What is laplacetransform (e^t-e^{-t})^2 ?

The answer to laplacetransform (e^t-e^{-t})^2 is 8/(s(s-2)(s+2))

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laplacetransform (e^t-e^{-t})^2

laplace transform

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

\frac{8}{s ( s - 2 ) ( s + 2 )}

Solution steps

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

Expand

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

= L {e^{2 t} - 2 + e^{- 2 t}}

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 {e^{2 t}} - L {2} + L {e^{- 2 t}}

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

L {2} : \frac{2}{s}

L {e^{- 2 t}} : \frac{1}{s + 2}

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

Simplify

\frac{1}{s - 2} - \frac{2}{s} + \frac{1}{s + 2} : \frac{8}{s ( s - 2 ) ( s + 2 )}

= \frac{8}{s ( s - 2 ) ( s + 2 )}

\int 512 x^{2} cos (8 x) d x

\frac{d}{d x} (ln (\frac{sin ( x )}{x}))

y = 4 ln (x), y = x ln (x)

x \to 4 lim (e^{\frac{3}{4 - x}})

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

What is laplacetransform (e^t-e^{-t})^2 ?
The answer to laplacetransform (e^t-e^{-t})^2 is 8/(s(s-2)(s+2))