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Cosh




Mathematica Notation

Traditional Notation









Elementary Functions > Cosh[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving trigonometric and exponential functions > Involving rational functions of sin, cos and exp > Involving ep zcosh(d z)(a sin2(e z)+b cos2(e z))-n





http://functions.wolfram.com/01.20.21.1331.01









  


  








Input Form





Integrate[(E^(p z) Cosh[d z])/(a Sin[e z]^2 + b Cos[e z]^2), z] == (1/2) (-((I E^((-d + 2 I e + p) z) ((Sqrt[-a] + I Sqrt[b])^2 Hypergeometric2F1[1 - (I (-d + p))/(2 e), 1, 2 - (I (-d + p))/(2 e), ((-a + b) E^(2 I e z))/(Sqrt[-a] - I Sqrt[b])^2] - (Sqrt[-a] - I Sqrt[b])^2 Hypergeometric2F1[1 - (I (-d + p))/(2 e), 1, 2 - (I (-d + p))/(2 e), ((-a + b) E^(2 I e z))/ (Sqrt[-a] + I Sqrt[b])^2]))/(Sqrt[-a] Sqrt[b] (-a + b) (-d + 2 I e + p))) - (I E^((d + 2 I e + p) z) ((Sqrt[-a] + I Sqrt[b])^2 Hypergeometric2F1[1 - (I (d + p))/(2 e), 1, 2 - (I (d + p))/(2 e), ((-a + b) E^(2 I e z))/(Sqrt[-a] - I Sqrt[b])^ 2] - (Sqrt[-a] - I Sqrt[b])^2 Hypergeometric2F1[ 1 - (I (d + p))/(2 e), 1, 2 - (I (d + p))/(2 e), ((-a + b) E^(2 I e z))/(Sqrt[-a] + I Sqrt[b])^2]))/ (Sqrt[-a] Sqrt[b] (-a + b) (d + 2 I e + p)))








Standard Form





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MathML Form







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</ci> </apply> </apply> <apply> <power /> <apply> <power /> <apply> <plus /> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <times /> <imaginaryi /> <apply> <power /> <ci> b </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> b </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <ci> b </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> </apply> <apply> <plus /> <ci> d </ci> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> e </ci> </apply> <ci> p </ci> </apply> </apply> <cn type='integer'> -1 </cn> </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