What is laplacetransform 2(t-3)^2 ?

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

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laplacetransform 2(t-3)^2

laplace transform

2 (t - 3)^{2}

2 (\frac{2}{s ^{3}} - \frac{6}{s ^{2}} + \frac{9}{s})

Solution steps

L {2 (t - 3)^{2}}

Use the constant multiplication property of Laplace Transform:

For function

f (t)

and constant

a : L {a \cdot f (t)} = a \cdot L {f (t)}

= 2 L {(t - 3)^{2}}

L {(t - 3)^{2}} : \frac{2}{s ^{3}} - \frac{6}{s ^{2}} + \frac{9}{s}

= 2 (\frac{2}{s ^{3}} - \frac{6}{s ^{2}} + \frac{9}{s})

f (x) = x^{4} - 3 x^{2} + 2, at x = 1

\frac{d}{d x} (7 + cot (x) - 2 csc (x))

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

\int_{0}^{2} t^{2} d t

\frac{d}{d t} (\frac{4}{3} π t^{3})

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