What is laplacetransform te^{8t} ?

The answer to laplacetransform te^{8t} is 1/((s-8)^2)

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laplacetransform te^{8t}

laplace transform

t e^{8 t}

\frac{1}{( s - 8 ) ^{2}}

Solution steps

L {e^{8 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^{8 t} : f (t) = e^{8 t}, k = 1

= (- 1)^{1} \frac{d}{d s} (L {e^{8 t}})

L {e^{8 t}} : \frac{1}{s - 8}

\frac{d}{d s} (\frac{1}{s - 8}) = - \frac{1}{( s - 8 ) ^{2}}

= (- 1)^{1} (- \frac{1}{( s - 8 ) ^{2}})

= \frac{1}{( s - 8 ) ^{2}}

x \to 9 - lim (\frac{5 x}{x - 9})

\frac{d}{d x} (- 4 x^{4} + 8 x^{3})

\frac{( 3 s + 1 )}{s ( s + 2 )}

y^{^{'}} - \frac{6}{x} y = \frac{( y ^{5} )}{x ^{18}}, y (1) = 1

g (x) = 3 (5 - 7 x)^{5}

What is laplacetransform te^{8t} ?
The answer to laplacetransform te^{8t} is 1/((s-8)^2)