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

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

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laplacetransform t^2e^{3t}

laplace transform

t^{2} e^{3 t}

\frac{2}{( s - 3 ) ^{3}}

Solution steps

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

Use Laplace Transform table:

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

For

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

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

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

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

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

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

\int sin^{2} (4 x) cos^{2} (4 x) d x

\frac{d}{d x} (5^{s i n (π x)})

\frac{e ^{x}}{1}

\frac{d}{d u} (4 u)

\int \frac{3 x - 3}{x ^{2} - x - 2} d x

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