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Integrate[Log[x]*Log[1 + x]^4, x] ==
-48 - 120*x + 24*x*Log[x] + 96*Log[1 + x] + 96*x*Log[1 + x] - 24*Log[x]*Log[1 + x] - 24*x*Log[x]*Log[1 + x] - 36*Log[1 + x]^2 - 36*x*Log[1 + x]^2 - 12*Log[-x]*Log[1 + x]^2 + 12*Log[x]*Log[1 + x]^2 + 12*x*Log[x]*Log[1 + x]^2 + 8*Log[1 + x]^3 + 8*x*Log[1 + x]^3 + 4*Log[-x]*Log[1 + x]^3 - 4*Log[x]*Log[1 + x]^3 - 4*x*Log[x]*Log[1 + x]^3 - Log[1 + x]^4 - x*Log[1 + x]^4 - Log[-x]*Log[1 + x]^4 + Log[x]*Log[1 + x]^4 + x*Log[x]*Log[1 + x]^4 - 24*PolyLog[2, -x] - 4*Log[1 + x]* (6 - 3*Log[1 + x] + Log[1 + x]^2)* PolyLog[2, 1 + x] + 24*PolyLog[3, 1 + x] - 24*Log[1 + x]*PolyLog[3, 1 + x] + 12*Log[1 + x]^2*PolyLog[3, 1 + x] + 24*PolyLog[4, 1 + x] - 24*Log[1 + x]* PolyLog[4, 1 + x] + 24*PolyLog[5, 1 + x]



                           4
Integrate[Log[x] Log[1 + x] , x] == 

-48 - 120 x + 24 x Log[x] + 96 Log[1 + x] + 
 
  96 x Log[1 + x] - 24 Log[x] Log[1 + x] - 
 
                                        2
  24 x Log[x] Log[1 + x] - 36 Log[1 + x]  - 
 
                 2                        2
  36 x Log[1 + x]  - 12 Log[-x] Log[1 + x]  + 
 
                      2                         2
  12 Log[x] Log[1 + x]  + 12 x Log[x] Log[1 + x]  + 
 
              3                 3
  8 Log[1 + x]  + 8 x Log[1 + x]  + 
 
                      3                      3
  4 Log[-x] Log[1 + x]  - 4 Log[x] Log[1 + x]  - 
 
                       3             4
  4 x Log[x] Log[1 + x]  - Log[1 + x]  - 
 
              4                     4
  x Log[1 + x]  - Log[-x] Log[1 + x]  + 
 
                   4                      4
  Log[x] Log[1 + x]  + x Log[x] Log[1 + x]  - 
 
  24 PolyLog[2, -x] - 
 
                                             2
  4 Log[1 + x] (6 - 3 Log[1 + x] + Log[1 + x] ) 
 
   PolyLog[2, 1 + x] + 24 PolyLog[3, 1 + x] - 
 
  24 Log[1 + x] PolyLog[3, 1 + x] + 
 
               2
  12 Log[1 + x]  PolyLog[3, 1 + x] + 
 
  24 PolyLog[4, 1 + x] - 
 
  24 Log[1 + x] PolyLog[4, 1 + x] + 
 
  24 PolyLog[5, 1 + x]

Time to compute: 0.29 second

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