What is laplacetransform te^t ?

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

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laplacetransform te^t

laplace transform

t e^{t}

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

Solution steps

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

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

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

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

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

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

\frac{d}{d x} (e^{x^{4}} + 7 x)

f (x) = x^{2} + 16, at x = 3

\int \frac{e ^{8 x}}{e ^{8 x} + 6} d x

y \to 1 lim (\frac{2 y ^{2} + 3}{y - 1})

\frac{d}{d t} (2 e^{- t} t - e^{- t} t^{2})

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