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(3*Cos[(a*x)/2] - 2*Cos[(3*a*x)/2] + 3*Sin[(a*x)/2])/(3*a*(Cos[(a*x)/2] + Sin[(a*x)/2])^3)


Integrate[Sin[a*x]/(1 + Sin[a*x])^2, x] ==
(3*Cos[(a*x)/2] - 2*Cos[(3*a*x)/2] + 3*Sin[(a*x)/2])/ (3*a*(Cos[(a*x)/2] + Sin[(a*x)/2])^3)



             Sin[a x]
Integrate[---------------, x] == 
                        2
          (1 + Sin[a x])

      a x          3 a x          a x
3 Cos[---] - 2 Cos[-----] + 3 Sin[---]
       2             2             2
--------------------------------------
               a x        a x  3
      3 a (Cos[---] + Sin[---])
                2          2

Time to compute: 0.07 second

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