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

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

           x
Integrate[d  x Sin[x], x] == 

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