What is laplacetransform 2/3 t^3*e^{-8t} ?

The answer to laplacetransform 2/3 t^3*e^{-8t} is 4/((s+8)^4)

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laplacetransform 2/3 t^3*e^{-8t}

laplace transform

\frac{2}{3} t^{3} \cdot e^{- 8 t}

\frac{4}{( s + 8 ) ^{4}}

Solution steps

L {\frac{2}{3} e^{- 8 t} t^{3}}

Use the constant multiplication property of Laplace Transform:

For function

f (t)

and constant

a : L {a \cdot f (t)} = a \cdot L {f (t)}

= \frac{2}{3} L {t^{3} e^{- 8 t}}

L {t^{3} e^{- 8 t}} : \frac{6}{( s + 8 ) ^{4}}

= \frac{2}{3} \cdot \frac{6}{( s + 8 ) ^{4}}

Refine

\frac{2}{3} \frac{6}{( s + 8 ) ^{4}} : \frac{4}{( s + 8 ) ^{4}}

= \frac{4}{( s + 8 ) ^{4}}

\frac{d}{d x} (\frac{4}{x ^{2}} - \frac{2}{x})

3 y^{3} e^{x} d x + e^{- x} d y = 3 y^{3} d x

\frac{d}{d x} (ln (1 - \frac{1}{x}))

\frac{\partial}{\partial x} (3 y^{2} + 20 x^{2} y^{3})

cos^{2} (π t)

What is laplacetransform 2/3 t^3*e^{-8t} ?
The answer to laplacetransform 2/3 t^3*e^{-8t} is 4/((s+8)^4)