What is inverse oflaplace 3/(2s) ?

The answer to inverse oflaplace 3/(2s) is 3/2 \H(t)

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inverse oflaplace 3/(2s)

inverse laplace

\frac{3}{2 s}

\frac{3}{2} H (t)

Solution steps

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

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

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

Use Inverse Laplace Transform table:

L^{- 1} {\frac{a}{s}} = a H (t)

Where

H (t)

is Heaviside step function

= \frac{1}{2} \cdot 3 H (t)

= \frac{3}{2} H (t)

\int x^{2} - x + 1 d x

\int 8 e^{5 x} d x

- x^{2} + 6 x, x^{2} - 4 x

f (x) = 27 sin (3 x)

\frac{\partial}{\partial y} (y^{\frac{y}{x}} sin (\frac{y}{x}))

What is inverse oflaplace 3/(2s) ?
The answer to inverse oflaplace 3/(2s) is 3/2 \H(t)