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

The answer to inverse oflaplace s/(2s+4) is 1/2 \delta(t)-e^{-2t}

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inverse oflaplace s/(2s+4)

inverse laplace

\frac{s}{2 s + 4}

\frac{1}{2} δ (t) - e^{- 2 t}

Solution steps

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

Take the partial fraction of

\frac{s}{2 s + 4} : \frac{1}{2} - \frac{1}{s + 2}

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

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

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

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

= \frac{1}{2} δ (t) - e^{- 2 t}

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\frac{d}{d x} (3^{\frac{x}{2}})

\frac{d}{d x} (x^{3} + x^{2} - 5 x)

\int x \cdot e^{5 x} d x

What is inverse oflaplace s/(2s+4) ?
The answer to inverse oflaplace s/(2s+4) is 1/2 \delta(t)-e^{-2t}