What is laplacetransform t^2+t+1 ?

The answer to laplacetransform t^2+t+1 is 2/(s^3)+1/(s^2)+1/s

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laplacetransform t^2+t+1

laplace transform

t^{2} + t + 1

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

Solution steps

L {t^{2} + t + 1}

Use the linearity property of Laplace Transform:

For functions

f (t), g (t)

and constants

a, b : L {a \cdot f (t) + b \cdot g (t)} = a \cdot L {f (t)} + b \cdot L {g (t)}

= L {t^{2}} + L {t} + L {1}

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

L {t} : \frac{1}{s ^{2}}

L {1} : \frac{1}{s}

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

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What is laplacetransform t^2+t+1 ?
The answer to laplacetransform t^2+t+1 is 2/(s^3)+1/(s^2)+1/s