What is laplacetransform (t-5)^2 ?

The answer to laplacetransform (t-5)^2 is 2/(s^3)-(10}{s^2}+\frac{25)/s

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laplacetransform (t-5)^2

laplace transform

(t - 5)^{2}

\frac{2}{s ^{3}} - \frac{10}{s ^{2}} + \frac{25}{s}

Solution steps

L {(t - 5)^{2}}

Expand

(t - 5)^{2} : t^{2} - 10 t + 25

= L {t^{2} - 10 t + 25}

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}} - 10 L {t} + L {25}

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

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

L {25} : \frac{25}{s}

= \frac{2}{s ^{3}} - 10 \cdot \frac{1}{s ^{2}} + \frac{25}{s}

Refine

\frac{2}{s ^{3}} - 10 \frac{1}{s ^{2}} + \frac{25}{s} : \frac{2}{s ^{3}} - \frac{10}{s ^{2}} + \frac{25}{s}

= \frac{2}{s ^{3}} - \frac{10}{s ^{2}} + \frac{25}{s}

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What is laplacetransform (t-5)^2 ?
The answer to laplacetransform (t-5)^2 is 2/(s^3)-(10}{s^2}+\frac{25)/s