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Beliebt Rechnen >

laplacetransform 2t^2-2t+1

Lösung

laplace transformation

2 t^{2} - 2 t + 1

Lösung

\frac{4}{s ^{3}} - \frac{2}{s ^{2}} + \frac{1}{s}

Schritte zur Lösung

L {2 t^{2} - 2 t + 1}

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)}

= 2 L {t^{2}} - 2 L {t} + L {1}

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

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

L {1} : \frac{1}{s}

= 2 \cdot \frac{2}{s ^{3}} - 2 \cdot \frac{1}{s ^{2}} + \frac{1}{s}

Fasse

2 \frac{2}{s ^{3}} - 2 \frac{1}{s ^{2}} + \frac{1}{s}

zusammen:

\frac{4}{s ^{3}} - \frac{2}{s ^{2}} + \frac{1}{s}

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

Beliebte Beispiele

derivative f(x)=e^{-x+1}x-2e^{-x+1}

d er i v a t i v e f (x) = e^{- x + 1} x - 2 e^{- x + 1}

derivative of sqrt(1+sin(2x))

\frac{d}{d x} (1 + sin (2 x))

derivative ln(x+sqrt(1+x^2))

d er i v a t i v e ln (x + 1 + x^{2})

limit as x approaches infinity of (256^{x/2})/(4^{2x)}

x \to \infty lim (\frac{25 6 ^{\frac{x}{2}}}{4 ^{2 x}})

integral of 6/(x^2+4)

\int \frac{6}{x ^{2} + 4} d x