What is inverse oflaplace 6/((s-2)^4) ?

The answer to inverse oflaplace 6/((s-2)^4) is e^{2t}t^3

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inverse oflaplace 6/((s-2)^4)

inverse laplace

\frac{6}{( s - 2 ) ^{4}}

e^{2 t} t^{3}

Solution steps

L^{- 1} {\frac{6}{( 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{6}{( s - 2 ) ^{4}} : a = 2, F (s) = \frac{6}{s ^{4}}

= e^{2 t} L^{- 1} {\frac{6}{s ^{4}}}

L^{- 1} {\frac{6}{s ^{4}}} : t^{3}

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

f (x) = x^{2} + 8

\int 4 x^{\frac{1}{3}} - 4 x^{- \frac{1}{3}} d x

\int - (sin (x))^{2} d x

f (t) = 2 sin^{2} (t)

\int_{- π}^{π} cos^{2} (5 x) d x

What is inverse oflaplace 6/((s-2)^4) ?
The answer to inverse oflaplace 6/((s-2)^4) is e^{2t}t^3