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



                  1
Integrate[-----------------, x] == 
                 n        m
          Cosh[x]  Sinh[x]

        1 - n                   1 + m  1 - n  3 - n
(Cosh[x]      Hypergeometric2F1[-----, -----, -----, 
                                  2      2      2
 
            2         1 - m          2 (-1 + m)/2
     Cosh[x] ] Sinh[x]      (-Sinh[x] )          ) / 
 
  (-1 + n)

Time to compute: 0.29 second

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