What is inverse oflaplace 3/(2s+1) ?

The answer to inverse oflaplace 3/(2s+1) is 3/2 e^{-t/2}

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inverse oflaplace 3/(2s+1)

inverse laplace

\frac{3}{2 s + 1}

\frac{3}{2} e^{- \frac{t}{2}}

Solution steps

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

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

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

Use Inverse Laplace Transform table:

L^{- 1} {\frac{1}{s - a}} = e^{a t}

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

= \frac{3}{2} e^{- \frac{t}{2}}

What is inverse oflaplace 3/(2s+1) ?
The answer to inverse oflaplace 3/(2s+1) is 3/2 e^{-t/2}