inverselaplace (s-1)/(s(s+1)(s+2))

Lösung

inverse laplace transformation

\frac{s - 1}{s ( s + 1 ) ( s + 2 )}

- \frac{1}{2} H (t) + 2 e^{- t} - \frac{3}{2} e^{- 2 t}

Schritte zur Lösung

L^{- 1} {\frac{s - 1}{s ( s + 1 ) ( s + 2 )}}

Ermittle den Partialbruch von

\frac{s - 1}{s ( s + 1 ) ( s + 2 )} : - \frac{1}{2 s} + \frac{2}{s + 1} - \frac{3}{2 ( s + 2 )}

= L^{- 1} {- \frac{1}{2 s} + \frac{2}{s + 1} - \frac{3}{2 ( s + 2 )}}

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{1}{2 s}} + L^{- 1} {\frac{2}{s + 1}} - L^{- 1} {\frac{3}{2 ( s + 2 )}}

L^{- 1} {\frac{1}{2 s}} : \frac{1}{2} H (t)

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

L^{- 1} {\frac{3}{2 ( s + 2 )}} : \frac{3}{2} e^{- 2 t}

= - \frac{1}{2} H (t) + 2 e^{- t} - \frac{3}{2} e^{- 2 t}

\int \frac{1}{3 - 5 x ^{2}} d x

\frac{\partial}{\partial x} (x^{3} - 12 x y + 8 y^{3})

d er i v a t i v e (x^{2} - 5 x + 1)^{4}

\int_{1}^{3} (2 x^{2} - 12 x + 13) d x

\int (\frac{ln ( x )}{x})^{2} d x