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Cos






Mathematica Notation

Traditional Notation









Elementary Functions > Cos[z] > Integration > Indefinite integration > Involving functions of the direct function and trigonometric functions > Involving algebraic functions of the direct function and trigonometric functions > Involving algebraic functions of sin > Involving (a+b sin(e z)+c cos(e z))beta





http://functions.wolfram.com/01.07.21.2382.01









  


  










Input Form





Integrate[(a + b Sin[e z] + c Cos[e z])^\[Beta], z] == (AppellF1[1 + \[Beta], 1/2, 1/2, 2 + \[Beta], (a + c Cos[e z] + b Sin[e z])/ (a - b Sqrt[1 + c^2/b^2]), (a + c Cos[e z] + b Sin[e z])/ (a + b Sqrt[1 + c^2/b^2])] Sec[e z + ArcTan[c/b]] Sqrt[((-c) Cos[e z] + b (Sqrt[1 + c^2/b^2] - Sin[e z]))/ (a + b Sqrt[1 + c^2/b^2])] (a + c Cos[e z] + b Sin[e z])^(1 + \[Beta]) Sqrt[(c Cos[e z] + b (Sqrt[1 + c^2/b^2] + Sin[e z]))/ (-a + b Sqrt[1 + c^2/b^2])])/(b Sqrt[1 + c^2/b^2] e (1 + \[Beta]))










Standard Form





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MathML Form







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</ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <plus /> <apply> <times /> <ci> c </ci> <apply> <cos /> <apply> <times /> <ci> e </ci> <ci> z </ci> </apply> </apply> </apply> <apply> <times /> <ci> b </ci> <apply> <plus /> <apply> <sin /> <apply> <times /> <ci> e </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <apply> <power /> <ci> c </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <ci> b </ci> <apply> <power /> <apply> <plus /> <apply> <times /> <apply> <power /> <ci> c </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </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