Li4 is an abbreviation for the weight 4 polylogarithm
function, i.e. Li4 = PolyLog[4, #]&.
Overview, Li2, Li3, SimplifyPolyLog.
Li4[x]\text{Li}_4(x)
Li4 // StandardForm
(*PolyLog[4, #1] &*)D[Li4[x], x]\frac{\text{Li}_3(x)}{x}
Integrate[Li3[x]/x, x]\text{Li}_4(x)