Cosine integral ($\mathrm{Ci}(x)=-{\int }_x^{\infty }\cos t/tdt$)

For real $x>0$, its small-argument expansion is $\mathrm{Ci}(x)={\gamma }_E+\log x+O(x^2)$. Integrating ${\mathrm{Ci}}^{\prime }(x)=\cos x/x$ separates the logarithm from the regular correction. Its conventional constant is the Euler--Mascheroni constant; the primary series normalization is dlmf.nist.gov/6.6.E6 .