de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

inverselaplace (-4s+8)/(s^2+6s+8)

Lösung

inverse laplace transformation

\frac{- 4 s + 8}{s ^{2} + 6 s + 8}

Lösung

8 e^{- 2 t} - 12 e^{- 4 t}

Schritte zur Lösung

L^{- 1} {\frac{- 4 s + 8}{s ^{2} + 6 s + 8}}

Ermittle den Partialbruch von

\frac{- 4 s + 8}{s ^{2} + 6 s + 8} : \frac{8}{s + 2} - \frac{12}{s + 4}

= L^{- 1} {\frac{8}{s + 2} - \frac{12}{s + 4}}

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{8}{s + 2}} - L^{- 1} {\frac{12}{s + 4}}

L^{- 1} {\frac{8}{s + 2}} : 8 e^{- 2 t}

L^{- 1} {\frac{12}{s + 4}} : 12 e^{- 4 t}

= 8 e^{- 2 t} - 12 e^{- 4 t}

Beliebte Beispiele

(\partial)/(\partial t)(e^{-4t}cos(pix))

\frac{\partial}{\partial t} (e^{- 4 t} cos (π x))

(d^2)/(dx^2)((x^2-6x)/(x+1))

\frac{d ^{2}}{d x ^{2}} (\frac{x ^{2} - 6 x}{x + 1})

limit as x approaches 1 of ((x^{5/2}-2x^{3/2}+x^{1/2}))/(x-1)

x \to 1 lim \frac{( x ^{\frac{5}{2}} - 2 x ^{\frac{3}{2}} + x ^{\frac{1}{2}} )}{x - 1}

derivative f(x)=(a-5x)(a+5x)

d er i v a t i v e f (x) = (a - 5 x) (a + 5 x)

integral of 4sec^6(t)

\int 4 sec^{6} (t) d t