What is laplacetransform t^3e^{7t} ?

The answer to laplacetransform t^3e^{7t} is 6/((s-7)^4)

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laplacetransform t^3e^{7t}

laplace transform

t^{3} e^{7 t}

\frac{6}{( s - 7 ) ^{4}}

Solution steps

L {e^{7 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^{7 t} : f (t) = e^{7 t}, k = 3

= (- 1)^{3} \frac{d ^{3}}{d s ^{3}} (L {e^{7 t}})

L {e^{7 t}} : \frac{1}{s - 7}

\frac{d ^{3}}{d s ^{3}} (\frac{1}{s - 7}) = - \frac{6}{( s - 7 ) ^{4}}

= (- 1)^{3} (- \frac{6}{( s - 7 ) ^{4}})

= \frac{6}{( s - 7 ) ^{4}}

\frac{\partial}{\partial y} (e^{x^{2}} - y)

\int sin (120 π x) d x

f (x) = 4 x^{2} - x^{3}, (1, 3)

y = - x^{2} - 2 x + 2, (- 3, - 1)

sin (x), 0

What is laplacetransform t^3e^{7t} ?
The answer to laplacetransform t^3e^{7t} is 6/((s-7)^4)