What is inverse oflaplace (8e^{(-3)})/(s^3) ?

The answer to inverse oflaplace (8e^{(-3)})/(s^3) is (4t^2)/(e^3)

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inverse oflaplace (8e^{(-3)})/(s^3)

inverse laplace

\frac{8 e ^{(- 3)}}{s ^{3}}

\frac{4 t ^{2}}{e ^{3}}

Solution steps

L^{- 1} {\frac{8 e ^{(- 3)}}{s ^{3}}}

= L^{- 1} {\frac{4}{e ^{3}} \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{4}{e ^{3}} 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{4}{e ^{3}} t^{2}

= \frac{4 t ^{2}}{e ^{3}}

\int 16 - y^{2} d y

\int x^{2} + 10 x d x

\int_{2}^{3} \frac{4}{3 - x} d x

\int \frac{2}{u ^{2}} d u

\frac{d}{d x} (arctan (sin (8 x)))

What is inverse oflaplace (8e^{(-3)})/(s^3) ?
The answer to inverse oflaplace (8e^{(-3)})/(s^3) is (4t^2)/(e^3)