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(E^(a*x)*(Cos[c]/a - (a*Cos[c + 2*b*x] + 2*b*Sin[c + 2*b*x])/(a^2 + 4*b^2)))/2

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

           a x
Integrate[E    Sin[b x] Sin[c + b x], x] == 

  a x  Cos[c]
(E    (------ - 
         a
 
       a Cos[c + 2 b x] + 2 b Sin[c + 2 b x]
       -------------------------------------)) / 2
                      2      2
                     a  + 4 b
Time to compute: 0.31 second
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