^{t}

Lösung

\frac{6}{( s - 1 ) ^{4}}

Schritte zur Lösung

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

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

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

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

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

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

Beliebte Beispiele

integral of sqrt(x^2+4x)

\int x^{2} + 4 x d x

integral of 1/(10-x)

\int \frac{1}{10 - x} d x

(dy)/(dt)+3y=t+e^{-2t}

\frac{d y}{d t} + 3 y = t + e^{- 2 t}

integral of (1+sin(2x))^2

\int (1 + sin (2 x))^{2} d x

\frac{d}{d t} (csc (t))