integrals.wolfram.com   Use one of Mathematica's 2500+ functions FREE online

Wolfram Mathematica Online Integrator
The world's only full-power integration solver
∫

An image showing the results of your requested integral.


Integrate[x^3*Log[x]*Log[1 + x]^2, x] ==
(6960*x - 1068*x^2 + 296*x^3 - 81*x^4 - 3600*x*Log[x] + 936*x^2*Log[x] - 336*x^3*Log[x] + 108*x^4*Log[x] - 3360*Log[1 + x] - 2160*x*Log[1 + x] + 648*x^2*Log[1 + x] - 336*x^3*Log[1 + x] + 216*x^4*Log[1 + x] + 3600*Log[x]*Log[1 + x] + 1728*x*Log[x]*Log[1 + x] - 864*x^2*Log[x]*Log[1 + x] + 576*x^3*Log[x]* Log[1 + x] - 432*x^4*Log[x]*Log[1 + x] + 216*Log[1 + x]^2 - 216*x^4*Log[1 + x]^2 + 864*Log[-x]*Log[1 + x]^2 - 864*Log[x]*Log[1 + x]^2 + 864*x^4*Log[x]* Log[1 + x]^2 + 3600*PolyLog[2, -x] + 1728*Log[1 + x]*PolyLog[2, 1 + x] - 1728*PolyLog[3, 1 + x])/3456



           3                  2
Integrate[x  Log[x] Log[1 + x] , x] == 

                2        3       4
(6960 x - 1068 x  + 296 x  - 81 x  - 3600 x Log[x] + 
 
         2               3               4
    936 x  Log[x] - 336 x  Log[x] + 108 x  Log[x] - 
 
    3360 Log[1 + x] - 2160 x Log[1 + x] + 
 
         2                   3
    648 x  Log[1 + x] - 336 x  Log[1 + x] + 
 
         4
    216 x  Log[1 + x] + 3600 Log[x] Log[1 + x] + 
 
    1728 x Log[x] Log[1 + x] - 
 
         2
    864 x  Log[x] Log[1 + x] + 
 
         3
    576 x  Log[x] Log[1 + x] - 
 
         4                                   2
    432 x  Log[x] Log[1 + x] + 216 Log[1 + x]  - 
 
         4           2                         2
    216 x  Log[1 + x]  + 864 Log[-x] Log[1 + x]  - 
 
                         2
    864 Log[x] Log[1 + x]  + 
 
         4                  2
    864 x  Log[x] Log[1 + x]  + 3600 PolyLog[2, -x] + 
 
    1728 Log[1 + x] PolyLog[2, 1 + x] - 
 
    1728 PolyLog[3, 1 + x]) / 3456

Time to compute: 0.33 second

Spread the word: