What is laplacetransform t^2e^t ?

The answer to laplacetransform t^2e^t is 2/((s-1)^3)

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laplacetransform t^2e^t

laplace transform

t^{2} e^{t}

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

Solution steps

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

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

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

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

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

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

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

t \to \infty lim (Q (t) + (100 - Q (t)) e^{- k t})

g (t) = 4 t^{- \frac{1}{8}} + 3 ln (t) + ln (5)

y^{^{'}} = (x + y + 1)^{2}

\int sec^{2} (θ) tan^{3} (θ) d θ

What is laplacetransform t^2e^t ?
The answer to laplacetransform t^2e^t is 2/((s-1)^3)