What is laplacetransform te^{3t} ?

The answer to laplacetransform te^{3t} is 1/((s-3)^2)

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laplacetransform te^{3t}

laplace transform

t e^{3 t}

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

Solution steps

L {e^{3 t} t}

Use Laplace Transform table:

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

For

t e^{3 t} : f (t) = e^{3 t}, k = 1

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

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

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

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

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

f (x) = \frac{1}{x - 8}, (- 1, - \frac{1}{9})

\frac{d}{d x} (e^{- 3 x} cos (2 x))

\int \frac{9}{25 + 16 r ^{2}} d r

\int 1 + 4 r^{2} \cdot r d r

\frac{d}{d x} ([x + (x + sin^{2} (x))^{7}]^{5})

What is laplacetransform te^{3t} ?
The answer to laplacetransform te^{3t} is 1/((s-3)^2)