Logarithmic Integral

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The function $\text{Li}(x)=\int_2^x~\frac{dx}{\log~x}$ is called the "logarithmic integral". According to the Prime Number Theorem, it is approximately equal to the number of primes below x. The function $\text{li}(x)=\int_0^x~\frac{dx}{\log~x}$ is also called the logarithmic integral; the two functions differ by a constant.

(Since the definition of $\text{li}(x)$ involves integrating through a singularity, some care is needed in interpreting the definition.)

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