What is laplacetransform x^2e^{3x} ?

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

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laplacetransform x^2e^{3x}

laplace transform

x^{2} e^{3 x}

\frac{2}{( s - 3 ) ^{3}}

Solution steps

L {e^{3 x} x^{2}}

Use Laplace Transform table:

L {t^{k} f (t)} = (- 1)^{k} \frac{d ^{k}}{d s ^{k}} (L {f (t)})

For

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

= (- 1)^{2} \frac{d ^{2}}{d s ^{2}} (L {e^{3 x}})

L {e^{3 x}} : \frac{1}{s - 3}

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

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

= \frac{2}{( s - 3 ) ^{3}}

\frac{d}{d x} ((arctan (2 x))^{2})

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

\frac{d}{d x} (x^{2} x - 5 x)

y = 2 - e^{x}, y = 10 e^{- x} - 5

f (x) = \frac{ln ( 4 )}{3} e^{x}

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