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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 sinh(c z)





http://functions.wolfram.com/01.19.21.1739.01









  


  










Input Form





Integrate[(a + b Sinh[2 c z])^(5/2) Sinh[c z], z] == (1/(96 c)) ((15/Sqrt[(-I) b]) ((a - I b)^3 ArcTan[(Sqrt[2] Sqrt[(-I) b] Sin[(1/4) (Pi - 4 I c z)])/ Sqrt[a + b Sinh[2 c z]]] + I (3 a^2 b - b^3) ArcTanh[(Sqrt[2] Sqrt[(-I) b] Cos[(1/4) (Pi - 4 I c z)])/ Sqrt[a + b Sinh[2 c z]]] + a (a^2 - 3 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[a + b Sinh[2 c z]] ((33 a^2 - 14 b^2) Cosh[c z] + b (-3 b Cosh[3 c z] + 2 b Cosh[5 c z] - 27 a Sinh[c z] + 13 a Sinh[3 c z])))










Standard Form





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MathML Form







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<cn type='integer'> 13 </cn> <ci> a </ci> <apply> <sinh /> <apply> <times /> <cn type='integer'> 3 </cn> <ci> c </ci> <ci> z </ci> </apply> </apply> </apply> </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