What is laplacetransform f(t)=e^{-3t}+3 ?

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

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laplacetransform f(t)=e^{-3t}+3

laplace transform

f (t) = e^{- 3 t} + 3

\frac{1}{s + 3} + \frac{3}{s}

Solution steps

L {e^{- 3 t} + 3}

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^{- 3 t}} + L {3}

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

L {3} : \frac{3}{s}

= \frac{1}{s + 3} + \frac{3}{s}

\frac{d}{d x} (x^{2} - ln (x))

sin (x^{2} + π)

2 x - \frac{1}{2 x}

y = arcsin (x^{4})

\frac{\partial}{\partial x} (\frac{1}{( 1 + x )})

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