What is inverse oflaplace (e^{2s})/(s^3) ?

The answer to inverse oflaplace (e^{2s})/(s^3) is (\H(t+2)(t+2)^2)/2

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inverse oflaplace (e^{2s})/(s^3)

inverse laplace

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

\frac{H ( t + 2 ) ( t + 2 ) ^{2}}{2}

Solution steps

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

Apply inverse transform rule:

L^{- 1} {F (s)} = f (t)

then

L^{- 1} {e^{- a s} F (s)} = H (t - a) f (t - a)

Where

H (t)

is Heaviside step function

= H (t + 2) L^{- 1} {\frac{1}{s ^{3}}} (t + 2)

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

= H (t + 2) \frac{( t + 2 ) ^{2}}{2}

= \frac{H ( t + 2 ) ( t + 2 ) ^{2}}{2}

\frac{\partial}{\partial x} (x y e^{s i n (π x y)})

x \to - 3 lim ((5 - x) \frac{4}{3})

\int \frac{5}{1 + 9 x ^{2}} d x

\int y^{2} cosh (7 y) d y

x \to 0 lim (\frac{x}{4 ^{x} - 2 ^{x}})

What is inverse oflaplace (e^{2s})/(s^3) ?
The answer to inverse oflaplace (e^{2s})/(s^3) is (\H(t+2)(t+2)^2)/2