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

Integrate[((1 + x^3)*Log[x])/(2 + x^4), x] ==
(2*(Log[x]*Log[1 + (-1/2)^(1/4)*x] + PolyLog[2, -((-1/2)^(1/4)*x)]) - (-1)^(3/4)*2^(1/4)* (Log[x]*Log[1 + (-1/2)^(1/4)*x] + PolyLog[2, -((-1/2)^(1/4)*x)]) + 2*(Log[x]*Log[1 - (-1/2)^(1/4)*x] + PolyLog[2, (-1/2)^(1/4)*x]) + (-1)^(3/4)*2^(1/4)* (Log[x]*Log[1 - (-1/2)^(1/4)*x] + PolyLog[2, (-1/2)^(1/4)*x]) + 2*(Log[x]*Log[1 + ((1 - I)*x)/2^(3/4)] + PolyLog[2, ((-1 + I)*x)/2^(3/4)]) + (-2)^(1/4)*(Log[x]*Log[1 + ((1 - I)*x)/2^(3/4)] + PolyLog[2, ((-1 + I)*x)/2^(3/4)]) + 2*(Log[x]*Log[1 - ((1 - I)*x)/2^(3/4)] + PolyLog[2, ((1 - I)*x)/2^(3/4)]) - (-2)^(1/4)*(Log[x]*Log[1 - ((1 - I)*x)/2^(3/4)] + PolyLog[2, ((1 - I)*x)/2^(3/4)]))/8

                3
          (1 + x ) Log[x]
Integrate[---------------, x] == 
                   4
              2 + x

                      1  1/4
(2 (Log[x] Log[1 + (-(-))    x] + 
                      2
 
                       1  1/4
       PolyLog[2, -((-(-))    x)]) - 
                       2
 
        3/4  1/4                    1  1/4
    (-1)    2    (Log[x] Log[1 + (-(-))    x] + 
                                    2
 
                       1  1/4
       PolyLog[2, -((-(-))    x)]) + 
                       2
 
                         1  1/4
    2 (Log[x] Log[1 - (-(-))    x] + 
                         2
 
                     1  1/4
       PolyLog[2, (-(-))    x]) + 
                     2
 
        3/4  1/4                    1  1/4
    (-1)    2    (Log[x] Log[1 - (-(-))    x] + 
                                    2
 
                     1  1/4
       PolyLog[2, (-(-))    x]) + 
                     2
 
                      (1 - I) x
    2 (Log[x] Log[1 + ---------] + 
                         3/4
                        2
 
                  (-1 + I) x
       PolyLog[2, ----------]) + 
                      3/4
                     2
 
        1/4                 (1 - I) x
    (-2)    (Log[x] Log[1 + ---------] + 
                               3/4
                              2
 
                  (-1 + I) x
       PolyLog[2, ----------]) + 
                      3/4
                     2
 
                      (1 - I) x
    2 (Log[x] Log[1 - ---------] + 
                         3/4
                        2
 
                  (1 - I) x
       PolyLog[2, ---------]) - 
                     3/4
                    2
 
        1/4                 (1 - I) x
    (-2)    (Log[x] Log[1 - ---------] + 
                               3/4
                              2
 
                  (1 - I) x
       PolyLog[2, ---------])) / 8
                     3/4
                    2