What is inverse oflaplace 3/(s*(s+2)) ?

The answer to inverse oflaplace 3/(s*(s+2)) is 3/2 \H(t)-3/2 e^{-2t}

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inverse oflaplace 3/(s*(s+2))

inverse laplace

\frac{3}{s \cdot ( s + 2 )}

\frac{3}{2} H (t) - \frac{3}{2} e^{- 2 t}

Solution steps

L^{- 1} {\frac{3}{s ( s + 2 )}}

Take the partial fraction of

\frac{3}{s ( s + 2 )} : \frac{3}{2 s} - \frac{3}{2 ( s + 2 )}

= L^{- 1} {\frac{3}{2 s} - \frac{3}{2 ( 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{3}{2 s}} - L^{- 1} {\frac{3}{2 ( s + 2 )}}

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

L^{- 1} {\frac{3}{2 ( s + 2 )}} : \frac{3}{2} e^{- 2 t}

= \frac{3}{2} H (t) - \frac{3}{2} e^{- 2 t}

8 x^{2} - 5 x, x^{3} - 8 x + 3

\int x + 10 d x

(e^{x} cos (x))^{^{'}}

\int_{0}^{\frac{π}{2}} cos (5 t) cos (10 t) d t

\int \frac{x ^{3}}{4} d x

What is inverse oflaplace 3/(s*(s+2)) ?
The answer to inverse oflaplace 3/(s*(s+2)) is 3/2 \H(t)-3/2 e^{-2t}