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(d^x*(Cos[x]*(1 + x*Log[d] - Log[d]^2 + x*Log[d]^3) + (x - 2*Log[d] + x*Log[d]^2)*Sin[x]))/(1 + Log[d]^2)^2

Integrate[d^x*x*Cos[x], x] ==
(d^x*(Cos[x]*(1 + x*Log[d] - Log[d]^2 + x*Log[d]^3) + (x - 2*Log[d] + x*Log[d]^2)*Sin[x]))/ (1 + Log[d]^2)^2 

           x
Integrate[d  x Cos[x], x] == 

  x                               2           3
(d  (Cos[x] (1 + x Log[d] - Log[d]  + x Log[d] ) + 
 
                              2
      (x - 2 Log[d] + x Log[d] ) Sin[x])) / 
 
             2 2
  (1 + Log[d] )
Time to compute: 0.11 second
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