Integrate[(x^3*Log[x]*Log[1 + x]^2)/(1 + x), x] ==
(-2600*x + 157*x^2 - 16*x^3 + 1020*x*Log[x] -
114*x^2*Log[x] + 16*x^3*Log[x] + 1580*Log[1 + x] +
1380*x*Log[1 + x] - 168*x^2*Log[1 + x] +
32*x^3*Log[1 + x] - 1020*Log[x]*Log[1 + x] -
792*x*Log[x]*Log[1 + x] + 180*x^2*Log[x]*
Log[1 + x] - 48*x^3*Log[x]*Log[1 + x] -
294*Log[1 + x]^2 - 216*x*Log[1 + x]^2 +
54*x^2*Log[1 + x]^2 - 24*x^3*Log[1 + x]^2 -
396*Log[-x]*Log[1 + x]^2 +
396*Log[x]*Log[1 + x]^2 + 216*x*Log[x]*
Log[1 + x]^2 - 108*x^2*Log[x]*Log[1 + x]^2 +
72*x^3*Log[x]*Log[1 + x]^2 +
72*Log[-x]*Log[1 + x]^3 - 72*Log[x]*Log[1 + x]^3 -
1020*PolyLog[2, -x] + 72*Log[1 + x]*
(-11 + 3*Log[1 + x])*PolyLog[2, 1 + x] +
792*PolyLog[3, 1 + x] - 432*Log[1 + x]*
PolyLog[3, 1 + x] + 432*PolyLog[4, 1 + x])/216
3 2
x Log[x] Log[1 + x]
Integrate[---------------------, x] ==
1 + x 2 3
(-2600 x + 157 x - 16 x + 1020 x Log[x] -
2 3
114 x Log[x] + 16 x Log[x] + 1580 Log[1 + x] +
2
1380 x Log[1 + x] - 168 x Log[1 + x] +
3
32 x Log[1 + x] - 1020 Log[x] Log[1 + x] -
792 x Log[x] Log[1 + x] +
2
180 x Log[x] Log[1 + x] -
3 2
48 x Log[x] Log[1 + x] - 294 Log[1 + x] -
2 2 2
216 x Log[1 + x] + 54 x Log[1 + x] -
3 2 2
24 x Log[1 + x] - 396 Log[-x] Log[1 + x] +
2
396 Log[x] Log[1 + x] +
2
216 x Log[x] Log[1 + x] -
2 2
108 x Log[x] Log[1 + x] +
3 2
72 x Log[x] Log[1 + x] +
3 3
72 Log[-x] Log[1 + x] - 72 Log[x] Log[1 + x] -
1020 PolyLog[2, -x] +
72 Log[1 + x] (-11 + 3 Log[1 + x])
PolyLog[2, 1 + x] + 792 PolyLog[3, 1 + x] -
432 Log[1 + x] PolyLog[3, 1 + x] +
432 PolyLog[4, 1 + x]) / 216