Integrate[x^3*Log[3 + x]*Log[1 + b*x]^2, x] ==
-(-10800*b - 13608*b^2 - 46656*b^3 - 6960*b*x -
9864*b^2*x - 21816*b^3*x - 61236*b^4*x +
1068*b^2*x^2 + 1872*b^3*x^2 + 3402*b^4*x^2 -
296*b^3*x^3 - 444*b^4*x^3 + 81*b^4*x^4 +
10800*b*Log[3 + x] + 8424*b^2*Log[3 + x] +
9072*b^3*Log[3 + x] + 8748*b^4*Log[3 + x] +
3600*b*x*Log[3 + x] - 936*b^2*x^2*Log[3 + x] +
336*b^3*x^3*Log[3 + x] - 108*b^4*x^4*Log[3 + x] +
3360*Log[1 + b*x] + 7056*b*Log[1 + b*x] +
18792*b^2*Log[1 + b*x] + 58320*b^3*Log[1 + b*x] +
2160*b*x*Log[1 + b*x] + 4320*b^2*x*Log[1 + b*x] +
12960*b^3*x*Log[1 + b*x] + 58320*b^4*x*
Log[1 + b*x] - 648*b^2*x^2*Log[1 + b*x] -
1728*b^3*x^2*Log[1 + b*x] - 5832*b^4*x^2*
Log[1 + b*x] + 336*b^3*x^3*Log[1 + b*x] +
1008*b^4*x^3*Log[1 + b*x] - 216*b^4*x^4*
Log[1 + b*x] - 5184*b*Log[3 + x]*Log[1 + b*x] -
7776*b^2*Log[3 + x]*Log[1 + b*x] -
15552*b^3*Log[3 + x]*Log[1 + b*x] -
34992*b^4*Log[3 + x]*Log[1 + b*x] -
1728*b*x*Log[3 + x]*Log[1 + b*x] +
864*b^2*x^2*Log[3 + x]*Log[1 + b*x] -
576*b^3*x^3*Log[3 + x]*Log[1 + b*x] +
432*b^4*x^4*Log[3 + x]*Log[1 + b*x] -
216*Log[1 + b*x]^2 - 864*b*Log[1 + b*x]^2 -
3888*b^2*Log[1 + b*x]^2 - 23328*b^3*
Log[1 + b*x]^2 - 23328*b^4*x*Log[1 + b*x]^2 +
3888*b^4*x^2*Log[1 + b*x]^2 -
864*b^4*x^3*Log[1 + b*x]^2 +
216*b^4*x^4*Log[1 + b*x]^2 + 864*Log[3 + x]*
Log[1 + b*x]^2 - 864*b^4*x^4*Log[3 + x]*
Log[1 + b*x]^2 - 864*Log[(b*(3 + x))/(-1 + 3*b)]*
Log[1 + b*x]^2 + 69984*b^4*
Log[(b*(3 + x))/(-1 + 3*b)]*Log[1 + b*x]^2 -
3600*Log[3 + x]*Log[(1 + b*x)/(1 - 3*b)] +
5184*b*Log[3 + x]*Log[(1 + b*x)/(1 - 3*b)] +
7776*b^2*Log[3 + x]*Log[(1 + b*x)/(1 - 3*b)] +
15552*b^3*Log[3 + x]*Log[(1 + b*x)/(1 - 3*b)] +
34992*b^4*Log[3 + x]*Log[(1 + b*x)/(1 - 3*b)] +
144*(-25 + 36*b + 54*b^2 + 108*b^3 + 243*b^4)*
PolyLog[2, (b*(3 + x))/(-1 + 3*b)] +
1728*(-1 + 81*b^4)*Log[1 + b*x]*
PolyLog[2, (1 + b*x)/(1 - 3*b)] +
1728*PolyLog[3, (1 + b*x)/(1 - 3*b)] -
139968*b^4*PolyLog[3, (1 + b*x)/(1 - 3*b)])/
(3456*b^4)
3 2 Integrate[x Log[3 + x] Log[1 + b x] , x] ==
2 3
-(-10800 b - 13608 b - 46656 b - 6960 b x -
2 3 4
9864 b x - 21816 b x - 61236 b x +
2 2 3 2 4 2
1068 b x + 1872 b x + 3402 b x -
3 3 4 3 4 4
296 b x - 444 b x + 81 b x +
2
10800 b Log[3 + x] + 8424 b Log[3 + x] +
3 4
9072 b Log[3 + x] + 8748 b Log[3 + x] +
2 2
3600 b x Log[3 + x] - 936 b x Log[3 + x] +
3 3 4 4
336 b x Log[3 + x] - 108 b x Log[3 + x] +
3360 Log[1 + b x] + 7056 b Log[1 + b x] +
2 3
18792 b Log[1 + b x] + 58320 b Log[1 + b x] +
2
2160 b x Log[1 + b x] + 4320 b x Log[1 + b x] +
3
12960 b x Log[1 + b x] +
4
58320 b x Log[1 + b x] -
2 2
648 b x Log[1 + b x] -
3 2
1728 b x Log[1 + b x] -
4 2
5832 b x Log[1 + b x] +
3 3
336 b x Log[1 + b x] +
4 3
1008 b x Log[1 + b x] -
4 4
216 b x Log[1 + b x] -
5184 b Log[3 + x] Log[1 + b x] -
2
7776 b Log[3 + x] Log[1 + b x] -
3
15552 b Log[3 + x] Log[1 + b x] -
4
34992 b Log[3 + x] Log[1 + b x] -
1728 b x Log[3 + x] Log[1 + b x] +
2 2
864 b x Log[3 + x] Log[1 + b x] -
3 3
576 b x Log[3 + x] Log[1 + b x] +
4 4
432 b x Log[3 + x] Log[1 + b x] -
2 2
216 Log[1 + b x] - 864 b Log[1 + b x] -
2 2 3 2
3888 b Log[1 + b x] - 23328 b Log[1 + b x] -
4 2
23328 b x Log[1 + b x] +
4 2 2
3888 b x Log[1 + b x] -
4 3 2
864 b x Log[1 + b x] +
4 4 2
216 b x Log[1 + b x] +
2
864 Log[3 + x] Log[1 + b x] -
4 4 2
864 b x Log[3 + x] Log[1 + b x] -
b (3 + x) 2
864 Log[---------] Log[1 + b x] +
-1 + 3 b
4 b (3 + x) 2
69984 b Log[---------] Log[1 + b x] -
-1 + 3 b
1 + b x
3600 Log[3 + x] Log[-------] +
1 - 3 b
1 + b x
5184 b Log[3 + x] Log[-------] +
1 - 3 b
2 1 + b x
7776 b Log[3 + x] Log[-------] +
1 - 3 b
3 1 + b x
15552 b Log[3 + x] Log[-------] +
1 - 3 b
4 1 + b x
34992 b Log[3 + x] Log[-------] +
1 - 3 b
2 3 4
144 (-25 + 36 b + 54 b + 108 b + 243 b )
b (3 + x)
PolyLog[2, ---------] +
-1 + 3 b
4
1728 (-1 + 81 b ) Log[1 + b x]
1 + b x
PolyLog[2, -------] +
1 - 3 b
1 + b x
1728 PolyLog[3, -------] -
1 - 3 b
4 1 + b x 4
139968 b PolyLog[3, -------]) / (3456 b )
1 - 3 b