What is inverse oflaplace (k^4)/((s+k)^5) ?

The answer to inverse oflaplace (k^4)/((s+k)^5) is (k^4e^{-kt}t^4)/(24)

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inverse oflaplace (k^4)/((s+k)^5)

inverse laplace

\frac{k ^{4}}{( s + k ) ^{5}}

\frac{k ^{4} e ^{- k t} t ^{4}}{24}

Solution steps

L^{- 1} {\frac{k ^{4}}{( s + k ) ^{5}}}

Apply inverse transform rule:

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

then

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

For

\frac{k ^{4}}{( s + k ) ^{5}} : a = - k, F (s) = \frac{k ^{4}}{s ^{5}}

= e^{- k t} L^{- 1} {\frac{k ^{4}}{s ^{5}}}

L^{- 1} {\frac{k ^{4}}{s ^{5}}} : \frac{k ^{4} t ^{4}}{24}

= \frac{k ^{4} e ^{- k t} t ^{4}}{24}

What is inverse oflaplace (k^4)/((s+k)^5) ?
The answer to inverse oflaplace (k^4)/((s+k)^5) is (k^4e^{-kt}t^4)/(24)