What is laplacetransform 2t^2-2t+1 ?

The answer to laplacetransform 2t^2-2t+1 is 4/(s^3)-2/(s^2)+1/s

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laplacetransform 2t^2-2t+1

laplace transform

2 t^{2} - 2 t + 1

\frac{4}{s ^{3}} - \frac{2}{s ^{2}} + \frac{1}{s}

Solution steps

L {2 t^{2} - 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)}

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

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

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

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

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

Refine

2 \frac{2}{s ^{3}} - 2 \frac{1}{s ^{2}} + \frac{1}{s} : \frac{4}{s ^{3}} - \frac{2}{s ^{2}} + \frac{1}{s}

= \frac{4}{s ^{3}} - \frac{2}{s ^{2}} + \frac{1}{s}

What is laplacetransform 2t^2-2t+1 ?
The answer to laplacetransform 2t^2-2t+1 is 4/(s^3)-2/(s^2)+1/s