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Integrate[x^n*ArcSech[x], x] ==
(x^n*(((x/(-1 + x))^(1 - n)*Sqrt[(1 - x)/(1 + x)]* Sqrt[(1 + x)/(-1 + x)]* (2*n*AppellF1[1 - n, -n, 1/2, 2 - n, (1 - x)^(-1), -2/(-1 + x)] - (-1 + n)*(-1 + x)*AppellF1[-n, -n, -1/2, 1 - n, (1 - x)^(-1), -2/(-1 + x)]))/((-1 + n)*n*x) + x*ArcSech[x]))/(1 + n) 

           n
Integrate[x  ArcSech[x], x] == 

  n      x    1 - n      1 - x       1 + x
(x  (((------)      Sqrt[-----] Sqrt[------] 
       -1 + x            1 + x       -1 + x
 
                                  1           1
         (2 n AppellF1[1 - n, -n, -, 2 - n, -----, 
                                  2         1 - x
 
               -2
             ------] - 
             -1 + x
 
           (-1 + n) (-1 + x) 
 
                               1            1
            AppellF1[-n, -n, -(-), 1 - n, -----, 
                               2          1 - x
 
               -2
             ------])) / ((-1 + n) n x) + x ArcSech[x]
             -1 + x
 
      )) / (1 + n)
Time to compute: 0.78 second
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