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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: 0.10 second

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