# Integration question

**URL:** <https://boards.straightdope.com/t/integration-question/323807>\
**Category:** Factual Questions\
**Created:** [September 28, 2005, 4:41am UTC](https://boards.straightdope.com/t/integration-question/323807 "2005-09-28T04:41:59Z")\
**Posts on this page:** 4\
**Page:** 2

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**Author:** ![Bytegeist](https://avatars.discourse-cdn.com/v4/letter/b/9dc877/32.png) [@Bytegeist](https://boards.straightdope.com/u/Bytegeist)\
**Post date:** [September 29, 2005, 6:37pm UTC](https://boards.straightdope.com/t/integration-question/323807/21 "2005-09-29T18:37:07Z")

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Not that it’s important, but I just spent most of the past two hours taking the derivative of the expression returned by the Wolfram site — after having blundered for one of the subexpressions, wasting a lot of paper and time, and needing to backtrack.

I’ve done such exercises in the past, so I wasn’t too surprised when it all worked out. Still, it’s nifty how this large expression expands into a _huge_ expression, then almost completely wipes itself out, distilling down to a simple sqrt(tan(x)) in the end.

Kind of like a good movie, only a lot cheaper to produce. Perhaps I’m easily entertained.

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**Author:** ![Bytegeist](https://avatars.discourse-cdn.com/v4/letter/b/9dc877/32.png) [@Bytegeist](https://boards.straightdope.com/u/Bytegeist)\
**Post date:** [September 29, 2005, 7:17pm UTC](https://boards.straightdope.com/t/integration-question/323807/22 "2005-09-29T19:17:49Z")

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I note in passing that the Wolfram site just gives up on “x^x” (_x[sup]x[/sup]_). Does this function not have a known anti-derivative, or does Mathematica simply balk?

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**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\
**Post date:** [September 29, 2005, 7:53pm UTC](https://boards.straightdope.com/t/integration-question/323807/23 "2005-09-29T19:53:20Z")

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Maple can’t handle it, either. At least it’s not returning it in the form of a limit of a sum (I’ve seen Maple do this before).

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**Author:** ![ultrafilter](https://avatars.discourse-cdn.com/v4/letter/u/3d9bf3/32.png) [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)\
**Post date:** [September 29, 2005, 8:10pm UTC](https://boards.straightdope.com/t/integration-question/323807/24 "2005-09-29T20:10:43Z")

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> [@Bytegeist](#):
>
> I note in passing that the Wolfram site just gives up on “x^x” (_x[sup]x[/sup]_). Does this function not have a known anti-derivative, or does Mathematica simply balk?

I think that one’s unknown. Complicated exponentials get out of the realm of closed forms very quickly.

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