inverselaplace (((s+1))/(s^4))^3

Lösung

inverse laplace transformation

(\frac{( s + 1 )}{s ^{4}})^{3}

\frac{t ^{8}}{40320} + \frac{t ^{9}}{120960} + \frac{t ^{10}}{1209600} + \frac{t ^{11}}{39916800}

Schritte zur Lösung

L^{- 1} {(\frac{( s + 1 )}{s ^{4}})^{3}}

Schreibe

(\frac{s + 1}{s ^{4}})^{3}

um:

\frac{1}{s ^{9}} + \frac{3}{s ^{10}} + \frac{3}{s ^{11}} + \frac{1}{s ^{12}}

= L^{- 1} {\frac{1}{s ^{9}} + \frac{3}{s ^{10}} + \frac{3}{s ^{11}} + \frac{1}{s ^{12}}}

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 ^{9}}} + L^{- 1} {\frac{3}{s ^{10}}} + L^{- 1} {\frac{3}{s ^{11}}} + L^{- 1} {\frac{1}{s ^{12}}}

L^{- 1} {\frac{1}{s ^{9}}} : \frac{t ^{8}}{40320}

L^{- 1} {\frac{3}{s ^{10}}} : \frac{t ^{9}}{120960}

L^{- 1} {\frac{3}{s ^{11}}} : \frac{t ^{10}}{1209600}

L^{- 1} {\frac{1}{s ^{12}}} : \frac{t ^{11}}{39916800}

= \frac{t ^{8}}{40320} + \frac{t ^{9}}{120960} + \frac{t ^{10}}{1209600} + \frac{t ^{11}}{39916800}

\int x (x + 1)^{5} d x

\int (3 x - 4) e^{(- x)} d x

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

\frac{\partial}{\partial x} (y \cdot e^{x y})

t an g e n t x^{2} - 9 x