What is laplacetransform (t-1)^2 ?

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

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laplacetransform (t-1)^2

laplace transform

(t - 1)^{2}

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

Solution steps

L {(t - 1)^{2}}

Expand

(t - 1)^{2} : t^{2} - 2 t + 1

= L {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)}

= 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}

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

Refine

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

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

\int e^{4 l n (x)} d x

\frac{d}{d x} (\frac{x ^{3}}{2})

x \to 2 + lim (4 x^{2} - 2 x + 3)

f (x) = 7 x, at x = 25

ln (x^{\frac{3}{2}})

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