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

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

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laplacetransform e^{3t}t^2

laplace transform

e^{3 t} t^{2}

\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

e^{3 t} t^{2} : 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 c^{3} t d t

(- 2, - 1), (3, 4)

\int \frac{x - 4}{x ^{2} - 8 x + 1} d x

t \to 3 - lim (\frac{t ^{2}}{9 - t ^{2}})

\int \frac{x ^{2}}{x ^{2} + 8} d x

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