# Primitive of Reciprocal of Logarithm of x has no Solution in Elementary Functions

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## Theorem

The primitive:

- $\ds \int \frac {\d x} {\ln x}$

cannot be expressed in terms of a finite number of elementary functions.

## Proof

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## Also see

## Historical Note

The proof that $\ds \int \dfrac {\d x} {\ln x}$ cannot be expressed with a finite number of elementary functions was first proved by Joseph Liouville.

## Sources

- 1992: George F. Simmons:
*Calculus Gems*... (previous) ... (next): Chapter $\text {A}.29$: Liouville ($\text {1809}$ – $\text {1882}$)