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Cosh






Mathematica Notation

Traditional Notation









Elementary Functions > Cosh[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving trigonometric and a power functions > Involving powers of cos and power > Involving zalpha-1 cosm(b zr+e) cosh(c zr)





http://functions.wolfram.com/01.20.21.1137.01









  


  










Input Form





Integrate[z^n Cos[b Sqrt[z] + e]^m Cosh[c Sqrt[z]], z] == ((-2^(-m)) Binomial[m, m/2] (Gamma[2 (1 + n), (-c) Sqrt[z]] + Gamma[2 (1 + n), c Sqrt[z]]) (1 - Mod[m, 2]))/c^(2 (1 + n)) - Sum[Binomial[m, k] ((E^(-2 I e k + I e m) Gamma[2 (1 + n), (-c + 2 I b k - I b m) Sqrt[z]])/(-c + 2 I b k - I b m)^ (2 (1 + n)) + (E^(-2 I e k + I e m) Gamma[2 (1 + n), (c + 2 I b k - I b m) Sqrt[z]])/(c + 2 I b k - I b m)^(2 (1 + n)) + (E^(2 I e k - I e m) Gamma[2 (1 + n), (-c - 2 I b k + I b m) Sqrt[z]])/ (-c - 2 I b k + I b m)^(2 (1 + n)) + (E^(2 I e k - I e m) Gamma[2 (1 + n), (c - 2 I b k + I b m) Sqrt[z]])/ (c - 2 I b k + I b m)^(2 (1 + n))), {k, 0, Floor[(1/2) (-1 + m)]}]/ 2^m /; Element[n, Integers] && n >= 0 && Element[m, Integers] && m > 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