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(1/4 + I/4)*x^m*(((-I)*Gamma[1 + m, (-1 - I)*x])/((-1 - I)*x)^m + Gamma[1 + m, (-1 + I)*x]/((-1 + I)*x)^m)


Integrate[E^x*x^m*Cos[x], x] ==
(1/4 + I/4)*x^m*(((-I)*Gamma[1 + m, (-1 - I)*x])/ ((-1 - I)*x)^m + Gamma[1 + m, (-1 + I)*x]/ ((-1 + I)*x)^m)



           x  m
Integrate[E  x  Cos[x], x] == 

 1   I   m  -I Gamma[1 + m, (-1 - I) x]
(- + -) x  (--------------------------- + 
 4   4                         m
                   ((-1 - I) x)
 
    Gamma[1 + m, (-1 + I) x]
    ------------------------)
                     m
         ((-1 + I) x)

Time to compute: 0.10 second

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