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Beliebt Rechnen >

laplacetransform 3t^2+3t-2

Lösung

laplace transformation

3 t^{2} + 3 t - 2

Lösung

\frac{6}{s ^{3}} + \frac{3}{s ^{2}} - \frac{2}{s}

Schritte zur Lösung

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

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)}

= 3 L {t^{2}} + 3 L {t} - L {2}

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

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

L {2} : \frac{2}{s}

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

Fasse

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

zusammen:

\frac{6}{s ^{3}} + \frac{3}{s ^{2}} - \frac{2}{s}

= \frac{6}{s ^{3}} + \frac{3}{s ^{2}} - \frac{2}{s}

Beliebte Beispiele

integral of (ln(3x))/(x^3)

\int \frac{ln ( 3 x )}{x ^{3}} d x

integral of 2x-3e^x

\int 2 x - 3 e^{x} d x

limit as t approaches 0 of (8^t-5^t)/t

t \to 0 lim (\frac{8 ^{t} - 5 ^{t}}{t})

integral of (y^2)/(y+1)

\int \frac{y ^{2}}{y + 1} d y

derivative of sqrt(2)sec(x)

\frac{d}{d x} (2 sec (x))