What is inverse oflaplace 7/((s-7)^8) ?

The answer to inverse oflaplace 7/((s-7)^8) is (e^{7t}t^7)/(720)

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inverse oflaplace 7/((s-7)^8)

inverse laplace

\frac{7}{( s - 7 ) ^{8}}

\frac{e ^{7 t} t ^{7}}{720}

Solution steps

L^{- 1} {\frac{7}{( s - 7 ) ^{8}}}

Apply inverse transform rule:

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

then

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

For

\frac{7}{( s - 7 ) ^{8}} : a = 7, F (s) = \frac{7}{s ^{8}}

= e^{7 t} L^{- 1} {\frac{7}{s ^{8}}}

L^{- 1} {\frac{7}{s ^{8}}} : \frac{t ^{7}}{720}

= \frac{e ^{7 t} t ^{7}}{720}

\int θ csc^{2} (θ) d θ

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\frac{x}{x ^{2} + 6}

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\int_{7}^{\infty} x e^{- 2 x} d x

What is inverse oflaplace 7/((s-7)^8) ?
The answer to inverse oflaplace 7/((s-7)^8) is (e^{7t}t^7)/(720)