What is inverse oflaplace 2/((s-2)^4) ?

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

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inverse oflaplace 2/((s-2)^4)

inverse laplace

\frac{2}{( s - 2 ) ^{4}}

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

Solution steps

L^{- 1} {\frac{2}{( s - 2 ) ^{4}}}

Apply inverse transform rule:

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

then

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

For

\frac{2}{( s - 2 ) ^{4}} : a = 2, F (s) = \frac{2}{s ^{4}}

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

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

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

\int \frac{x \cdot arcsin ( x )}{1 - x ^{2}} d x

f (x) = sin^{2} (x) cos (x)

- x e^{- x} + e^{- x}

y = e^{- x} - e^{- x} x

\frac{d}{d x} (2 e^{x} + e^{x} x)

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