What is laplacetransform (-2)^{t-1} ?

The answer to laplacetransform (-2)^{t-1} is -1/(2(s-ln(-2)))

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laplacetransform (-2)^{t-1}

laplace transform

(- 2)^{t - 1}

- \frac{1}{2 ( s - ln ( - 2 ) )}

Solution steps

L {(- 2)^{t - 1}}

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)^{- 1} L {(- 2)^{t}}

L {(- 2)^{t}} : \frac{1}{s - ln ( - 2 )}

= (- 2)^{- 1} \frac{1}{s - ln ( - 2 )}

Refine

(- 2)^{- 1} \frac{1}{s - ln ( - 2 )} : - \frac{1}{2 ( s - ln ( - 2 ) )}

= - \frac{1}{2 ( s - ln ( - 2 ) )}

\int \frac{3 x ( e ^{- 2 x} - 7 x )}{5} d x

\int (arcsin (x))^{2} d x

g (x) = \frac{2}{x ^{3}} - \frac{1}{x ^{2}}

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

What is laplacetransform (-2)^{t-1} ?
The answer to laplacetransform (-2)^{t-1} is -1/(2(s-ln(-2)))