It sounds a bit strange in English (although we have the term in Dutch), so I'm not sure whether this is a generally known/used mathematical term: 'primitivable'. If not, it just comes down to find a primitive function F of f, so that F'=f. Specifically, I'm wondering about primitive functions in terms of (a finite number of) elementary functions.(adsbygoogle = window.adsbygoogle || []).push({});

Recently, someone asked me to find

[tex]\int {x\tan xdx} [/tex]

Using integration by parts, this comes down to finding

[tex]\int {\ln \left( {\cos x} \right)dx} [/tex]

Because of this, and the result from Mathematica (involving poly logarithms), I told the guy that this function probably doesn't have a primitive function, at least not expressed as a finite number of elementary functions. I answer the same thing when someone asks to find the indefinite integral of the more known e^(-x²).

Now on http://mathworld.wolfram.com/IndefiniteIntegral.html" [Broken], it says that this is exactly the case for a few of those well-known integrals (numbered line 8). But what interests me is that it also states that Liouville was able to show this. I was wondering how one can show/prove such a thing, in general or for these specific functions. I wasn't able to find anything while searching, perhaps because I'm searching on the wrong terms.

Perhaps someone knows how this is done, can be done or where it can be found? I'd love to see this shown for e^(-x²) for example.

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# Primitivable math function term

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