What is inverse oflaplace 1/(s^4) ?

The answer to inverse oflaplace 1/(s^4) is (t^3)/6

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inverse oflaplace 1/(s^4)

inverse laplace

\frac{1}{s ^{4}}

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

Solution steps

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

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

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

x^{^{''}} = - k^{2} x

(2 + x) y^{^{'}} - x y = 0

e^{s}

x \to c lim (5)

f (x) = x^{4} - 5 x^{2} + 4, at x = 2

What is inverse oflaplace 1/(s^4) ?
The answer to inverse oflaplace 1/(s^4) is (t^3)/6