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Beliebt Rechnen >

laplacetransform 2(t-3)^2+15(t-3)+26

Lösung

laplace transformation

2 (t - 3)^{2} + 15 (t - 3) + 26

Lösung

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

Schritte zur Lösung

L {2 (t - 3)^{2} + 15 (t - 3) + 26}

Schreibe

2 (t - 3)^{2} + 15 (t - 3) + 26

um:

2 t^{2} + 3 t - 1

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

Fasse

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

zusammen:

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

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

Beliebte Beispiele

derivative of (8(4^x)/(x^4))

\frac{d}{d x} (\frac{8 ( 4 ^{x} )}{x ^{4}})

integral from 0 to 1/3 of 5/(1+9x^2)

\int_{0}^{\frac{1}{3}} \frac{5}{1 + 9 x ^{2}} d x

derivative of 1/2 ln(x/2)

\frac{d}{d x} (\frac{1}{2} ln (\frac{x}{2}))

derivative of x^{2/3}(x-4)

\frac{d}{d x} (x^{\frac{2}{3}} (x - 4))

derivative of (2x-8^5)

\frac{d}{d x} ((2 x - 8)^{5})