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Sinh




Mathematica Notation

Traditional Notation









Elementary Functions > Sinh[z] > Integration > Indefinite integration > Involving functions of the direct function and trigonometric functions > Involving rational functions of the direct function and trigonometric functions > Involving cos > Involving cos(d z)(a+b sinh(c z))-n





http://functions.wolfram.com/01.19.21.2791.01









  


  








Input Form





Integrate[Cos[d z]/(a + b Sinh[c z])^2, z] == (-(1/(2 (a^2 + b^2)^(3/2)))) (b ((a E^((c - I d) z) Hypergeometric2F1[1 - (I d)/c, 1, 2 - (I d)/c, (b E^(c z))/(-a + Sqrt[a^2 + b^2])])/((-a + Sqrt[a^2 + b^2]) (c - I d)) + (a E^((c - I d) z) Hypergeometric2F1[1 - (I d)/c, 1, 2 - (I d)/c, -((b E^(c z))/(a + Sqrt[a^2 + b^2]))])/ ((a + Sqrt[a^2 + b^2]) (c - I d)) - (Sqrt[a^2 + b^2] E^((c - I d) z) Hypergeometric2F1[1 - (I d)/c, 2, 2 - (I d)/c, (b E^(c z))/(-a + Sqrt[a^2 + b^2])])/ ((-a + Sqrt[a^2 + b^2]) (c - I d)) + (Sqrt[a^2 + b^2] E^((c - I d) z) Hypergeometric2F1[1 - (I d)/c, 2, 2 - (I d)/c, -((b E^(c z))/(a + Sqrt[a^2 + b^2]))])/ ((a + Sqrt[a^2 + b^2]) (c - I d)) + (a E^((c + I d) z) Hypergeometric2F1[1 + (I d)/c, 1, 2 + (I d)/c, (b E^(c z))/(-a + Sqrt[a^2 + b^2])])/((-a + Sqrt[a^2 + b^2]) (c + I d)) + (a E^((c + I d) z) Hypergeometric2F1[1 + (I d)/c, 1, 2 + (I d)/c, -((b E^(c z))/(a + Sqrt[a^2 + b^2]))])/ ((a + Sqrt[a^2 + b^2]) (c + I d)) - (Sqrt[a^2 + b^2] E^((c + I d) z) Hypergeometric2F1[1 + (I d)/c, 2, 2 + (I d)/c, (b E^(c z))/(-a + Sqrt[a^2 + b^2])])/ ((-a + Sqrt[a^2 + b^2]) (c + I d)) + (Sqrt[a^2 + b^2] E^((c + I d) z) Hypergeometric2F1[1 + (I d)/c, 2, 2 + (I d)/c, -((b E^(c z))/(a + Sqrt[a^2 + b^2]))])/ ((a + Sqrt[a^2 + b^2]) (c + I d))))








Standard Form





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MathML Form







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-1 </cn> <ci> a </ci> </apply> </apply> <apply> <plus /> <ci> c </ci> <apply> <times /> <imaginaryi /> <ci> d </ci> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <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='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <exponentiale /> <apply> <times /> <apply> <plus /> <ci> c </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> d </ci> </apply> </apply> </apply> <ci> z </ci> </apply> </apply> <apply> <ci> Hypergeometric2F1 </ci> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> d </ci> <apply> <power /> <ci> c </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <cn type='integer'> 2 </cn> <apply> <plus /> <cn type='integer'> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> d </ci> <apply> <power /> <ci> c </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <ci> b </ci> <apply> <power /> <exponentiale /> <apply> <times /> <ci> c </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <plus /> <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='rational'> 1 <sep /> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <plus /> <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='rational'> 1 <sep /> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> </apply> <apply> <plus /> <ci> c </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> d </ci> </apply> </apply> </apply> </apply> <cn type='integer'> -1 </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