Integrate[x^3*Log[x]*Log[1 + x]^4, x] ==
360005/20736 + (40999*x)/576 - (851*x^2)/288 +
(781*x^3)/2592 - (15*x^4)/512 -
(5845*x*Log[x])/288 + (865*x^2*Log[x])/576 -
(175*x^3*Log[x])/864 + (3*x^4*Log[x])/128 -
(29309*Log[1 + x])/576 - (13385*x*Log[1 + x])/288 +
(2135*x^2*Log[1 + x])/576 - (175*x^3*Log[1 + x])/
288 + (3*x^4*Log[1 + x])/32 +
(5845*Log[x]*Log[1 + x])/288 +
(415*x*Log[x]*Log[1 + x])/24 -
(115*x^2*Log[x]*Log[1 + x])/48 +
(37*x^3*Log[x]*Log[1 + x])/72 -
(3*x^4*Log[x]*Log[1 + x])/32 +
(8405*Log[1 + x]^2)/576 + (145*x*Log[1 + x]^2)/12 -
(89*x^2*Log[1 + x]^2)/48 + (37*x^3*Log[1 + x]^2)/
72 - (9*x^4*Log[1 + x]^2)/64 +
(415*Log[-x]*Log[1 + x]^2)/48 -
(415*Log[x]*Log[1 + x]^2)/48 -
(25*x*Log[x]*Log[1 + x]^2)/4 +
(13*x^2*Log[x]*Log[1 + x]^2)/8 -
(7*x^3*Log[x]*Log[1 + x]^2)/12 +
(3*x^4*Log[x]*Log[1 + x]^2)/16 -
(35*Log[1 + x]^3)/18 - (5*x*Log[1 + x]^3)/4 +
(3*x^2*Log[1 + x]^3)/8 - (7*x^3*Log[1 + x]^3)/36 +
(x^4*Log[1 + x]^3)/8 - (25*Log[-x]*Log[1 + x]^3)/
12 + (25*Log[x]*Log[1 + x]^3)/12 +
x*Log[x]*Log[1 + x]^3 - (x^2*Log[x]*Log[1 + x]^3)/
2 + (x^3*Log[x]*Log[1 + x]^3)/3 -
(x^4*Log[x]*Log[1 + x]^3)/4 + Log[1 + x]^4/16 -
(x^4*Log[1 + x]^4)/16 + (Log[-x]*Log[1 + x]^4)/4 -
(Log[x]*Log[1 + x]^4)/4 + (x^4*Log[x]*Log[1 + x]^4)/
4 + (5845*PolyLog[2, -x])/288 +
((415*Log[1 + x])/24 - (25*Log[1 + x]^2)/4 +
Log[1 + x]^3)*PolyLog[2, 1 + x] -
(415*PolyLog[3, 1 + x])/24 +
(25*Log[1 + x]*PolyLog[3, 1 + x])/2 -
3*Log[1 + x]^2*PolyLog[3, 1 + x] -
(25*PolyLog[4, 1 + x])/2 + 6*Log[1 + x]*
PolyLog[4, 1 + x] - 6*PolyLog[5, 1 + x]
3 4 Integrate[x Log[x] Log[1 + x] , x] ==
2 3 4
360005 40999 x 851 x 781 x 15 x
------ + ------- - ------ + ------ - ----- -
20736 576 288 2592 512
2 3
5845 x Log[x] 865 x Log[x] 175 x Log[x]
------------- + ------------- - ------------- +
288 576 864
4
3 x Log[x] 29309 Log[1 + x]
----------- - ---------------- -
128 576
2
13385 x Log[1 + x] 2135 x Log[1 + x]
------------------ + ------------------ -
288 576
3 4
175 x Log[1 + x] 3 x Log[1 + x]
----------------- + --------------- +
288 32
5845 Log[x] Log[1 + x] 415 x Log[x] Log[1 + x]
---------------------- + ----------------------- -
288 24
2
115 x Log[x] Log[1 + x]
------------------------ +
48
3 4
37 x Log[x] Log[1 + x] 3 x Log[x] Log[1 + x]
----------------------- - ---------------------- +
72 32
2 2
8405 Log[1 + x] 145 x Log[1 + x]
---------------- + ----------------- -
576 12
2 2 3 2
89 x Log[1 + x] 37 x Log[1 + x]
----------------- + ----------------- -
48 72
4 2 2
9 x Log[1 + x] 415 Log[-x] Log[1 + x]
---------------- + ----------------------- -
64 48
2 2
415 Log[x] Log[1 + x] 25 x Log[x] Log[1 + x]
---------------------- - ----------------------- +
48 4
2 2
13 x Log[x] Log[1 + x]
------------------------ -
8
3 2 4 2
7 x Log[x] Log[1 + x] 3 x Log[x] Log[1 + x]
----------------------- + ----------------------- -
12 16
3 3
35 Log[1 + x] 5 x Log[1 + x]
-------------- - --------------- +
18 4
2 3 3 3
3 x Log[1 + x] 7 x Log[1 + x]
---------------- - ---------------- +
8 36
4 3 3
x Log[1 + x] 25 Log[-x] Log[1 + x]
-------------- - ---------------------- +
8 12
3
25 Log[x] Log[1 + x] 3
--------------------- + x Log[x] Log[1 + x] -
12
2 3 3 3
x Log[x] Log[1 + x] x Log[x] Log[1 + x]
--------------------- + --------------------- -
2 3
4 3 4
x Log[x] Log[1 + x] Log[1 + x]
--------------------- + ----------- -
4 16
4 4 4
x Log[1 + x] Log[-x] Log[1 + x]
-------------- + ------------------- -
16 4
4 4 4
Log[x] Log[1 + x] x Log[x] Log[1 + x]
------------------ + --------------------- +
4 4
5845 PolyLog[2, -x]
------------------- +
288
2
415 Log[1 + x] 25 Log[1 + x] 3
(-------------- - -------------- + Log[1 + x] )
24 4
415 PolyLog[3, 1 + x]
PolyLog[2, 1 + x] - --------------------- +
24
25 Log[1 + x] PolyLog[3, 1 + x]
------------------------------- -
2
2
3 Log[1 + x] PolyLog[3, 1 + x] -
25 PolyLog[4, 1 + x]
-------------------- +
2
6 Log[1 + x] PolyLog[4, 1 + x] - 6 PolyLog[5, 1 + x]