What is laplacetransform (t-2)e^{-4t} ?

The answer to laplacetransform (t-2)e^{-4t} is 1/((s+4)^2)-2/(s+4)

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laplacetransform (t-2)e^{-4t}

laplace transform

(t - 2) e^{- 4 t}

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

Solution steps

L {e^{- 4 t} (t - 2)}

Apply transform rule:

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

then

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

For

(t - 2) e^{- 4 t} : f (t) = (t - 2), a = - 4

= L {(t - 2)} (s + 4)

L {(t - 2)} : \frac{1}{s ^{2}} - \frac{2}{s}

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

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

4 x + \frac{144}{x} + 80

\frac{d}{d x} (lo g_{e} (x^{2} + x + 1))

\frac{d}{d x} ((- 3 x^{5} - 3)^{3})

\int x (1 - x)^{\frac{2}{3}} d x

x \to 0 + lim (2 x^{3 x})

What is laplacetransform (t-2)e^{-4t} ?
The answer to laplacetransform (t-2)e^{-4t} is 1/((s+4)^2)-2/(s+4)