What is laplacetransform 1+5e^{3t} ?

The answer to laplacetransform 1+5e^{3t} is 1/s+5/(s-3)

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laplacetransform 1+5e^{3t}

laplace transform

1 + 5 e^{3 t}

\frac{1}{s} + \frac{5}{s - 3}

Solution steps

L {1 + 5 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 {1} + 5 L {e^{3 t}}

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

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

= \frac{1}{s} + 5 \cdot \frac{1}{s - 3}

Refine

\frac{1}{s} + 5 \frac{1}{s - 3} : \frac{1}{s} + \frac{5}{s - 3}

= \frac{1}{s} + \frac{5}{s - 3}

\frac{d}{d x} (ln (x^{5}) + 8 ln (x))

f (x) = x^{2} + 6 x - 16, at x = 2

x \to 0 lim (\frac{h ( x )}{g ( x )})

(8 x - x^{2})^{3}

e^{t} \cdot cos (t) + j \cdot e^{t} \cdot sin (t)

What is laplacetransform 1+5e^{3t} ?
The answer to laplacetransform 1+5e^{3t} is 1/s+5/(s-3)