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


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



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

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

Time to compute: 0.04 second

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