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Sin[a*x]/(a*(Cos[a*x] - Sin[a*x]))

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

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

       Sin[a x]
-----------------------
a (Cos[a x] - Sin[a x])
Time to compute: 0.04 second
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