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(x^(1 + n)*((2 + n)*ArcTanh[x] - x*Hypergeometric2F1[1, 1 + n/2, 2 + n/2, x^2]))/(2 + 3*n + n^2)

Integrate[x^n*ArcTanh[x], x] ==
(x^(1 + n)*((2 + n)*ArcTanh[x] - x*Hypergeometric2F1[1, 1 + n/2, 2 + n/2, x^2]))/ (2 + 3*n + n^2) 

           n
Integrate[x  ArcTanh[x], x] == 

  1 + n
(x      ((2 + n) ArcTanh[x] - 
 
                                 n      n   2
      x Hypergeometric2F1[1, 1 + -, 2 + -, x ])) / 
                                 2      2
 
              2
  (2 + 3 n + n )
Time to compute: 0.09 second
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