What is laplacetransform e^{5t}t ?

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

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laplacetransform e^{5t}t

laplace transform

e^{5 t} 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

e^{5 t} 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}}

\frac{d}{d x} (x^{2} - 6 x + 9)

\int_{1}^{2} \frac{1}{x ( ln ( x ) ) ^{1}} d x

\int_{1}^{\infty} \frac{1}{1 + e ^{x}} d x

2 x, 5, \frac{2}{x ^{2}}

x \to \infty lim (2 x - 4 x^{2} - 2 x)

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