What is inverse oflaplace 5/(s^8) ?

The answer to inverse oflaplace 5/(s^8) is (t^7)/(1008)

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inverse oflaplace 5/(s^8)

inverse laplace

\frac{5}{s ^{8}}

\frac{t ^{7}}{1008}

Solution steps

L^{- 1} {\frac{5}{s ^{8}}}

= L^{- 1} {\frac{1}{1008} \cdot \frac{5040}{s ^{8}}}

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}{1008} L^{- 1} {\frac{5040}{s ^{8}}}

Use Inverse Laplace Transform table:

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

L^{- 1} {\frac{5040}{s ^{8}}} = t^{7}

= \frac{1}{1008} t^{7}

= \frac{t ^{7}}{1008}

x \to 1 lim (i n^{4} x + e^{x})

\int_{0}^{\frac{π}{6}} sin^{4} (6 x) d x

\int \frac{( x + 4 )}{x ^{3} + 3 x ^{2} - 10 x} d x

\frac{d}{d x} (- 6 x^{2})

y^{^{'}} = (y + 5) (x + 2), y (0) = 1

What is inverse oflaplace 5/(s^8) ?
The answer to inverse oflaplace 5/(s^8) is (t^7)/(1008)