Logarithmic integral function

Definition

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

$\underset{0}{\overset{x}{\int }}\frac{dt}{\log t}$.

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.