What is laplacetransform te^{5t} ?

The answer to laplacetransform te^{5t} is 1/((s-5)^2)

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laplacetransform te^{5t}

laplace transform

t e^{5 t}

\frac{1}{( s - 5 ) ^{2}}

Solution steps

L {e^{5 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^{5 t} : f (t) = e^{5 t}, k = 1

= (- 1)^{1} \frac{d}{d s} (L {e^{5 t}})

L {e^{5 t}} : \frac{1}{s - 5}

\frac{d}{d s} (\frac{1}{s - 5}) = - \frac{1}{( s - 5 ) ^{2}}

= (- 1)^{1} (- \frac{1}{( s - 5 ) ^{2}})

= \frac{1}{( s - 5 ) ^{2}}

w \to - 2 lim (\frac{w + 2}{w ^{2} - 6 w - 16})

\int tan (t) d t

\int 3 θ cos (\frac{θ}{5}) d θ

\int - e^{- x} cos (x) d x

\int \frac{1}{x ^{2} a ^{2}} d x

What is laplacetransform te^{5t} ?
The answer to laplacetransform te^{5t} is 1/((s-5)^2)