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-Csc[x/2]^2/8 - Log[Cos[x/2]]/2 + Log[Sin[x/2]]/2 + Sec[x/2]^2/8

Integrate[Csc[x]^3, x] ==
-Csc[x/2]^2/8 - Log[Cos[x/2]]/2 + Log[Sin[x/2]]/2 + Sec[x/2]^2/8 

                3
Integrate[Csc[x] , x] == 

     x 2           x             x         x 2
-Csc[-]    Log[Cos[-]]   Log[Sin[-]]   Sec[-]
     2             2             2         2
-------- - ----------- + ----------- + -------
   8            2             2           8
Time to compute: 0.01 second
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