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Tan






Mathematica Notation

Traditional Notation









Elementary Functions > Tan[z] > Integration > Indefinite integration > Involving functions of the direct function > Involving rational functions of the direct function > Involving (a+b tan(c z))-n





http://functions.wolfram.com/01.08.21.0098.01









  


  










Input Form





Integrate[(A + B Tan[z] + C Tan[z]^2)/(a + b Tan[z])^3, z] == (Sec[z] (a Cos[z] + b Sin[z]) ((-b) (a^2 + b^2) (A b^2 + a ((-b) B + a C)) + (1/a) (2 (a^2 + b^2) (-2 a^2 b B + b^3 B + a b^2 (3 A - 2 C) + a^3 C) Sin[z] (a Cos[z] + b Sin[z])) + 2 (3 a^2 b B - b^3 B + a^3 (A - C) + 3 a b^2 (-A + C)) z (a Cos[z] + b Sin[z])^2 - 2 (a^3 B - 3 a b^2 B + b^3 (A - C) + 3 a^2 b (-A + C)) Log[a Cos[z] + b Sin[z]] (a Cos[z] + b Sin[z])^2) (A + B Tan[z] + C Tan[z]^2))/((a^2 + b^2)^3 (A + C + (A - C) Cos[2 z] + B Sin[2 z]) (a + b Tan[z])^3)










Standard Form





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MathML Form







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</cn> <apply> <plus /> <apply> <times /> <ci> B </ci> <apply> <power /> <ci> a </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 3 </cn> <ci> b </ci> <apply> <plus /> <ci> C </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> A </ci> </apply> </apply> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 3 </cn> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <ci> B </ci> <ci> a </ci> </apply> </apply> <apply> <times /> <apply> <power /> <ci> b </ci> <cn type='integer'> 3 </cn> </apply> <apply> <plus /> <ci> A </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> C </ci> </apply> </apply> </apply> </apply> <apply> <ln /> <apply> <plus /> <apply> <times /> <ci> a </ci> <apply> <cos /> <ci> z </ci> </apply> </apply> <apply> <times /> <ci> b </ci> <apply> <sin /> <ci> z </ci> </apply> </apply> </apply> </apply> 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</apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <ci> C </ci> <apply> <power /> <ci> a </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> <ci> B </ci> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 3 </cn> <ci> A </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> C </ci> </apply> </apply> </apply> <ci> a </ci> </apply> <apply> <times /> <apply> <power /> <ci> b </ci> <cn type='integer'> 3 </cn> </apply> <ci> B </ci> </apply> </apply> <apply> <sin /> <ci> z </ci> </apply> <apply> <plus /> <apply> <times /> <ci> a </ci> <apply> <cos /> <ci> z </ci> </apply> </apply> <apply> <times /> <ci> b </ci> <apply> <sin /> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <ci> C </ci> <apply> <power /> <apply> <tan /> <ci> z </ci> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <ci> B </ci> <apply> <tan /> <ci> z </ci> </apply> </apply> <ci> A </ci> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <power /> <apply> <plus /> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> 3 </cn> </apply> <apply> <plus /> <ci> A </ci> <ci> C </ci> <apply> <times /> <apply> <plus /> <ci> A </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> C </ci> </apply> </apply> <apply> <cos /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> </apply> </apply> </apply> <apply> <times /> <ci> B </ci> <apply> <sin /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <ci> a </ci> <apply> <times /> <ci> b </ci> <apply> <tan /> <ci> z </ci> </apply> </apply> </apply> <cn type='integer'> 3 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2002-12-18