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


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



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

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

Time to compute: 0.33 second

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