What is laplacetransform t^5e^{-6t} ?

The answer to laplacetransform t^5e^{-6t} is (120)/((s+6)^6)

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laplacetransform t^5e^{-6t}

laplace transform

t^{5} e^{- 6 t}

\frac{120}{( s + 6 ) ^{6}}

Solution steps

L {e^{- 6 t} t^{5}}

Use Laplace Transform table:

L {t^{k} f (t)} = (- 1)^{k} \frac{d ^{k}}{d s ^{k}} (L {f (t)})

For

t^{5} e^{- 6 t} : f (t) = e^{- 6 t}, k = 5

= (- 1)^{5} \frac{d ^{5}}{d s ^{5}} (L {e^{- 6 t}})

L {e^{- 6 t}} : \frac{1}{s + 6}

\frac{d ^{5}}{d s ^{5}} (\frac{1}{s + 6}) = - \frac{120}{( s + 6 ) ^{6}}

= (- 1)^{5} (- \frac{120}{( s + 6 ) ^{6}})

= \frac{120}{( s + 6 ) ^{6}}

f (t) = \frac{t}{t ^{2} + 7}

\int_{1}^{e^{5}} \frac{ln ^{2} ( x ^{2} )}{x} d x

y = 3 x + sin (5 x)

\frac{d}{d x} ((x^{2} - x)^{4})

\int \frac{x ^{2} + y ^{2} - 5}{( 1 + x ) ^{3}} d x

What is laplacetransform t^5e^{-6t} ?
The answer to laplacetransform t^5e^{-6t} is (120)/((s+6)^6)