What is laplacetransform t^3e^{b*t} ?

The answer to laplacetransform t^3e^{b*t} is 6/((s-b)^4)

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laplacetransform t^3e^{b*t}

laplace transform

t^{3} e^{b \cdot t}

\frac{6}{( s - b ) ^{4}}

Solution steps

L {e^{b t} t^{3}}

Use Laplace Transform table:

L {t^{k} f (t)} = (- 1)^{k} \frac{d ^{k}}{d s ^{k}} (L {f (t)})

For

t^{3} e^{b t} : f (t) = e^{b t}, k = 3

= (- 1)^{3} \frac{d ^{3}}{d s ^{3}} (L {e^{b t}})

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

\frac{d ^{3}}{d s ^{3}} (\frac{1}{s - b}) = - \frac{6}{( s - b ) ^{4}}

= (- 1)^{3} (- \frac{6}{( s - b ) ^{4}})

= \frac{6}{( s - b ) ^{4}}

\frac{\partial}{\partial x} (ln (x + y^{4}))

x \to \infty lim (- \frac{x}{2})

x \to \frac{π}{2} lim (5 sin (x))

f (x) = - 9 x^{2}, at x = 2

e^{\frac{- x}{2}}

What is laplacetransform t^3e^{b*t} ?
The answer to laplacetransform t^3e^{b*t} is 6/((s-b)^4)