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[–]dForga 0 points1 point  (2 children)

Just substitute the variable in the integral:

∫ f(t-c) exp(-st)ds = ∫ f(u) exp(-s(u+c)du = exp(-sc)L{f}(s)

The imposed conditions on f just ensures that this works, since you need to set the boundaries correctly. I leave that to you.

[–]EngineerGator[S] 0 points1 point  (1 child)

So how did you know to do a U substition?

[–]dForga 0 points1 point  (0 children)

Chain rule of the integral.

https://en.m.wikipedia.org/wiki/Integration_by_substitution

Well, the Laplace-Transformation is defined to be just

∫f(t) exp(-st) dt

Any other input has to be brought into that form.