What is laplacetransform e^{2t}t^3 ?

The answer to laplacetransform e^{2t}t^3 is 6/((s-2)^4)

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laplacetransform e^{2t}t^3

laplace transform

e^{2 t} t^{3}

\frac{6}{( s - 2 ) ^{4}}

Solution steps

L {e^{2 t} t^{3}}

Use Laplace Transform table:

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

For

e^{2 t} t^{3} : f (t) = e^{2 t}, k = 3

= (- 1)^{3} \frac{d ^{3}}{d s ^{3}} (L {e^{2 t}})

L {e^{2 t}} : \frac{1}{s - 2}

\frac{d ^{3}}{d s ^{3}} (\frac{1}{s - 2}) = - \frac{6}{( s - 2 ) ^{4}}

= (- 1)^{3} (- \frac{6}{( s - 2 ) ^{4}})

= \frac{6}{( s - 2 ) ^{4}}

\int \frac{2}{x ^{3} x ^{2} - 1} d x

\int (2 x - y) d x

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

\frac{d}{d x} (0.00037 x^{2})

ln (1 + 5 x)

What is laplacetransform e^{2t}t^3 ?
The answer to laplacetransform e^{2t}t^3 is 6/((s-2)^4)