What is laplacetransform (t+2)^2 ?

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

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laplacetransform (t+2)^2

laplace transform

(t + 2)^{2}

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

Solution steps

L {(t + 2)^{2}}

Expand

(t + 2)^{2} : t^{2} + 4 t + 4

= L {t^{2} + 4 t + 4}

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}} + 4 L {t} + L {4}

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

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

L {4} : \frac{4}{s}

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

Refine

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

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

\int 9 x e^{3 x} d x

x \to - 2 - lim (\frac{- 2}{x ^{2} - 4})

\frac{d}{d x} (A sin (2 x) + B cos (2 x))

y = 12 cos (x)

\frac{d}{d t} (k t)

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