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2*Log[Cos[x/2]] + x*Tan[x/2]

Integrate[x/(1 + Cos[x]), x] ==
2*Log[Cos[x/2]] + x*Tan[x/2] 

              x
Integrate[----------, x] == 
          1 + Cos[x]

          x           x
2 Log[Cos[-]] + x Tan[-]
          2           2
Time to compute: 0.05 second
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