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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 cos > Involving cosm(b zr) cosh(c z)





http://functions.wolfram.com/01.20.21.0698.01









  


  










Input Form





Integrate[Cos[b z^2] Cosh[c z], z] == (1/2) Sqrt[Pi/2] ((-(1/Sqrt[-b])) (Cos[c^2/(4 b)] FresnelC[(I c + 2 b z)/ (Sqrt[-b] Sqrt[2 Pi])] + FresnelS[(I c + 2 b z)/(Sqrt[-b] Sqrt[2 Pi])] Sin[c^2/(4 b)]) + (1/Sqrt[b]) (Cos[c^2/(4 b)] FresnelC[((-I) c + 2 b z)/ (Sqrt[b] Sqrt[2 Pi])] - FresnelS[((-I) c + 2 b z)/(Sqrt[b] Sqrt[2 Pi])] Sin[c^2/(4 b)]))










Standard Form





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MathML Form







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2 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <sin /> <apply> <times /> <apply> <power /> <ci> c </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> b </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <power /> <ci> b </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <plus /> <apply> <times /> <apply> <cos /> <apply> <times /> <apply> <power /> <ci> c </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> b </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <ci> FresnelC </ci> 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Rule Form





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





2002-12-18