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**[SOLVED] Laplace Transform**

## Homework Statement

Suppose F(s) = [tex]\displaystyle\mathcal{L}(f(t)) [/tex]

Show that [tex]\displaystyle\mathcal{L}(f(ct)) = 1/c F(s/c) [/tex]

## Homework Equations

## The Attempt at a Solution

[tex]\displaystyle\mathcal{L}(f(t)) = \int_0^{inf} e^{-st} f(t) dt[/tex]

[tex]\displaystyle\mathcal{L}(f(ct)) = \int_0^{inf} e^{-st} f(ct) dt[/tex]

I'm not quite sure what to do after this...

I could play around with integration by parts, but in this case I don't think it yields anything useful

[tex]\frac{F(ct)}{c} e^{-st} - \int \frac{F(ct)}{c} (-s e^{-st} ) dt[/tex]

[tex]{F(t)e^{-st} + \int F(t) se^{-st} dt}{}[/tex]

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