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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(b zr) sinh(f z+g)





http://functions.wolfram.com/01.19.21.0708.01









  


  










Input Form





Integrate[Cos[b Sqrt[z]] Sinh[f z + g], z] == (1/4) I ((1/((-I) f)^(3/2)) (-2 Sqrt[(-I) f] Cos[(-I) g + b Sqrt[z] - I f z] - b Sqrt[2 Pi] Cosh[b^2/(4 f) + g] FresnelS[(b - 2 I f Sqrt[z])/ (Sqrt[(-I) f] Sqrt[2 Pi])] + I b Sqrt[2 Pi] FresnelC[(b - 2 I f Sqrt[z])/(Sqrt[(-I) f] Sqrt[2 Pi])] Sinh[b^2/(4 f) + g]) + (1/((-I) f)^(3/2)) (-2 Sqrt[(-I) f] Cos[I g + b Sqrt[z] + I f z] - b Sqrt[2 Pi] Cosh[b^2/(4 f) + g] FresnelS[(b + 2 I f Sqrt[z])/ (Sqrt[(-I) f] Sqrt[2 Pi])] + I b Sqrt[2 Pi] FresnelC[(b + 2 I f Sqrt[z])/(Sqrt[(-I) f] Sqrt[2 Pi])] Sinh[b^2/(4 f) + g]))










Standard Form





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MathML Form







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</ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <power /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <imaginaryi /> </apply> <ci> f </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> <sinh /> <apply> <plus /> <apply> <times /> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> f </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <ci> g </ci> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2002-12-18