What is laplacetransform t^2*e^{,\at} ?

The answer to laplacetransform t^2*e^{,\at} is e^{,\at} 2/(s^3)

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laplacetransform t^2*e^{,\at}

laplace transform

t^{2} \cdot e^{, at}

e^{, at} \frac{2}{s ^{3}}

Solution steps

L {e^{, at} t^{2}}

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^{, at} L {t^{2}}

L {t^{2}} : \frac{2}{s ^{3}}

= e^{, at} \frac{2}{s ^{3}}

\int \frac{cos ( 5 x )}{sin ( 5 x ) + 4} d x

\int \frac{- 3 x ^{2}}{x ^{4} - 1} d x

\frac{1}{2 s ^{2} + 3 s + 1}

x^{6} cos (x)

y (s) = \frac{1}{s + k e ^{s}}

What is laplacetransform t^2*e^{,\at} ?
The answer to laplacetransform t^2*e^{,\at} is e^{,\at} 2/(s^3)