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(2*Log[Cos[(a*x)/2]] + a*x*Tan[(a*x)/2])/a^2

Integrate[x/(1 + Cos[a*x]), x] ==
(2*Log[Cos[(a*x)/2]] + a*x*Tan[(a*x)/2])/a^2 

               x
Integrate[------------, x] == 
          1 + Cos[a x]

          a x             a x
2 Log[Cos[---]] + a x Tan[---]
           2               2
------------------------------
               2
              a
Time to compute: 0.10 second
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