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}}

f (x) = x (4 - x)^{3}, at x = 2

f (t) = 3 sin (4 t) - 2 e^{2 t}

h (t) = 6 ln (t^{8})

\frac{d}{d x} (144 - x)

\int (5 - x^{3})^{4} x^{2} d x

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