Antiderivative.nb

2/3 ArcCoth[3 + 2 x]^2 (Pi^2 + 2 ArcCoth[3 + 2 x]^2) + Log[x]^4/3 - 6 Log[1 + x] + Log[x]^2 Log[1 + x] -
1/3 Log[x]^3 Log[1 + x] + 2 Log[1 + x]^2 + Log[4] Log[x] Log[1 + x]^2 - 2 Log[x]^2 Log[1 + x]^2 + 
1/3 Log[1 + x]^3 - 4/3 Log[2] Log[1 + x]^3 + 3 Log[x] Log[1 + x]^3 - 13/12 Log[1 + x]^4 + 
4 Log[x] Log[2/(2 + x)] + 2 Log[x]^2 Log[(2 + x)/2] - Log[x]^3 Log[2 + x] + 4 Log[1 + x] Log[2 + x] - 
Log[x]^2 Log[1 + x] Log[2 + x] + 3 Log[x] Log[1 + x]^2 Log[2 + x] - 2/3 Log[1 + x]^3 Log[2 + x] + 
Log[x]^2 Log[2 + x]^2 - Log[x] Log[1 + x] Log[2 + x]^2 + 4/3 ArcCoth[1 + 2 x] Log[2 + x]^3 + 
x Log[1 + 1/x] (2 Log[x (1 + x)] - Log[x] Log[1 + x] - 6 + 
(2 - Log[x] + (Log[x] - 1) Log[1 + x]) Log[2 + x]) + Pi^2/12 (3 Log[x]^2 - 3 Log[2 + x]^2 - 
2 Log[x] (4 Log[1 + x] + Log[2 + x]) + 4 Log[1 + x] (3 Log[2 + x] - 1)) - 2 Log[1 + x]^2 Log[x (2 + x)] + 
(2 - Log[x]^2 + 2 (Log[x] - 1) Log[1 + x]) PolyLog[2, -1 - x] + 
2 Log[1 + 1/x] (Log[2 + x] - 1) PolyLog[2, -x] + 2 (Log[1 + x]^2 - 
2 Log[x] (Log[1 + x] - 1) - 2) PolyLog[2, -x/2] + 2 (1 + Log[x] - 2 Log[1 + x]) PolyLog[3, -1 - x] + 
2 (Log[3 + 2/x + x] - 1) PolyLog[3, -x] + 4 (Log[x] - 1) PolyLog[3, -x/2] + 
2 (2 Log[1 + x] + Log[2 + x] - 2 Log[x] - 1) PolyLog[3, 1/(1 + x)] + 
2 Log[x/(1 + x)] PolyLog[3, 1/(2 + x)] + 2 Log[x/(1 + x)] PolyLog[3, x/(2 + x)] + 
2 Log[1 + 1/x] PolyLog[3, -(2 + x)/x] + 4 Log[1 + 1/x] PolyLog[3, x/(2 + 2 x)] + 
2 PolyLog[4, -1 - x] - 2 PolyLog[4, -x] - 4 PolyLog[4, -x/2] + 2 PolyLog[4, 1/(1 + x)] - 
6 PolyLog[4, x/(1 + x)] + PolyLog[4, -x/(2 + x)] - PolyLog[4, x/(2 + x)] + 2 PolyLog[4, (1 + x)/(2 + x)] + 
1/2 PolyLog[4, x (2 + x)/(1 + x)^2] + 4 PolyLog[4, x/(2 + 2 x)] + 
1/4 (15 Log[x] - 14 Log[1 + x] - Log[2 + x]) Zeta[3]