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Cosh




Mathematica Notation

Traditional Notation









Elementary Functions > Cosh[z] > Integration > Indefinite integration > Involving functions of the direct function, hyperbolic and exponential functions > Involving rational functions of the direct function, hyperbolic and exponential functions > Involving rational functions of sinh and exp > Involving ep z(a sinh2(e z)+b sinh(2 e z)+c cosh2(e z))-n





http://functions.wolfram.com/01.20.21.4719.01









  


  








Input Form





Integrate[E^(p z)/(a Sinh[e z]^2 + b Sinh[2 e z] + c Cosh[e z]^2), z] == -((a + 2 b + c) E^((2 e + p) z) ((a - c + 2 Sqrt[b^2 - a c]) Hypergeometric2F1[1 + p/(2 e), 1, 2 + p/(2 e), ((a + 2 b + c) E^(2 e z))/(a - c - 2 Sqrt[b^2 - a c])] + (-a + c + 2 Sqrt[b^2 - a c]) Hypergeometric2F1[1 + p/(2 e), 1, 2 + p/(2 e), ((a + 2 b + c) E^(2 e z))/(a - c + 2 Sqrt[b^2 - a c])]))/ (Sqrt[b^2 - a c] (a - c + 2 Sqrt[b^2 - a c]) (-a + c + 2 Sqrt[b^2 - a c]) (2 e + p))








Standard Form





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MathML Form







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type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> a </ci> <ci> c </ci> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> c </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <plus /> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> a </ci> <ci> c </ci> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> <ci> c </ci> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <plus /> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> a </ci> <ci> c </ci> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> e </ci> </apply> <ci> p </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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Date Added to functions.wolfram.com (modification date)





2002-12-18