Integrate3 contains the integral table used by Integrate2. Integration is performed in a distributional sense. Integrate3 works more effectively on a sum of expressions if they are expanded or collected with respect to the integration variable. See the examples in Integrate2.
Integrate3[x^OPEm Log[x], {x, 0, 1}]-\frac{1}{(m+1)^2}
Integrate3[(x^OPEm Log[x] Log[1 - x])/(1 - x), {x, 0, 1}]\zeta (2) S_1(m)-S_{12}(m)-S_{21}(m)+\zeta (3)
Integrate3[a (x^OPEm Log[x] Log[1 - x])/(1 - x) + b (x^OPEm PolyLog[3, -x])/(1 + x), {x, 0, 1}]a \left(\zeta (2) S_1(m)-S_{12}(m)-S_{21}(m)+\zeta (3)\right)+b (-1)^m \left(\frac{\zeta (2)^2}{8}+\frac{1}{2} \zeta (2) S_{-2}(m)-\frac{3}{4} \zeta (3) S_{-1}(m)+S_{3-1}(m)+\log (2) \left(S_3(m)-S_{-3}(m)\right)-\frac{3}{4} \zeta (3) \log (2)\right)
Integrate3[DeltaFunctionPrime[1 - x], {x, 0, 1}]0
Integrate3[f[x] DeltaFunctionPrime[1 - x], {x, 0, 1}]f'(1)
Integrate3[1/(1 - x), {x, 0, 1}]0