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

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

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

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