What is inverse oflaplace a/(2s^3) ?

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

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inverse oflaplace a/(2s^3)

inverse laplace

\frac{a}{2 s ^{3}}

\frac{a t ^{2}}{4}

Solution steps

L^{- 1} {\frac{a}{2 s ^{3}}}

= L^{- 1} {\frac{a}{4} \cdot \frac{2}{s ^{3}}}

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{a}{4} L^{- 1} {\frac{2}{s ^{3}}}

Use Inverse Laplace Transform table:

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

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

= \frac{a}{4} t^{2}

= \frac{a t ^{2}}{4}

tan (x e^{x})

x \to 0 lim (x^{2} + 5 x)

f (x) = x^{2} + 6 x + 1

y = (x^{2} + e^{x}) x

\frac{d}{d y} (x sin (y))

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