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Sinh






Mathematica Notation

Traditional Notation









Elementary Functions > Sinh[z] > Integration > Indefinite integration > Involving functions of the direct function > Involving algebraic functions of the direct function > Involving (a+b sinh(2c z))beta sinhv(c z)





http://functions.wolfram.com/01.19.21.1753.01









  


  










Input Form





Integrate[Sqrt[a + b Sinh[2 c z]] Sinh[c z]^3, z] == (1/(16 c)) ((1/(2 ((-I) b)^(3/2))) ((-a^2 + 6 I a b + 5 b^2) ArcTan[(Sqrt[2] Sqrt[(-I) b] Sin[(1/4) (Pi - 4 I c z)])/ Sqrt[a + b Sinh[2 c z]]] + (a^2 - 5 b^2) ArcTanh[(Sqrt[2] Sqrt[(-I) b] Cos[(1/4) (Pi - 4 I c z)])/ Sqrt[a + b Sinh[2 c z]]] + 6 I a b Log[Sqrt[(-I) b] Cosh[c z] + (b Sinh[c z])/Sqrt[(-I) b] + Sqrt[a + b Sinh[2 c z]]]) + (1/b) (-6 b Cosh[c z] + b Cosh[3 c z] + a Sinh[c z]) Sqrt[a + b Sinh[2 c z]])










Standard Form





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MathML Form







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b </ci> <apply> <cosh /> <apply> <times /> <cn type='integer'> 3 </cn> <ci> c </ci> <ci> z </ci> </apply> </apply> </apply> <apply> <times /> <ci> a </ci> <apply> <sinh /> <apply> <times /> <ci> c </ci> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <ci> a </ci> <apply> <times /> <ci> b </ci> <apply> <sinh /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> <ci> z </ci> </apply> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> b </ci> <cn type='integer'> -1 </cn> </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