What is laplacetransform 1-e^{-0.4t} ?

The answer to laplacetransform 1-e^{-0.4t} is 1/s-1/(s+0.4)

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laplacetransform 1-e^{-0.4t}

laplace transform

1 - e^{- 0.4 t}

\frac{1}{s} - \frac{1}{s + 0.4}

Solution steps

L {1 - e^{- 0.4 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 {1} - L {e^{- 0.4 t}}

L {1} : \frac{1}{s}

L {e^{- 0.4 t}} : \frac{1}{s + 0.4}

= \frac{1}{s} - \frac{1}{s + 0.4}

\int \frac{1}{5 + 2 x} d x

(x^{2} + 1)^{(x + 1)}

\frac{d}{d x} (\frac{2 x + 5}{3})

f (x) = x arctan (x)

x \to 0 lim (\frac{1}{x ^{\frac{2}{3}}})

What is laplacetransform 1-e^{-0.4t} ?
The answer to laplacetransform 1-e^{-0.4t} is 1/s-1/(s+0.4)