What is laplacetransform 2/3 t^2+5e^{-4t} ?

The answer to laplacetransform 2/3 t^2+5e^{-4t} is 4/(3s^3)+5/(s+4)

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laplacetransform 2/3 t^2+5e^{-4t}

laplace transform

\frac{2}{3} t^{2} + 5 e^{- 4 t}

\frac{4}{3 s ^{3}} + \frac{5}{s + 4}

Solution steps

L {\frac{2}{3} t^{2} + 5 e^{- 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)}

= \frac{2}{3} L {t^{2}} + 5 L {e^{- 4 t}}

L {t^{2}} : \frac{2}{s ^{3}}

L {e^{- 4 t}} : \frac{1}{s + 4}

= \frac{2}{3} \cdot \frac{2}{s ^{3}} + 5 \cdot \frac{1}{s + 4}

Refine

\frac{2}{3} \frac{2}{s ^{3}} + 5 \frac{1}{s + 4} : \frac{4}{3 s ^{3}} + \frac{5}{s + 4}

= \frac{4}{3 s ^{3}} + \frac{5}{s + 4}

x \to \infty lim (ln (3 x))

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

sin (x^{2})

\int \frac{( x ^{3} )}{x ^{2} + 4} d x

\frac{d y}{d x} = e^{3 x}

What is laplacetransform 2/3 t^2+5e^{-4t} ?
The answer to laplacetransform 2/3 t^2+5e^{-4t} is 4/(3s^3)+5/(s+4)