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


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



                  2
Integrate[Csc[a x]  Sec[a x], x] == 

     a x            a x        a x
-Cot[---]   Log[Cos[---] - Sin[---]]
      2              2          2
--------- - ------------------------ + 
   2 a                 a
 
          a x        a x         a x
  Log[Cos[---] + Sin[---]]   Tan[---]
           2          2           2
  ------------------------ - --------
             a                 2 a

Time to compute: 0.02 second

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