Integrate[Log[x]*Log[1 + x]^4, x] ==
-48 - 120*x + 24*x*Log[x] + 96*Log[1 + x] +
96*x*Log[1 + x] - 24*Log[x]*Log[1 + x] -
24*x*Log[x]*Log[1 + x] - 36*Log[1 + x]^2 -
36*x*Log[1 + x]^2 - 12*Log[-x]*Log[1 + x]^2 +
12*Log[x]*Log[1 + x]^2 + 12*x*Log[x]*Log[1 + x]^2 +
8*Log[1 + x]^3 + 8*x*Log[1 + x]^3 +
4*Log[-x]*Log[1 + x]^3 - 4*Log[x]*Log[1 + x]^3 -
4*x*Log[x]*Log[1 + x]^3 - Log[1 + x]^4 -
x*Log[1 + x]^4 - Log[-x]*Log[1 + x]^4 +
Log[x]*Log[1 + x]^4 + x*Log[x]*Log[1 + x]^4 -
24*PolyLog[2, -x] - 4*Log[1 + x]*
(6 - 3*Log[1 + x] + Log[1 + x]^2)*
PolyLog[2, 1 + x] + 24*PolyLog[3, 1 + x] -
24*Log[1 + x]*PolyLog[3, 1 + x] +
12*Log[1 + x]^2*PolyLog[3, 1 + x] +
24*PolyLog[4, 1 + x] - 24*Log[1 + x]*
PolyLog[4, 1 + x] + 24*PolyLog[5, 1 + x]
4 Integrate[Log[x] Log[1 + x] , x] ==
-48 - 120 x + 24 x Log[x] + 96 Log[1 + x] +
96 x Log[1 + x] - 24 Log[x] Log[1 + x] -
2
24 x Log[x] Log[1 + x] - 36 Log[1 + x] -
2 2
36 x Log[1 + x] - 12 Log[-x] Log[1 + x] +
2 2
12 Log[x] Log[1 + x] + 12 x Log[x] Log[1 + x] +
3 3
8 Log[1 + x] + 8 x Log[1 + x] +
3 3
4 Log[-x] Log[1 + x] - 4 Log[x] Log[1 + x] -
3 4
4 x Log[x] Log[1 + x] - Log[1 + x] -
4 4
x Log[1 + x] - Log[-x] Log[1 + x] +
4 4
Log[x] Log[1 + x] + x Log[x] Log[1 + x] -
24 PolyLog[2, -x] -
2
4 Log[1 + x] (6 - 3 Log[1 + x] + Log[1 + x] )
PolyLog[2, 1 + x] + 24 PolyLog[3, 1 + x] -
24 Log[1 + x] PolyLog[3, 1 + x] +
2
12 Log[1 + x] PolyLog[3, 1 + x] +
24 PolyLog[4, 1 + x] -
24 Log[1 + x] PolyLog[4, 1 + x] +
24 PolyLog[5, 1 + x]