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

Integrate[Sec[x]^3, x] ==
(-Log[Cos[x/2] - Sin[x/2]] + Log[Cos[x/2] + Sin[x/2]] + Sec[x]*Tan[x])/2 

                3
Integrate[Sec[x] , x] == 

          x        x             x        x
(-Log[Cos[-] - Sin[-]] + Log[Cos[-] + Sin[-]] + 
          2        2             2        2
 
    Sec[x] Tan[x]) / 2
Time to compute: 0.13 second
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