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Possible Duplicate:
How can you prove that a function has no closed form integral?
Why can't erf be expressed in terms of elementary functions?

By trivial primitives I mean expressions involving logarithms, polynomials, and trigonometrical or exponential functions.

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    http://en.wikipedia.org/wiki/Picard%E2%80%93Vessiot_theory2012-08-28
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    **Related**: http://math.stackexchange.com/questions/155/how-can-you-prove-that-a-function-has-no-closed-form-integral2012-08-28
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    Brian Conrad's [Impossibility theorems for elementary integration](http://www.claymath.org/programs/outreach/academy/LectureNotes05/Conrad.pdf) is a very nice place to start, in my opinion.2012-08-28
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    The answer to this question in general is found in the link that @cardinal supplied. This particular function is addressed in the link from Arybhata's comment on Eric Haengel's answer ([here](http://www.math.niu.edu/~rusin/known-math/97/nonelem_integr2)). Thus, I'm flagging to close as a duplicate.2012-08-28

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