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Tanh






Mathematica Notation

Traditional Notation









Elementary Functions > Tanh[z] > Integration > Indefinite integration > Involving functions of the direct function, hyperbolic and exponential functions > Involving powers of the direct function, hyperbolic and exponential functions > Involving cosh and exp > Involving ep zcosh(b z) tanhv( c z)





http://functions.wolfram.com/01.21.21.0380.01









  


  










Input Form





Integrate[(Cosh[b z] Tanh[c z]^\[Nu])/E^(b z), z] == (1/(8 b c (-1 + \[Nu]))) (((-Sinh[c z]^2)^((1/2) (-1 - \[Nu])) (b (1 - E^(-2 c z))^\[Nu] (-1 + E^(4 c z)) Hypergeometric2F1[ (1 - \[Nu])/2, (1 - \[Nu])/2, (3 - \[Nu])/2, Cosh[c z]^2] - 2 c E^(2 (-b + c) z) (1 + E^(-2 c z))^\[Nu] (-1 + \[Nu]) AppellF1[b/c, \[Nu], -\[Nu], (b + c)/c, -E^(-2 c z), E^(-2 c z)] (-Sinh[c z]^2)^((1 + \[Nu])/2)) Tanh[c z]^\[Nu])/ (E^(2 c z) (1 - E^(-2 c z))^\[Nu]))










Standard Form





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MathML Form







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Rule Form





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Date Added to functions.wolfram.com (modification date)





2002-12-18