What is inverse oflaplace 6/(s^5) ?

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

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inverse oflaplace 6/(s^5)

inverse laplace

\frac{6}{s ^{5}}

\frac{t ^{4}}{4}

Solution steps

L^{- 1} {\frac{6}{s ^{5}}}

= L^{- 1} {\frac{1}{4} \cdot \frac{24}{s ^{5}}}

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}{4} L^{- 1} {\frac{24}{s ^{5}}}

Use Inverse Laplace Transform table:

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

L^{- 1} {\frac{24}{s ^{5}}} = t^{4}

= \frac{1}{4} t^{4}

= \frac{t ^{4}}{4}

\frac{d y}{d t} - \frac{8}{t} \cdot y = t^{5}

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

cos (3 t + 5) e^{2 t}

\frac{d ^{2}}{d x ^{2}} (4 x - 5 x^{\frac{3}{4}})

\int - 4 sin (3 x) sin (n x) d x

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