What is laplacetransform (x-2)^2 ?

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

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laplacetransform (x-2)^2

laplace transform

(x - 2)^{2}

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

Solution steps

L {(x - 2)^{2}}

Expand

(x - 2)^{2} : x^{2} - 4 x + 4

= L {x^{2} - 4 x + 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 {x^{2}} - 4 L {x} + L {4}

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

L {x} : \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}

\frac{d}{d x} (sin (x) sin (2 x))

\frac{d}{d x} (3 x^{4} - 16 x^{3} - 18 x^{2})

10 x + 1

f (x) = (4 t - 5)^{4} + (4 t + 5)^{4}

y = [x (x^{5} + 4)^{4}]

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