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

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

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inverse oflaplace 3/((s+2)^3)

inverse laplace

\frac{3}{( s + 2 ) ^{3}}

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

Solution steps

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

Apply inverse transform rule:

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

then

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

For

\frac{3}{( s + 2 ) ^{3}} : a = - 2, F (s) = \frac{3}{s ^{3}}

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

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

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

y = x^{3} - 2 x^{2} + 2, y = 3 x^{2} + 5 x - 23, - 1, 7

\frac{\partial}{\partial x} (x^{2} e^{- \frac{x}{y}})

\int_{1}^{5} \frac{e ^{\frac{x}{2}}}{x ^{3}} d x

3 e^{x}, 3 x e^{x^{2}}, [0, 1]

x \to 6 lim (2 x - 7)

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