What is laplacetransform t^2e^{4t} ?

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

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laplacetransform t^2e^{4t}

laplace transform

t^{2} e^{4 t}

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

Solution steps

L {e^{4 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^{4 t} : f (t) = e^{4 t}, k = 2

= (- 1)^{2} \frac{d ^{2}}{d s ^{2}} (L {e^{4 t}})

L {e^{4 t}} : \frac{1}{s - 4}

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

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

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

\frac{d}{d x} (e^{a r c s i n (x)})

x \to 2 lim (x^{2} + 3 x)

\int arccos (3 x) d x

f (x) = 3 x^{3}

\int sin^{2} (3 x) \cdot cos^{4} (3 x) d x

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