What is inverse oflaplace 5/(s^3) ?

The answer to inverse oflaplace 5/(s^3) is (5t^2)/2

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inverse oflaplace 5/(s^3)

inverse laplace

\frac{5}{s ^{3}}

\frac{5 t ^{2}}{2}

Solution steps

L^{- 1} {\frac{5}{s ^{3}}}

= L^{- 1} {\frac{5}{2} \cdot \frac{2}{s ^{3}}}

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{5}{2} L^{- 1} {\frac{2}{s ^{3}}}

Use Inverse Laplace Transform table:

L^{- 1} {\frac{( n ) !}{s ^{n + 1}}} = t^{n}

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

= \frac{5}{2} t^{2}

= \frac{5 t ^{2}}{2}

\int \frac{6}{x - 2} d x

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

4 x

x \to 2 - lim (\frac{2 x + 1}{x - 2})

\frac{d}{d x} (x^{2} tanh (\frac{1}{x}))

What is inverse oflaplace 5/(s^3) ?
The answer to inverse oflaplace 5/(s^3) is (5t^2)/2