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

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

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

inverse laplace

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

2 e^{- t} sin (t)

Solution steps

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

Use the constant multiplication property of Inverse Laplace Transform:

For function

f (t)

and constant

a : L^{- 1} {a \cdot f (t)} = a \cdot L^{- 1} {f (t)}

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

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

= 2 e^{- t} sin (t)

y = \frac{23}{5} x - 12

\frac{d}{d x} (- 5 e^{- 5 x})

f (x) = \frac{1}{x ^{6}}, (1, 1)

\frac{d}{d x} (\frac{1}{4 x ^{3}} - \frac{5}{2 x})

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