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Sinh






Mathematica Notation

Traditional Notation









Elementary Functions > Sinh[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving trigonometric functions > Involving cos > Involving cos(d z) sinh(c zr+f z)





http://functions.wolfram.com/01.19.21.0743.01









  


  










Input Form





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










Standard Form





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MathML Form







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</cn> <imaginaryi /> <ci> c </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <power /> <apply> <times /> <imaginaryi /> <ci> c </ci> </apply> <cn type='rational'> 1 <sep /> 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> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <apply> <ci> FresnelC </ci> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> d </ci> </apply> <apply> <times /> <imaginaryi /> <ci> f </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> c </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <power /> <apply> <times /> <imaginaryi /> <ci> c </ci> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <times /> <cn 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Rule Form





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





2002-12-18