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

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

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

-x   Log[-Cos[x] - Sin[x]]      x Sin[x]
-- + --------------------- + ---------------
2              2             Cos[x] + Sin[x]
Time to compute: 0.09 second
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