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How do I solve this?

$$\int \frac{\text{d}x}{x^2 + x \ln x}$$

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    Have you tried changing the variable to $t=\ln x$?2011-05-03
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    Wolfram: (no result found in terms of standard mathematical functions), so others don't have to check.2011-05-03
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    to Dennis : yes, and also :$ t = \frac{\lnx}{x} $ but ..and thanks to Cplayer.2011-05-03
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    Other than using this software is there any algorithm which can say if the integrable is solvable?(in terms of elementary functions)2011-05-03
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    @Dinesh - see [here](http://en.wikipedia.org/wiki/Liouville%27s_theorem_(differential_algebra) and [here](http://en.wikipedia.org/wiki/Risch_algorithm)2011-05-03
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    @Dinesh, yes, there is a theory of integration in closed form (that's what the software is based on). http://en.wikipedia.org/wiki/Risch_algorithm will get you started. @Doman; one solves a problem; one computes an antiderivative.2011-05-03
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    @Dinesh: Also this: http://en.wikipedia.org/wiki/Differential_Galois_theory2011-05-03
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    oh yes..Differential Galois Theory, that will do.2011-05-03
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    Is there a purpose of computing the integral? You might consider a series expansion before doing the integration.2011-05-03

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