What is laplacetransform t^6e^{-,\at} ?

The answer to laplacetransform t^6e^{-,\at} is e^{-,\at}(720)/(s^7)

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laplacetransform t^6e^{-,\at}

laplace transform

t^{6} e^{-, at}

e^{-, at} \frac{720}{s ^{7}}

Solution steps

L {e^{-, at} t^{6}}

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^{6}}

L {t^{6}} : \frac{720}{s ^{7}}

= e^{-, at} \frac{720}{s ^{7}}

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What is laplacetransform t^6e^{-,\at} ?
The answer to laplacetransform t^6e^{-,\at} is e^{-,\at}(720)/(s^7)