What is laplacetransform t^3e^{-,\at} ?

The answer to laplacetransform t^3e^{-,\at} is e^{-,\at} 6/(s^4)

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laplacetransform t^3e^{-,\at}

laplace transform

t^{3} e^{-, at}

e^{-, at} \frac{6}{s ^{4}}

Solution steps

L {e^{-, at} t^{3}}

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^{3}}

L {t^{3}} : \frac{6}{s ^{4}}

= e^{-, at} \frac{6}{s ^{4}}

\int \frac{x}{6 x + 1} d x

arctan (\frac{2 x}{5})

4 x 3 x^{2} + 2

\frac{x ^{5}}{10} + \frac{1}{6 x ^{3}}

t \cdot \frac{d y}{d t} = t^{3} + 14 t^{3} y

What is laplacetransform t^3e^{-,\at} ?
The answer to laplacetransform t^3e^{-,\at} is e^{-,\at} 6/(s^4)