What is laplacetransform e^{-6t}+1/2 e^{-3t}+1/2 e^{-t} ?

The answer to laplacetransform e^{-6t}+1/2 e^{-3t}+1/2 e^{-t} is 1/(s+6)+1/(2(s+3))+1/(2(s+1))

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laplacetransform e^{-6t}+1/2 e^{-3t}+1/2 e^{-t}

laplace transform

e^{- 6 t} + \frac{1}{2} e^{- 3 t} + \frac{1}{2} e^{- t}

\frac{1}{s + 6} + \frac{1}{2 ( s + 3 )} + \frac{1}{2 ( s + 1 )}

Solution steps

L {e^{- 6 t} + \frac{1}{2} e^{- 3 t} + \frac{1}{2} e^{- 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^{- 6 t}} + \frac{1}{2} L {e^{- 3 t}} + \frac{1}{2} L {e^{- t}}

L {e^{- 6 t}} : \frac{1}{s + 6}

L {e^{- 3 t}} : \frac{1}{s + 3}

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

= \frac{1}{s + 6} + \frac{1}{2} \cdot \frac{1}{s + 3} + \frac{1}{2} \cdot \frac{1}{s + 1}

Refine

\frac{1}{s + 6} + \frac{1}{2} \frac{1}{s + 3} + \frac{1}{2} \frac{1}{s + 1} : \frac{1}{s + 6} + \frac{1}{2 ( s + 3 )} + \frac{1}{2 ( s + 1 )}

= \frac{1}{s + 6} + \frac{1}{2 ( s + 3 )} + \frac{1}{2 ( s + 1 )}

\int 16 sin^{4} (x) d x

n = 1 \sum \infty \frac{n 2 ^{n}}{7 ^{n}}

y^{^{'}} = \frac{( 2 x y ^{2} + 6 x )}{x ^{2} y + y}

\frac{\partial}{\partial y} (arctan (x y))

\frac{d}{d x} (a^{x} + sin (x) + x)

What is laplacetransform e^{-6t}+1/2 e^{-3t}+1/2 e^{-t} ?
The answer to laplacetransform e^{-6t}+1/2 e^{-3t}+1/2 e^{-t} is 1/(s+6)+1/(2(s+3))+1/(2(s+1))