Logarithmic integral function

Definition

For $x$ a positive real number, the logarithmic integral at $x$, denoted $\operatorname {li} (x)$, is defined as:

$\int _{0}^{x}{\frac {dt}{\log t}}$.

Note that there is no elementary function representing the indefinite integral, and hence, the logarithmic integral function is not expressible in terms of elementary functions.