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

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

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laplacetransform 2+3e^{-3t}

laplace transform

2 + 3 e^{- 3 t}

\frac{2}{s} + \frac{3}{s + 3}

Solution steps

L {2 + 3 e^{- 3 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 {2} + 3 L {e^{- 3 t}}

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

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

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

Refine

\frac{2}{s} + 3 \frac{1}{s + 3} : \frac{2}{s} + \frac{3}{s + 3}

= \frac{2}{s} + \frac{3}{s + 3}

\int x^{5} e^{- x^{2}} d x

f (x) = \frac{2}{3} x^{3} + 4 x^{2} + 6 x - 5

x \to 4 + lim (x + 1)

\int x^{2} x d x

\int e^{3 x} \cdot sin (2 x) d x

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