What is laplacetransform t^5e^{3t} ?

The answer to laplacetransform t^5e^{3t} is (120)/((s-3)^6)

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laplacetransform t^5e^{3t}

laplace transform

t^{5} e^{3 t}

\frac{120}{( s - 3 ) ^{6}}

Solution steps

L {e^{3 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^{3 t} : f (t) = e^{3 t}, k = 5

= (- 1)^{5} \frac{d ^{5}}{d s ^{5}} (L {e^{3 t}})

L {e^{3 t}} : \frac{1}{s - 3}

\frac{d ^{5}}{d s ^{5}} (\frac{1}{s - 3}) = - \frac{120}{( s - 3 ) ^{6}}

= (- 1)^{5} (- \frac{120}{( s - 3 ) ^{6}})

= \frac{120}{( s - 3 ) ^{6}}

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What is laplacetransform t^5e^{3t} ?
The answer to laplacetransform t^5e^{3t} is (120)/((s-3)^6)