*Find the inverse Laplace transforms of the following functions:*

**Note that as soon as we step inside the exam hall we write down the following rule that is on the tables but not nearly in as nice a form:**

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## (i)

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### Solution

This looks quite tricky but all it needs is a little trick. Multiply out by hand (or by memory or by the Binomial Theorem (in tables)) to get:

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Now taking advantage of the linearity of the inverse Laplace transform (*I’m just going to write instead of . To get a nice inverse Laplace transform symbol I have to type \mathcal{L}^{-1} — along with some dollar signs and I’m sick of it! — no keyboard shortcuts on this page — the notes have shortcuts.*)

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Now using the tables;

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## (ii)

### Solution

Now this looks like

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which we know how to deal with. It is our job to get it looking a bit more like this. We can do this by taking out a out of the bottom line:

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Now using linearity, and the tables, this has inverse transform:

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