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

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

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

-Cos[(a - b) x]   Cos[(a + b) x]
--------------- - --------------
   2 (a - b)        2 (a + b)
Time to compute: 0.13 second
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