What is inverse oflaplace 3/(s^4) ?

The answer to inverse oflaplace 3/(s^4) is (t^3)/2

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inverse oflaplace 3/(s^4)

inverse laplace

\frac{3}{s ^{4}}

\frac{t ^{3}}{2}

Solution steps

L^{- 1} {\frac{3}{s ^{4}}}

= L^{- 1} {\frac{1}{2} \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}{2} 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}{2} t^{3}

= \frac{t ^{3}}{2}

x^{2} + 2

\int 1 - 2 cos (x) + cos^{2} (x) d x

\int \frac{e ^{\frac{6}{x}}}{x ^{2}} d x

7 e^{x} + \frac{2}{3 x}

\int \frac{1}{s} d s

What is inverse oflaplace 3/(s^4) ?
The answer to inverse oflaplace 3/(s^4) is (t^3)/2