What is laplacetransform t^3e^{2t} ?

The answer to laplacetransform t^3e^{2t} is 6/((s-2)^4)

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laplacetransform t^3e^{2t}

laplace transform

t^{3} e^{2 t}

\frac{6}{( s - 2 ) ^{4}}

Solution steps

L {e^{2 t} t^{3}}

Use Laplace Transform table:

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

For

t^{3} e^{2 t} : f (t) = e^{2 t}, k = 3

= (- 1)^{3} \frac{d ^{3}}{d s ^{3}} (L {e^{2 t}})

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

\frac{d ^{3}}{d s ^{3}} (\frac{1}{s - 2}) = - \frac{6}{( s - 2 ) ^{4}}

= (- 1)^{3} (- \frac{6}{( s - 2 ) ^{4}})

= \frac{6}{( s - 2 ) ^{4}}

\frac{d}{d x} (sin^{2} (3 x^{2} - 1))

\frac{3 ( x - 1 )}{4 x x}

t e^{- 2 t} cos (3 t)

\int \frac{1}{k s} d s

\int \frac{1}{x ^{2} - 0.01} d x

What is laplacetransform t^3e^{2t} ?
The answer to laplacetransform t^3e^{2t} is 6/((s-2)^4)