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(Cos[x/2]*(-2*Cos[x/2] + 8*Cos[x/2]^3*Log[Cos[x/2]] + x*(3*Sin[x/2] + Sin[(3*x)/2])))/(3*(1 + Cos[x])^2)

Integrate[x/(1 + Cos[x])^2, x] ==
(Cos[x/2]*(-2*Cos[x/2] + 8*Cos[x/2]^3*Log[Cos[x/2]] + x*(3*Sin[x/2] + Sin[(3*x)/2])))/(3*(1 + Cos[x])^2) 

                x
Integrate[-------------, x] == 
                      2
          (1 + Cos[x])

     x          x          x 3         x
(Cos[-] (-2 Cos[-] + 8 Cos[-]  Log[Cos[-]] + 
     2          2          2           2
 
               x        3 x                      2
      x (3 Sin[-] + Sin[---]))) / (3 (1 + Cos[x]) )
               2         2
Time to compute: 0.16 second
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