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Cosh






Mathematica Notation

Traditional Notation









Elementary Functions > Cosh[z] > Integration > Indefinite integration > Involving functions of the direct function and hyperbolic functions > Involving powers of the direct function and hyperbolic functions > Involving powers of sinh > Involving sinhmu(c z)coshv(a z+b)





http://functions.wolfram.com/01.20.21.4143.01









  


  










Input Form





Integrate[Sinh[c z]^\[Mu] Cosh[b + a z]^v, z] == (1/(c \[Mu])) ((Sinh[c z]^\[Mu] (Binomial[v, v/2] Hypergeometric2F1[-(\[Mu]/2), -\[Mu], 1 - \[Mu]/2, E^(2 c z)] (-1 + Mod[v, 2]) + c \[Mu] Sum[E^(2 b s - b v) Binomial[v, s] (-(E^((-2 s + v) (2 b + a z)) Hypergeometric2F1[ -((2 a s - a v + c \[Mu])/(2 c)), -\[Mu], (1/2) (2 + (a (-2 s + v))/c - \[Mu]), E^(2 c z)])/(2 a s - a v + c \[Mu]) + (E^(a (2 s - v) z) Hypergeometric2F1[ -((-2 a s + a v + c \[Mu])/(2 c)), -\[Mu], -((a (-2 s + v) + c (-2 + \[Mu]))/(2 c)), E^(2 c z)])/ (2 a s - a v - c \[Mu])), {s, 0, Floor[(1/2) (-1 + v)]}]))/ (2^v (1 - E^(2 c z))^\[Mu])) /; Element[v, Integers] && v > 0










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