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Integrate[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))



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

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

Time to compute: 0.27 second

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