What is laplacetransform (te)^3e^{-2t}e^{-2} ?

The answer to laplacetransform (te)^3e^{-2t}e^{-2} is (6e)/((s+2)^4)

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laplacetransform (te)^3e^{-2t}e^{-2}

laplace transform

(t e)^{3} e^{- 2 t} e^{- 2}

\frac{6 e}{( s + 2 ) ^{4}}

Solution steps

L {e^{- 2} e^{- 2 t} (e t)^{3}}

Use the constant multiplication property of Laplace Transform:

For function

f (t)

and constant

a : L {a \cdot f (t)} = a \cdot L {f (t)}

= e^{- 2} L {(t e)^{3} e^{- 2 t}}

L {(t e)^{3} e^{- 2 t}} : \frac{6 e ^{3}}{( s + 2 ) ^{4}}

= e^{- 2} \frac{6 e ^{3}}{( s + 2 ) ^{4}}

Refine

e^{- 2} \frac{6 e ^{3}}{( s + 2 ) ^{4}} : \frac{6 e}{( s + 2 ) ^{4}}

= \frac{6 e}{( s + 2 ) ^{4}}

\frac{d P}{d t} = P (950 - P)

\frac{d y}{d x} = sin (x)

\int x ln^{2} (x) d x

y = 3 (x + 1), y = 4 (x + 1), x = 7

What is laplacetransform (te)^3e^{-2t}e^{-2} ?
The answer to laplacetransform (te)^3e^{-2t}e^{-2} is (6e)/((s+2)^4)