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

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

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

laplace transform

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

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

Solution steps

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

Apply transform rule:

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

then

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

For

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

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

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

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

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