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Beliebt Rechnen >

inverselaplace 4/s+6/(s^5)-1/(s+8)

Lösung

inverse laplace transformation

\frac{4}{s} + \frac{6}{s ^{5}} - \frac{1}{s + 8}

Lösung

4 H (t) + \frac{t ^{4}}{4} - e^{- 8 t}

Schritte zur Lösung

L^{- 1} {\frac{4}{s} + \frac{6}{s ^{5}} - \frac{1}{s + 8}}

Wende die lineare Eigenschaftder inversen Laplace-Transformation an:

Für Funktionen

f (s), g (s)

und Konstanten

a, b : L^{- 1} {a \cdot f (s) + b \cdot g (s)} = a \cdot L^{- 1} {f (s)} + b \cdot L^{- 1} {g (s)}

= L^{- 1} {\frac{4}{s}} + L^{- 1} {\frac{6}{s ^{5}}} - L^{- 1} {\frac{1}{s + 8}}

L^{- 1} {\frac{4}{s}} : 4 H (t)

L^{- 1} {\frac{6}{s ^{5}}} : \frac{t ^{4}}{4}

L^{- 1} {\frac{1}{s + 8}} : e^{- 8 t}

= 4 H (t) + \frac{t ^{4}}{4} - e^{- 8 t}

Beliebte Beispiele

derivative of sqrt(2+5x)

\frac{d}{d x} (2 + 5 x)

limit as x approaches infinity of sqrt(9x^2+x)-3

x \to \infty lim (9 x^{2} + x - 3)

integral of 1/((x+1)sqrt(x^2+2x-8))

\int \frac{1}{( x + 1 ) x ^{2} + 2 x - 8} d x

integral of (3x-1)/(x^2+9)

\int \frac{3 x - 1}{x ^{2} + 9} d x

derivative of ln({g}(x))

\frac{d}{d x} (ln (g (x)))