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}}

\frac{d}{d x} (2 arctan (8 x))

\int \frac{x}{2 x + 5} d x

\int_{0}^{2} x \cdot e^{- x} d x

x \to 0 + lim (\frac{1}{sin ( x )})

\frac{d}{d x} ((x^{2} + 7) (5 - x))

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