What is laplacetransform (t+6)^3 ?

The answer to laplacetransform (t+6)^3 is 6/(s^4)+(36}{s^3}+(108)/(s^2)+\frac{216)/s

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laplacetransform (t+6)^3

laplace transform

(t + 6)^{3}

\frac{6}{s ^{4}} + \frac{36}{s ^{3}} + \frac{108}{s ^{2}} + \frac{216}{s}

Solution steps

L {(t + 6)^{3}}

Expand

(t + 6)^{3} : t^{3} + 18 t^{2} + 108 t + 216

= L {t^{3} + 18 t^{2} + 108 t + 216}

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^{3}} + 18 L {t^{2}} + 108 L {t} + L {216}

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

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

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

L {216} : \frac{216}{s}

= \frac{6}{s ^{4}} + 18 \cdot \frac{2}{s ^{3}} + 108 \cdot \frac{1}{s ^{2}} + \frac{216}{s}

Refine

\frac{6}{s ^{4}} + 18 \frac{2}{s ^{3}} + 108 \frac{1}{s ^{2}} + \frac{216}{s} : \frac{6}{s ^{4}} + \frac{36}{s ^{3}} + \frac{108}{s ^{2}} + \frac{216}{s}

= \frac{6}{s ^{4}} + \frac{36}{s ^{3}} + \frac{108}{s ^{2}} + \frac{216}{s}

What is laplacetransform (t+6)^3 ?
The answer to laplacetransform (t+6)^3 is 6/(s^4)+(36}{s^3}+(108)/(s^2)+\frac{216)/s