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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))m)+-1/2sinh(c z)





http://functions.wolfram.com/01.19.21.1746.01









  


  










Input Form





Integrate[Sqrt[(a + b Sinh[2 c z])^3] Sinh[c z], z] == (1/(8 c)) Sqrt[(a + b Sinh[2 c z])^3] (3 (((a - I b)^2 ArcTan[(Sqrt[2] Sqrt[(-I) b] Sin[(1/4) (Pi - 4 I c z)])/ Sqrt[a + b Sinh[2 c z]]] + 2 I a b ArcTanh[(Sqrt[2] Sqrt[(-I) b] Cos[(1/4) (Pi - 4 I c z)])/ Sqrt[a + b Sinh[2 c z]]] + (a^2 - b^2) Log[Sqrt[(-I) b] Cosh[c z] + (b Sinh[c z])/Sqrt[(-I) b] + Sqrt[a + b Sinh[2 c z]]])/(2 Sqrt[(-I) b] (a + b Sinh[2 c z])^ (3/2))) + (5 a Cosh[c z] + b (-2 Sinh[c z] + Sinh[3 c z]))/ (a + b Sinh[2 c z]))










Standard Form





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MathML Form







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<apply> <sinh /> <apply> <times /> <ci> c </ci> <ci> z </ci> </apply> </apply> </apply> </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='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