New rule for dilogarithms

[benruijl]

Currently, Rubi rules for dilogs do not support cases such as PolyLog[2,(a + b x)/(c + d x)], even though the resulting recursive integral can be solved with existing Rubi rules. The new IBP rule below treats these cases:

Int[PolyLog[2,u_],x_Symbol] :=
          With[{v=SimplifyIntegrand[x*D[u,x]*Log[1-u]/u,x]},
            x*PolyLog[2,u] + Int[v,x]] /;
        With[{w=Together[u]}, RationalFunctionQ[w,x] && Not[FreeQ[w,x]] &&
          0<=Expon[Numerator[w],x]<=2 && 0<=Expon[Denominator[w],x]<=2]

Going out of the specified exponent range requires RootSum.

I have implemented this rule in symbolica-integrate (see also this blog post).