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(-Cos[a + 2*x] + 2*x*Sin[a])/4

Integrate[Cos[x]*Sin[a + x], x] ==
(-Cos[a + 2*x] + 2*x*Sin[a])/4 

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

-Cos[a + 2 x] + 2 x Sin[a]
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            4
Time to compute: 0.04 second
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