Hello again.(adsbygoogle = window.adsbygoogle || []).push({});

First off, I wasn't sure how to say this in the title but I'm not taking the inverse Laplace transform of a unit step function. I'm taking the Laplace transform of something that comes out to the unit step function.

I have this question, which is a similar version of the question I am trying to solve. This is also the solution but I have no idea what happened.

(sorry, I don't know why that is so small, click to make it bigger)

So the first part of that image is just the inverse Laplace transform I am trying to solve. The first step I saw was to do partial fractions. When I do that I get:

[itex]\frac{e}{s+1} + \frac{1}{s}[/itex]

I'm omitting the inverse Laplace transform here because I don't know how to do it in latex.

But as you can see, the solution maunual got:

[itex]\frac{e^{-s}}{s} - \frac{e^{-s}}{s+1}[/itex]

Clearly there is something I do not understand about this. I can get the correct answer after this, I just don't understand this step.

Any help would be greatly appreciated.

Thank you.

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# Inverse Laplace transform with unit step function

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