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-Cos[(m - n)*x]/(2*(m - n)) - Cos[(m + n)*x]/(2*(m + n))

Integrate[Cos[n*x]*Sin[m*x], x] ==
-Cos[(m - n)*x]/(2*(m - n)) - Cos[(m + n)*x]/ (2*(m + n)) 

Integrate[Cos[n x] Sin[m x], x] == 

-Cos[(m - n) x]   Cos[(m + n) x]
--------------- - --------------
   2 (m - n)        2 (m + n)
Time to compute: 0.11 second
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