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

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

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

 a x
E    (-(b Cos[b x]) + a Sin[b x])
---------------------------------
              2    2
             a  + b
Time to compute: 0.03 second
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