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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(c z+d)coshv(a z+b)





http://functions.wolfram.com/01.20.21.4044.01









  


  










Input Form





Integrate[Sinh[d + c z] Cosh[b + a z]^v, z] == (1/(2^v c)) Binomial[v, v/2] (1 - Mod[v, 2]) Cosh[d + c z] + 2^(1 - v) Sum[(Binomial[v, s] ((-c) Cosh[(2 s - v) (b + a z)] Cosh[d + c z] + a (2 s - v) Sinh[(2 s - v) (b + a z)] Sinh[d + c z]))/(-c^2 + a^2 (-2 s + v)^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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</ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2002-12-18