What is inverse oflaplace 5/(s^4) ?

The answer to inverse oflaplace 5/(s^4) is (5t^3)/6

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inverse oflaplace 5/(s^4)

inverse laplace

\frac{5}{s ^{4}}

\frac{5 t ^{3}}{6}

Solution steps

L^{- 1} {\frac{5}{s ^{4}}}

= L^{- 1} {\frac{5}{6} \cdot \frac{6}{s ^{4}}}

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}{6} L^{- 1} {\frac{6}{s ^{4}}}

Use Inverse Laplace Transform table:

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

L^{- 1} {\frac{6}{s ^{4}}} = t^{3}

= \frac{5}{6} t^{3}

= \frac{5 t ^{3}}{6}

y^{^{'}} = - x

\frac{d}{d x} (200 x - 0.2 x^{\frac{5}{2}})

n = 1 \sum \infty n^{5} (1 + n^{6})^{3}

x \to 0 + lim (3 x^{7 x})

x \to 0 - lim (sin (\frac{2}{5 x}))

What is inverse oflaplace 5/(s^4) ?
The answer to inverse oflaplace 5/(s^4) is (5t^3)/6