What is laplacetransform 3(t-2)^2+10(t-2)+9 ?

The answer to laplacetransform 3(t-2)^2+10(t-2)+9 is 6/(s^3)-2/(s^2)+1/s

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laplacetransform 3(t-2)^2+10(t-2)+9

laplace transform

3 (t - 2)^{2} + 10 (t - 2) + 9

\frac{6}{s ^{3}} - \frac{2}{s ^{2}} + \frac{1}{s}

Solution steps

L {3 (t - 2)^{2} + 10 (t - 2) + 9}

Expand

3 (t - 2)^{2} + 10 (t - 2) + 9 : 3 t^{2} - 2 t + 1

= L {3 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)}

= 3 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}

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

Refine

3 \frac{2}{s ^{3}} - 2 \frac{1}{s ^{2}} + \frac{1}{s} : \frac{6}{s ^{3}} - \frac{2}{s ^{2}} + \frac{1}{s}

= \frac{6}{s ^{3}} - \frac{2}{s ^{2}} + \frac{1}{s}

\int \frac{( x ^{2} + 1 ) ^{3}}{x} d x

\int \frac{4 x ^{2}}{3} d x

\int \frac{x - 3}{x ^{2} - 4 x + 5} d x

x \to - 1 lim (2 x - 1)

1 + x^{3}

What is laplacetransform 3(t-2)^2+10(t-2)+9 ?
The answer to laplacetransform 3(t-2)^2+10(t-2)+9 is 6/(s^3)-2/(s^2)+1/s