Integral with a natural logarithm in the denominator
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How do I solve this?
$$\int \frac{\text{d}x}{x^2 + x \ln x}$$
integration
asked 2011-05-03
user id:10401
21
33bronze badges
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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_theory – 2011-05-03
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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