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

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

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laplacetransform t^3e^{3t}

laplace transform

t^{3} e^{3 t}

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

Solution steps

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

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

L {e^{3 t}} : \frac{1}{s - 3}

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

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

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

\int ln (\frac{x}{x}) d x

f (x) = a x^{4} + (a - 9) x^{2} - 9

n = 1 \sum \infty \frac{3 n}{n ^{2} + 4}

\int cos^{2} (k x) d x

\int_{2}^{4} \frac{x}{x ^{2} + 6 x + 13} d x

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