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-x + 2*Log[-Cos[x/2] - Sin[x/2]] + (2*x*Sin[x/2])/(Cos[x/2] + Sin[x/2])


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



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

                                         x
                                 2 x Sin[-]
                x        x               2
-x + 2 Log[-Cos[-] - Sin[-]] + ---------------
                2        2         x        x
                               Cos[-] + Sin[-]
                                   2        2

Time to compute: 0.08 second

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