Riemann Prime Counting Function correction/pairing terms by Mathematica

Question

Riemann Prime Counting Function:

The second correction/paring terms:

I tried to use Mathematica function LogIntegral to plot this second correction/paring terms, for example, when I only include the first 2 non-trivial zeros, and plot with range x from 1 to 5:

Plot[Sum[LogIntegral[x^ZetaZero[k]] + LogIntegral[x^(1 - ZetaZero[k])], {k, 1, 2}], {x, 1, 5}]

However, I got very large value instead of small correction:

I can also use simplified equation provided by[ ref 1]:

Plot[Sum[Exp[ZetaZero[k]*Log[x]]/(ZetaZero[k]*Log[x]), {k, 1, 2}] + Sum[Exp[(1 -ZetaZero[k])*Log[x]]/((1 - ZetaZero[k])*Log[x]), {k, 1, 2}], {x, 1, 5}]

Then I got the correct result:

Anyone knows what is wrong for the LogIntegral one?

Thank you!

ref [1]: H. Riesel and G Gohl, "Some Calculations Related to Riemann's Prime Number Formula," Mathematics of Computation, 24(112), 1970 pp. 969–983.