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-Cos[(a - b)*x]/(2*(a - b)) - Cos[(a + b)*x]/(2*(a + b))

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

Integrate[Cos[b x] Sin[a x], x] == 

-Cos[(a - b) x]   Cos[(a + b) x]
--------------- - --------------
   2 (a - b)        2 (a + b)
Time to compute: 0.11 second
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