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Integrate[d^x*x^3*Cos[x], x] ==
(d^x*(Cos[x]*(3*(-2 + x^2) + x*(-18 + x^2)*Log[d] + 3*(12 + x^2)*Log[d]^2 + 3*x*(-4 + x^2)* Log[d]^3 - 3*(2 + x^2)*Log[d]^4 + 3*x*(2 + x^2)*Log[d]^5 - 3*x^2*Log[d]^6 + x^3*Log[d]^7) + (x*(-6 + x^2) - 6*(-4 + x^2)*Log[d] + 3*x*(4 + x^2)*Log[d]^2 - 12*(2 + x^2)*Log[d]^3 + 3*x*(6 + x^2)*Log[d]^4 - 6*x^2*Log[d]^5 + x^3*Log[d]^6)*Sin[x]))/ (1 + Log[d]^2)^4



           x  3
Integrate[d  x  Cos[x], x] == 

  x                   2              2
(d  (Cos[x] (3 (-2 + x ) + x (-18 + x ) Log[d] + 
 
                  2        2
         3 (12 + x ) Log[d]  + 
 
                    2        3           2        4
         3 x (-4 + x ) Log[d]  - 3 (2 + x ) Log[d]  + 
 
                   2        5      2       6
         3 x (2 + x ) Log[d]  - 3 x  Log[d]  + 
 
          3       7
         x  Log[d] ) + 
 
                2             2
      (x (-6 + x ) - 6 (-4 + x ) Log[d] + 
 
                   2        2            2        3
         3 x (4 + x ) Log[d]  - 12 (2 + x ) Log[d]  + 
 
                   2        4      2       5
         3 x (6 + x ) Log[d]  - 6 x  Log[d]  + 
 
          3       6                        2 4
         x  Log[d] ) Sin[x])) / (1 + Log[d] )

Time to compute: 0.39 second

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