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(Coth[x]^(1 + n)*Hypergeometric2F1[1, (1 + n)/2, 1 + (1 + n)/2, Coth[x]^2])/(1 + n)


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



                 n
Integrate[Coth[x] , x] == 

        1 + n                      1 + n      1 + n
(Coth[x]      Hypergeometric2F1[1, -----, 1 + -----, 
                                     2          2
 
            2
     Coth[x] ]) / (1 + n)

Time to compute: 0.08 second

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