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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 rational functions of the direct function and trigonometric functions > Involving rational functions of sin > Involving (a sin2(e z)+b sin(2 e z)+c cos2(e z))-n





http://functions.wolfram.com/01.07.21.2279.01









  


  








Input Form





Integrate[(A Sin[z]^2 + B Sin[2 z] + C Cos[z]^2 + D)/ (a Sin[z]^2 + b Sin[2 z] + c Cos[z]^2), z] == ((4 b B + a (A - C) + c (-A + C)) z - (1/Sqrt[-b^2 + a c]) ((-2 b B c + A (2 b^2 + c (-a + c)) + 2 b^2 C + 4 b^2 D + c^2 D + a^2 (C + D) - a (2 b B + c C + 2 c D)) ArcTan[(-b - a Tan[z])/Sqrt[-b^2 + a c]]) + ((-A) b + a B - B c + b C) Log[a + c + (-a + c) Cos[2 z] + 2 b Sin[2 z]])/(a^2 + 4 b^2 - 2 a c + c^2)








Standard Form





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MathML Form







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type='integer'> 4 </cn> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <power /> <ci> c </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> b </ci> <ci> B </ci> </apply> <apply> <times /> <ci> a </ci> <apply> <plus /> <ci> A </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> C </ci> </apply> </apply> </apply> <apply> <times /> <ci> c </ci> <apply> <plus /> <ci> C </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> A </ci> </apply> </apply> </apply> </apply> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <power /> <apply> <plus /> <apply> <times /> <ci> a </ci> <ci> c </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <apply> <plus /> <ci> C </ci> <ci> D </ci> </apply> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> <ci> B </ci> </apply> <apply> <times /> <ci> c </ci> <ci> C </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> <ci> D </ci> </apply> </apply> <ci> a </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> <ci> B </ci> <ci> c </ci> </apply> </apply> <apply> <times /> <ci> A </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <ci> c </ci> 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Rule Form





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





2002-12-18