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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 cos and exp > Involving ep zr cos(b z)cosh(c zr)





http://functions.wolfram.com/01.20.21.1266.01









  


  








Input Form





Integrate[E^(p Sqrt[z]) Cos[b z] Cosh[c Sqrt[z]], z] == (1/8) (((c - p) Sqrt[Pi] Erfi[(-c + p - 2 I b Sqrt[z])/(2 Sqrt[(-I) b])])/ (E^((I (c - p)^2)/(4 b)) ((-I) b)^(3/2)) + (Sqrt[(-I) b] (c + p) Sqrt[Pi] Erfi[(c + p - 2 I b Sqrt[z])/ (2 Sqrt[(-I) b])])/(E^((I (c + p)^2)/(4 b)) b^2) - (Sqrt[I b] E^((I (c - p)^2)/(4 b)) (c - p) Sqrt[Pi] Erfi[(-c + p + 2 I b Sqrt[z])/(2 Sqrt[I b])])/b^2 - (E^((I (c + p)^2)/(4 b)) (c + p) Sqrt[Pi] Erfi[(c + p + 2 I b Sqrt[z])/(2 Sqrt[I b])])/(I b)^(3/2) + (8 E^(p Sqrt[z]) Cosh[c Sqrt[z]] Sin[b z])/b)








Standard Form





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MathML Form







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</apply> <apply> <plus /> <ci> c </ci> <ci> p </ci> </apply> <apply> <power /> <pi /> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <ci> Erfi </ci> <apply> <times /> <apply> <plus /> <ci> c </ci> <ci> p </ci> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> b </ci> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <times /> <imaginaryi /> <ci> b </ci> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <power /> <apply> <times /> <imaginaryi /> <ci> b </ci> </apply> <cn type='rational'> 3 <sep /> 2 </cn> </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