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}}

\frac{d}{d x} ((x^{3} - 1)^{100})

y = x^{4}, x = y^{7}, 1

\int 8 + 2 x - x^{2} d x

x \to 1 + lim (ln x^{2} - 1)

\int_{0}^{1} x 5 x + 4 d x

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