What is laplacetransform t*e^t ?

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

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laplacetransform t*e^t

laplace transform

t \cdot 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}}

\int_{0}^{\frac{π}{2}} cos^{2} (x) d x

cos (f (x) - 2)

\frac{1}{t ^{3}}

11

e^{\cdot \frac{1}{4} t}

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