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Integrate[x*Log[x]*Log[1 + x]^3, x] ==
(-45 - 270*x + 12*x^2 + 84*x*Log[x] - 6*x^2*Log[x] +
186*Log[1 + x] + 168*x*Log[1 + x] -
18*x^2*Log[1 + x] - 84*Log[x]*Log[1 + x] -
72*x*Log[x]*Log[1 + x] + 12*x^2*Log[x]*Log[1 + x] -
48*Log[1 + x]^2 - 36*x*Log[1 + x]^2 +
12*x^2*Log[1 + x]^2 - 36*Log[-x]*Log[1 + x]^2 +
36*Log[x]*Log[1 + x]^2 + 24*x*Log[x]*Log[1 + x]^2 -
12*x^2*Log[x]*Log[1 + x]^2 + 4*Log[1 + x]^3 -
4*x^2*Log[1 + x]^3 + 8*Log[-x]*Log[1 + x]^3 -
8*Log[x]*Log[1 + x]^3 + 8*x^2*Log[x]*Log[1 + x]^3 -
84*PolyLog[2, -x] + 24*(-3 + Log[1 + x])*Log[1 + x]*
PolyLog[2, 1 + x] + 72*PolyLog[3, 1 + x] -
48*Log[1 + x]*PolyLog[3, 1 + x] +
48*PolyLog[4, 1 + x])/16
3 Integrate[x Log[x] Log[1 + x] , x] ==
2 2
(-45 - 270 x + 12 x + 84 x Log[x] - 6 x Log[x] +
186 Log[1 + x] + 168 x Log[1 + x] -
2
18 x Log[1 + x] - 84 Log[x] Log[1 + x] -
72 x Log[x] Log[1 + x] +
2 2
12 x Log[x] Log[1 + x] - 48 Log[1 + x] -
2 2 2
36 x Log[1 + x] + 12 x Log[1 + x] -
2 2
36 Log[-x] Log[1 + x] + 36 Log[x] Log[1 + x] +
2
24 x Log[x] Log[1 + x] -
2 2 3
12 x Log[x] Log[1 + x] + 4 Log[1 + x] -
2 3 3
4 x Log[1 + x] + 8 Log[-x] Log[1 + x] -
3 2 3
8 Log[x] Log[1 + x] + 8 x Log[x] Log[1 + x] -
84 PolyLog[2, -x] +
24 (-3 + Log[1 + x]) Log[1 + x]
PolyLog[2, 1 + x] + 72 PolyLog[3, 1 + x] -
48 Log[1 + x] PolyLog[3, 1 + x] +
48 PolyLog[4, 1 + x]) / 16
Time to compute: 0.34 second
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