What is inverse oflaplace 4/(s(s^2+s)) ?

The answer to inverse oflaplace 4/(s(s^2+s)) is -4\H(t)+4t+4e^{-t}

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inverse oflaplace 4/(s(s^2+s))

inverse laplace

\frac{4}{s ( s ^{2} + s )}

- 4 H (t) + 4 t + 4 e^{- t}

Solution steps

L^{- 1} {\frac{4}{s ( s ^{2} + s )}}

Take the partial fraction of

\frac{4}{s ( s ^{2} + s )} : - \frac{4}{s} + \frac{4}{s ^{2}} + \frac{4}{s + 1}

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

Use the linearity property of Inverse Laplace Transform:

For functions

f (s), g (s)

and constants

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

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

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

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

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

\int 2 x - 6 y d x

\frac{\partial}{\partial x} (x^{4} y - 2 x^{3} y^{2})

\int e \frac{x}{2} d x

x \to 3 + lim (\frac{3 - x}{∣ x - 3 ∣})

y^{^{'}} = ln (x)

What is inverse oflaplace 4/(s(s^2+s)) ?
The answer to inverse oflaplace 4/(s(s^2+s)) is -4\H(t)+4t+4e^{-t}