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Tan






Mathematica Notation

Traditional Notation









Elementary Functions > Tan[z] > Integration > Indefinite integration > Involving functions of the direct function > Involving algebraic functions of the direct function > Involving ((a+b tan2(c z))n)beta





http://functions.wolfram.com/01.08.21.0120.01









  


  










Input Form





Integrate[Sqrt[(a + b Tan[c z]^2)^3], z] == (I Sqrt[(a + b Tan[c z]^2)^3] ((3 a - 2 b) Sqrt[-b] Log[2 (I Sqrt[-b] Tan[c z] + Sqrt[a + b Tan[c z]^2])] + (a - b)^(3/2) (-Log[-((4 (a - I b Tan[c z] + Sqrt[a - b] Sqrt[a + b Tan[c z]^2]))/ ((a - b)^(5/2) (-1 + I Tan[c z])))] + Log[(4 (a + I b Tan[c z] + Sqrt[a - b] Sqrt[a + b Tan[c z]^2]))/ ((a - b)^(5/2) (1 + I Tan[c z]))]) - I b Tan[c z] Sqrt[a + b Tan[c z]^2]))/(2 c (a + b Tan[c z]^2)^(3/2))










Standard Form





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MathML Form







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





© 1998-2014 Wolfram Research, Inc.