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Cos




Mathematica Notation

Traditional Notation









Elementary Functions > Cos[z] > Integration > Indefinite integration > Involving functions of the direct function > Involving products of the direct > Involving products of several direct functions > Involving cos(a z+alpha) cos(b z+beta) cos(c z+gamma)





http://functions.wolfram.com/01.07.21.1100.01









  


  








Input Form





Integrate[Cos[a z + \[Alpha]] Cos[b z + \[Beta]] Cos[c z + \[Gamma]], z] == (1/4) ((Cos[\[Alpha] - \[Beta] - \[Gamma]] Sin[(a - b - c) z])/(a - b - c) + (Cos[\[Alpha] + \[Beta] - \[Gamma]] Sin[(a + b - c) z])/(a + b - c) + (Cos[\[Alpha] - \[Beta] + \[Gamma]] Sin[(a - b + c) z])/(a - b + c) + (Cos[\[Alpha] + \[Beta] + \[Gamma]] Sin[(a + b + c) z])/(a + b + c) + (Cos[(a - b - c) z] Sin[\[Alpha] - \[Beta] - \[Gamma]])/(a - b - c) + (Cos[(a + b - c) z] Sin[\[Alpha] + \[Beta] - \[Gamma]])/(a + b - c) + (Cos[(a - b + c) z] Sin[\[Alpha] - \[Beta] + \[Gamma]])/(a - b + c) + (Cos[(a + b + c) z] Sin[\[Alpha] + \[Beta] + \[Gamma]])/(a + b + c))








Standard Form





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MathML Form







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</mo> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> - </mo> <mi> b </mi> <mo> + </mo> <mi> c </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> &#945; </mi> <mo> - </mo> <mi> &#946; </mi> <mo> + </mo> <mi> &#947; </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mi> a </mi> <mo> - </mo> <mi> b </mi> <mo> + </mo> <mi> c </mi> </mrow> </mfrac> <mo> + </mo> <mfrac> <mrow> <mrow> <mi> cos </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> + </mo> <mi> b </mi> <mo> + </mo> <mi> c </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> &#945; </mi> <mo> + </mo> <mi> &#946; </mi> <mo> + </mo> <mi> &#947; </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mi> a </mi> <mo> + </mo> <mi> b </mi> <mo> + </mo> <mi> c </mi> </mrow> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <int /> <bvar> <ci> z </ci> </bvar> <apply> <times /> <apply> <cos /> <apply> <plus /> <apply> <times /> <ci> a </ci> <ci> z </ci> </apply> <ci> &#945; 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Rule Form





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





2002-12-18