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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 functions > Involving powers of cos > Involving cosm(b zr) cosh(f z+g)





http://functions.wolfram.com/01.20.21.0787.01









  


  










Input Form





Integrate[Cos[b Sqrt[z]]^m Cosh[f z + g], z] == ((-(1/2))^m Binomial[m, m/2] (1 - Mod[m, 2]) Sinh[g + f z])/f + 2^(-1 - m) Sum[Binomial[m, s] ((1/((-I) f)^(3/2)) (Sqrt[2 Pi] ((-b) m + 2 b s) Cosh[g + (b m - 2 b s)^2/(4 f)] FresnelC[(b m - 2 b s - 2 I f Sqrt[z])/(Sqrt[(-I) f] Sqrt[2 Pi])] - I Sqrt[2 Pi] (b m - 2 b s) FresnelS[(b m - 2 b s - 2 I f Sqrt[z])/ (Sqrt[(-I) f] Sqrt[2 Pi])] Sinh[g + (b m - 2 b s)^2/(4 f)] - 2 I Sqrt[(-I) f] Sinh[g + I (b m - 2 b s) Sqrt[z] + f z]) + (1/((-I) f)^(3/2)) (Sqrt[2 Pi] (b m - 2 b s) Cosh[g + ((-b) m + 2 b s)^2/(4 f)] FresnelC[ ((-b) m + 2 b s - 2 I f Sqrt[z])/(Sqrt[(-I) f] Sqrt[2 Pi])] - I Sqrt[2 Pi] ((-b) m + 2 b s) FresnelS[((-b) m + 2 b s - 2 I f Sqrt[z])/(Sqrt[(-I) f] Sqrt[2 Pi])] Sinh[g + ((-b) m + 2 b s)^2/(4 f)] - 2 I Sqrt[(-I) f] Sinh[g + I ((-b) m + 2 b s) Sqrt[z] + f z])), {s, 0, Floor[(1/2) (-1 + m)]}] /; 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