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(-6*Log[Cos[x/2] - Sin[x/2]] + 6*Log[Cos[x/2] + Sin[x/2]] + (Sec[x]^4*(11*Sin[x] + 3*Sin[3*x]))/2)/16

Integrate[Sec[x]^5, x] ==
(-6*Log[Cos[x/2] - Sin[x/2]] + 6*Log[Cos[x/2] + Sin[x/2]] + (Sec[x]^4*(11*Sin[x] + 3*Sin[3*x]))/2)/16 

                5
Integrate[Sec[x] , x] == 

            x        x               x        x
(-6 Log[Cos[-] - Sin[-]] + 6 Log[Cos[-] + Sin[-]] + 
            2        2               2        2
 
          4
    Sec[x]  (11 Sin[x] + 3 Sin[3 x])
    --------------------------------) / 16
                   2
Time to compute: 0.33 second
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