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

The answer to inverse oflaplace 6/((s-2)^6) is (e^{2t}t^5)/(20)

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

inverse laplace

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

\frac{e ^{2 t} t ^{5}}{20}

Solution steps

L^{- 1} {\frac{6}{( s - 2 ) ^{6}}}

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 ) ^{6}} : a = 2, F (s) = \frac{6}{s ^{6}}

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

L^{- 1} {\frac{6}{s ^{6}}} : \frac{t ^{5}}{20}

= \frac{e ^{2 t} t ^{5}}{20}

f (x) = \frac{π}{x}

\int \frac{42 x ^{7} - 7 x}{7 x ^{5}} d x

\int \frac{1}{2 x ^{6}} d x

f (x) = - x^{2} - 3 x + 4, at x = - 3

\int \frac{x ^{2} - 144}{x} d x

What is inverse oflaplace 6/((s-2)^6) ?
The answer to inverse oflaplace 6/((s-2)^6) is (e^{2t}t^5)/(20)