What is laplacetransform t^{10}e^{-7t} ?

The answer to laplacetransform t^{10}e^{-7t} is (3628800)/((s+7)^{11)}

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laplacetransform t^{10}e^{-7t}

laplace transform

t^{10} e^{- 7 t}

\frac{3628800}{( s + 7 ) ^{11}}

Solution steps

L {e^{- 7 t} t^{10}}

Use Laplace Transform table:

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

For

t^{10} e^{- 7 t} : f (t) = e^{- 7 t}, k = 10

= (- 1)^{10} \frac{d ^{10}}{d s ^{10}} (L {e^{- 7 t}})

L {e^{- 7 t}} : \frac{1}{s + 7}

\frac{d ^{10}}{d s ^{10}} (\frac{1}{s + 7}) = \frac{3628800}{( s + 7 ) ^{11}}

= (- 1)^{10} \frac{3628800}{( s + 7 ) ^{11}}

= \frac{3628800}{( s + 7 ) ^{11}}

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What is laplacetransform t^{10}e^{-7t} ?
The answer to laplacetransform t^{10}e^{-7t} is (3628800)/((s+7)^{11)}