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Beliebt Rechnen >

laplacetransform (t-1)(3(t-1)^2+9(t-1)+3)

Lösung

laplace transformation

(t - 1) (3 (t - 1)^{2} + 9 (t - 1) + 3)

Lösung

\frac{18}{s ^{4}} - \frac{6}{s ^{2}} + \frac{3}{s}

Schritte zur Lösung

L {(t - 1) (3 (t - 1)^{2} + 9 (t - 1) + 3)}

Schreibe

(t - 1) (3 (t - 1)^{2} + 9 (t - 1) + 3)

um:

3 t^{3} - 6 t + 3

= L {3 t^{3} - 6 t + 3}

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^{3}} - 6 L {t} + L {3}

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

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

L {3} : \frac{3}{s}

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

Fasse

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

zusammen:

\frac{18}{s ^{4}} - \frac{6}{s ^{2}} + \frac{3}{s}

= \frac{18}{s ^{4}} - \frac{6}{s ^{2}} + \frac{3}{s}

Beliebte Beispiele

integral of 1/(sec(y))

\int \frac{1}{sec ( y )} d y

limit as x approaches 0 of x(sin(1/x))

x \to 0 lim (x (sin (\frac{1}{x})))

(\partial)/(\partial x)(ln(y^2+x^2))

\frac{\partial}{\partial x} (ln (y^{2} + x^{2}))

integral of 1 (e^{x^2}y)

\int \frac{d}{1} (e^{x^{2}} y) d x

integral of-3t^2cos(t)

\int - 3 t^{2} cos (t) d t