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

The answer to laplacetransform (t^2-3)^2 is (24)/(s^5)-(12)/(s^3)+9/s

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laplacetransform (t^2-3)^2

laplace transform

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

\frac{24}{s ^{5}} - \frac{12}{s ^{3}} + \frac{9}{s}

Solution steps

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

Expand

(t^{2} - 3)^{2} : t^{4} - 6 t^{2} + 9

= L {t^{4} - 6 t^{2} + 9}

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^{4}} - 6 L {t^{2}} + L {9}

L {t^{4}} : \frac{24}{s ^{5}}

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

L {9} : \frac{9}{s}

= \frac{24}{s ^{5}} - 6 \cdot \frac{2}{s ^{3}} + \frac{9}{s}

Refine

\frac{24}{s ^{5}} - 6 \frac{2}{s ^{3}} + \frac{9}{s} : \frac{24}{s ^{5}} - \frac{12}{s ^{3}} + \frac{9}{s}

= \frac{24}{s ^{5}} - \frac{12}{s ^{3}} + \frac{9}{s}

\frac{d}{d x} (\frac{x + 3}{x - 2})

\frac{\partial}{\partial x} (x y^{3} + 2 x y)

x \to \infty lim (tan (\frac{2 x π}{1 + 8 x}))

\int \frac{1}{36 x ^{2} - 49} d x

\frac{d}{d x} (\frac{4 x}{( x ^{2} + 2 ) ^{2}})

What is laplacetransform (t^2-3)^2 ?
The answer to laplacetransform (t^2-3)^2 is (24)/(s^5)-(12)/(s^3)+9/s