What is inverse oflaplace 1/(s^6) ?

The answer to inverse oflaplace 1/(s^6) is (t^5)/(120)

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inverse oflaplace 1/(s^6)

inverse laplace

\frac{1}{s ^{6}}

\frac{t ^{5}}{120}

Solution steps

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

= L^{- 1} {\frac{1}{120} \cdot \frac{120}{s ^{6}}}

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}{120} L^{- 1} {\frac{120}{s ^{6}}}

Use Inverse Laplace Transform table:

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

L^{- 1} {\frac{120}{s ^{6}}} = t^{5}

= \frac{1}{120} t^{5}

= \frac{t ^{5}}{120}

e^{- s t}

\int sin (3 x) cos (6 x) d x

\int_{1}^{2} e^{x} d x

\int x e^{- a x} d x

\frac{1}{( 1 + s ^{2} ) ( s ^{2} + 3 )}

What is inverse oflaplace 1/(s^6) ?
The answer to inverse oflaplace 1/(s^6) is (t^5)/(120)