The exponential integral

Observe that the integral defining li diverges as u→∞. Indeed, entry 4.211.1 states that

(11.1.5)

dx

lnx = +∞.

This is evident from the change of variables t = lnx, which yields

(11.1.6)

dx

lnx =

et dt

t ≥ ∫ ∞ 1

dt

t =∞.