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


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



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

Sin[(a - b) x]   Sin[(a + b) x]
-------------- - --------------
  2 (a - b)        2 (a + b)

Time to compute: 0.17 second

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