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Beliebt Rechnen >

inverselaplace ((s+1)^3)/(s^5)

Lösung

inverse laplace transformation

\frac{( s + 1 ) ^{3}}{s ^{5}}

Lösung

t + \frac{3 t ^{2}}{2} + \frac{t ^{3}}{2} + \frac{t ^{4}}{24}

Schritte zur Lösung

L^{- 1} {\frac{( s + 1 ) ^{3}}{s ^{5}}}

Schreibe

\frac{( s + 1 ) ^{3}}{s ^{5}}

um:

\frac{1}{s ^{2}} + \frac{3}{s ^{3}} + \frac{3}{s ^{4}} + \frac{1}{s ^{5}}

= L^{- 1} {\frac{1}{s ^{2}} + \frac{3}{s ^{3}} + \frac{3}{s ^{4}} + \frac{1}{s ^{5}}}

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}{s ^{2}}} + L^{- 1} {\frac{3}{s ^{3}}} + L^{- 1} {\frac{3}{s ^{4}}} + L^{- 1} {\frac{1}{s ^{5}}}

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

L^{- 1} {\frac{3}{s ^{3}}} : \frac{3 t ^{2}}{2}

L^{- 1} {\frac{3}{s ^{4}}} : \frac{t ^{3}}{2}

L^{- 1} {\frac{1}{s ^{5}}} : \frac{t ^{4}}{24}

= t + \frac{3 t ^{2}}{2} + \frac{t ^{3}}{2} + \frac{t ^{4}}{24}

Beliebte Beispiele

limit as x approaches 5 of ((x-5))/(sqrt(x^2+5))

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

integral from 0 to infinity of 4sin^2(a)

\int_{0}^{\infty} 4 sin^{2} (a) d a

integral of 9t^6

\int 9 t^{6} d t

laplacetransform 5sin(3t)

l a pl a ce t r an s f or m 5 sin (3 t)

derivative e^{x^6}

d er i v a t i v e e^{x^{6}}