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(-4*I)*PolyLog[2, -E^(I*x)] + x*((-I)*x + 4*Log[1 + E^(I*x)] + x*Tan[x/2])


Integrate[x^2/(1 + Cos[x]), x] ==
(-4*I)*PolyLog[2, -E^(I*x)] + x*((-I)*x + 4*Log[1 + E^(I*x)] + x*Tan[x/2])



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

                    I x
(-4 I) PolyLog[2, -E   ] + 
 
                       I x          x
  x (-I x + 4 Log[1 + E   ] + x Tan[-])
                                    2

Time to compute: 0.19 second

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