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Integrate[d^x*x^2*Cos[x], x] ==
(d^x*(Cos[x]*(2*x + (-6 + x^2)*Log[d] + 2*(1 + x^2)*Log[d]^3 - 2*x*Log[d]^4 + x^2*Log[d]^5) + (-2 + x^2 - 4*x*Log[d] + 2*(3 + x^2)*Log[d]^2 - 4*x*Log[d]^3 + x^2*Log[d]^4)*Sin[x]))/(1 + Log[d]^2)^3



           x  2
Integrate[d  x  Cos[x], x] == 

  x                       2
(d  (Cos[x] (2 x + (-6 + x ) Log[d] + 
 
                 2        3             4    2       5
         2 (1 + x ) Log[d]  - 2 x Log[d]  + x  Log[d]
 
                    2
         ) + (-2 + x  - 4 x Log[d] + 
 
                 2        2             3    2       4
         2 (3 + x ) Log[d]  - 4 x Log[d]  + x  Log[d]
 
                                 2 3
         ) Sin[x])) / (1 + Log[d] )

Time to compute: 0.19 second

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