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



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

                  2                 -I x
I Pi x - (1 + I) x  + 4 Pi Log[1 + E    ] + 
 
                  I x                   I x
  2 Pi Log[1 - I E   ] + 4 x Log[1 - I E   ] - 
 
               x                  Pi + 2 x
  4 Pi Log[Cos[-]] - 2 Pi Log[Sin[--------]] - 
               2                     4
 
                                  2     x
                               2 x  Sin[-]
                      I x               2
  (4 I) PolyLog[2, I E   ] + ---------------
                                 x        x
                             Cos[-] + Sin[-]
                                 2        2

Time to compute: 0.27 second

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