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

The answer to laplacetransform e^{-2t}(3t)^2 is (18)/((s+2)^3)

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

laplace transform

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

\frac{18}{( s + 2 ) ^{3}}

Solution steps

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

Apply transform rule:

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

then

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

For

e^{- 2 t} (3 t)^{2} : f (t) = (3 t)^{2}, a = - 2

= L {(3 t)^{2}} (s + 2)

L {(3 t)^{2}} : \frac{18}{s ^{3}}

= \frac{18}{( s + 2 ) ^{3}}

\frac{d}{d x} ((f (x) (3 x))^{2} + 5)

x \to 2 lim (5 x^{2} - 3 x + 1)

\frac{d}{d x} (ln (x 4 x - 1))

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

\int_{3}^{5} e^{x} d x

What is laplacetransform e^{-2t}(3t)^2 ?
The answer to laplacetransform e^{-2t}(3t)^2 is (18)/((s+2)^3)