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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 sinh > Involving sinh(b zr) coshv(c z)





http://functions.wolfram.com/01.20.21.4046.01









  


  










Input Form





Integrate[Sinh[b Sqrt[z]] Cosh[c z]^v, z] == 2^(-2 - v) (-((1/b^2) ((4 (1 + E^(2 b Sqrt[z]) (-1 + b Sqrt[z]) + b Sqrt[z]) Binomial[v, v/2] (-1 + Mod[v, 2]))/E^(b Sqrt[z]))) + Sum[Binomial[v, s] ((8 Sinh[b Sqrt[z]] Sinh[c (2 s - v) z])/ (c (2 s - v)) + (b E^(b^2/(-8 c s + 4 c v)) Sqrt[Pi] Erfi[(-b + 2 c (-2 s + v) Sqrt[z])/(2 Sqrt[c (2 s - v)])])/ (c (2 s - v))^(3/2) - (b E^(b^2/(8 c s - 4 c v)) Sqrt[Pi] Erfi[(-b + 2 c (-2 s + v) Sqrt[z])/(2 Sqrt[c (-2 s + v)])])/ (c (-2 s + v))^(3/2) + (b E^(b^2/(-8 c s + 4 c v)) Sqrt[Pi] Erfi[(b + 2 c (-2 s + v) Sqrt[z])/(2 Sqrt[c (2 s - v)])])/ (c (2 s - v))^(3/2) - (b E^(b^2/(8 c s - 4 c v)) Sqrt[Pi] Erfi[(b + 2 c (-2 s + v) Sqrt[z])/(2 Sqrt[c (-2 s + v)])])/ (c (-2 s + v))^(3/2)), {s, 0, Floor[(1/2) (-1 + v)]}]) /; 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