How to integrate $\frac{1}{\log(x)}$?
I have tried integration by parts, but it is a never ending series with no specific general term.
PS: It is indefinite integration.
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Look up https://en.wikipedia.org/wiki/Logarithmic_integral_function – Vasili Oct 25 '18 at 13:38
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There exists no elementary solution of this integral – Dr. Sonnhard Graubner Oct 25 '18 at 13:39
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There is no indefinite integral expressible in terms of elementary functions. A special function has to be defined for this purpose, and it is known as the Logarithmic Integral Function.
Note that many, many seemingly elementary functions do not have indefinite integrals that can be expressed in terms of elementary functions. Another famous example is $e^{-x^2}$.
Deepak
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Just curious : how can we prove that there is no existing function that matches ? – Arnaud Mégret Oct 25 '18 at 13:41
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2@ArnaudMégret This might help. https://math.stackexchange.com/questions/155/how-can-you-prove-that-a-function-has-no-closed-form-integral – Deepak Oct 25 '18 at 13:45