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


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



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

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

Time to compute: 0.03 second

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