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Cos






Mathematica Notation

Traditional Notation









Elementary Functions > Cos[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving trigonometric functions > Involving sin > Involving sin(b zr+e) cos(f z+g)





http://functions.wolfram.com/01.07.21.0602.01









  


  










Input Form





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










Standard Form





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MathML Form







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</apply> </apply> <apply> <cos /> <apply> <plus /> <apply> <times /> <ci> f </ci> <ci> z </ci> </apply> <ci> g </ci> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <power /> <apply> <times /> <pi /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <cos /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <ci> f </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> <ci> e </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> g </ci> </apply> </apply> </apply> </apply> <apply> <ci> FresnelS </ci> <apply> <times /> <apply> <plus /> <ci> f </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> <ci> z </ci> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </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 /> <apply> <cos /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <ci> f </ci> <cn type='integer'> 2 </cn> </apply> 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<times /> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> <cn type='rational'> 3 <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> <sin /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <ci> f </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> <ci> e </ci> <ci> g </ci> </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