What is laplacetransform (t^2e^{-2t})/2 ?

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

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laplacetransform (t^2e^{-2t})/2

laplace transform

\frac{t ^{2} e ^{- 2 t}}{2}

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

Solution steps

L {\frac{e ^{- 2 t} t ^{2}}{2}}

Apply transform rule:

L {f (t)} = F (s)

then

L {e^{a t} f (t)} = F (s - a)

For

\frac{t ^{2} e ^{- 2 t}}{2} : f (t) = \frac{t ^{2}}{2}, a = - 2

= L {\frac{t ^{2}}{2}} (s + 2)

L {\frac{t ^{2}}{2}} : \frac{1}{s ^{3}}

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

\int \frac{1}{u ^{2} - 3} d u

\frac{d}{d x} (\frac{x + 8}{3})

x \to 4 lim (\frac{1}{( x - 4 ) ^{3}})

\int 2 x sec (x) tan (x) d x

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