# How do you take the inverse laplace transform of this function?
**URL:** https://boards.straightdope.com/t/how-do-you-take-the-inverse-laplace-transform-of-this-function/569840
**Category:** Factual Questions
**Created:** [February 2, 2011, 12:15am UTC](https://boards.straightdope.com/t/how-do-you-take-the-inverse-laplace-transform-of-this-function/569840 "2011-02-02T00:15:38Z")
**Posts on this page:** 5
**Page:** 1
### Author:  [@MattProle](https://boards.straightdope.com/u/MattProle)
#### Post date: [February 2, 2011, 12:15am UTC](https://boards.straightdope.com/t/how-do-you-take-the-inverse-laplace-transform-of-this-function/569840/1 "2011-02-02T00:15:38Z")
A friend of mine needs to take the inverse laplace transform of ((1/s)(1/cosh(s^.5))cosh((s^.5)\*x)), bringing s to the t domain. I’ve only been exposed to laplace transforms for one week, so I couldn’t do much. If anyone knows of the appropriate methods or has a link to the necessary tables it would be greatly appreciated.
Thanks!
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### Author:  [@RickJay](https://boards.straightdope.com/u/RickJay)
#### Post date: [February 2, 2011, 1:29am UTC](https://boards.straightdope.com/t/how-do-you-take-the-inverse-laplace-transform-of-this-function/569840/2 "2011-02-02T01:29:19Z")
I opened this thread because I’d thought it said “lapdance.”
Carry on.
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### Author:  [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)
#### Post date: [February 2, 2011, 5:25am UTC](https://boards.straightdope.com/t/how-do-you-take-the-inverse-laplace-transform-of-this-function/569840/3 "2011-02-02T05:25:25Z")
Use Wolfram Alpha.
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### Author:  [@standingwave](https://boards.straightdope.com/u/standingwave)
#### Post date: [February 2, 2011, 10:19pm UTC](https://boards.straightdope.com/t/how-do-you-take-the-inverse-laplace-transform-of-this-function/569840/4 "2011-02-02T22:19:12Z")
I haven’t had to derive a Laplace transform in thirty years, though I use them often in circuit analysis. As I remember, it’s just a matter of meticulous cranking through the integral. With hairy integrations such as these, [integration-by-parts](http://en.wikipedia.org/wiki/Integration_by_parts) is your best friend. Khan Academy has some excellent videos beginning with [this one](http://www.khanacademy.org/video/laplace-transform-1?playlist=Differential%20Equations).
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### Author:  [@MikeS](https://boards.straightdope.com/u/MikeS)
#### Post date: [February 2, 2011, 11:06pm UTC](https://boards.straightdope.com/t/how-do-you-take-the-inverse-laplace-transform-of-this-function/569840/5 "2011-02-02T23:06:01Z")
Is this even well-defined? How do you integrate s over the negative part of its range (-∞ to 0) when you have a square root in the function? I suppose you could use the identity that cosh(ix) = cos x, but it seems to me that some care is required.
Is this a homework problem, or something that arose outside of a classroom?