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## Main Question or Discussion Point

I am trying to show that L[t^m] = m!/s^m+1, unfortunately I can not understand why integral from 0 to inf of (t^m)(e^-st)dt = (-d/ds)^m. integral 0 to inf of e^-stdt...... ????????

- Thread starter catcherintherye
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I am trying to show that L[t^m] = m!/s^m+1, unfortunately I can not understand why integral from 0 to inf of (t^m)(e^-st)dt = (-d/ds)^m. integral 0 to inf of e^-stdt...... ????????

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marcusl

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HallsofIvy

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[tex]\int_0^\infty t^m e^{-st}dt[/tex]

Let u= t

[tex]-\frac{m}{s}\int_0^\infty t^{m-1}e^{-st}dt[/tex]

since uv= 0 at both ends.

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