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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(d z+e) cos(c zr)





http://functions.wolfram.com/01.07.21.0611.01









  


  










Input Form





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










Standard Form





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MathML Form







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type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <sin /> <apply> <plus /> <apply> <times /> <apply> <power /> <ci> c </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> d </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> e </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