What is laplacetransform f(t)= 2/3 t^3e^{-8t} ?

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

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laplacetransform f(t)= 2/3 t^3e^{-8t}

laplace transform

f (t) = \frac{2}{3} t^{3} 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}}

x \to 5 lim (8)

y^{^{'}} + y = \frac{1}{( cos ( 2 x ) ) ^{\frac{3}{2}}}

\frac{14}{2 x + 16}

\int \frac{x}{7 - x ^{2}} d x

f (x) = e^{x} (- 4 + 7 x + 4 x^{2}), at x = 0

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