What is laplacetransform 2(t-3)^2+14(t-3)+27 ?

The answer to laplacetransform 2(t-3)^2+14(t-3)+27 is 4/(s^3)+2/(s^2)+3/s

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laplacetransform 2(t-3)^2+14(t-3)+27

laplace transform

2 (t - 3)^{2} + 14 (t - 3) + 27

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

Solution steps

L {2 (t - 3)^{2} + 14 (t - 3) + 27}

Expand

2 (t - 3)^{2} + 14 (t - 3) + 27 : 2 t^{2} + 2 t + 3

= L {2 t^{2} + 2 t + 3}

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)}

= 2 L {t^{2}} + 2 L {t} + L {3}

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

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

L {3} : \frac{3}{s}

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

Refine

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

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

f (x) = 2 x^{2} - 4 x + 5, (- 1, 11)

\frac{\frac{d y}{d x}}{2} = y

\int \frac{1}{2 x lo g _{5} ( x )} d x

x \to 2 lim (2 x^{3} + x^{2} + 7)

\frac{d}{d x} ((\frac{1}{x}) d x)

What is laplacetransform 2(t-3)^2+14(t-3)+27 ?
The answer to laplacetransform 2(t-3)^2+14(t-3)+27 is 4/(s^3)+2/(s^2)+3/s