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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 zr)cosh(c z)





http://functions.wolfram.com/01.20.21.1258.01









  


  








Input Form





Integrate[E^(p Sqrt[z]) Cos[b Sqrt[z]] Cosh[c z], z] == (1/8) ((8 E^(p Sqrt[z]) Cos[b Sqrt[z]] Sinh[c z])/c + (c ((-I) b + p) Sqrt[Pi] Erfi[((-I) b + p - 2 c Sqrt[z])/(2 Sqrt[-c])])/ (E^((b + I p)^2/(4 c)) (-c)^(5/2)) + (c E^((I b + p)^2/(4 c)) (I b + p) Sqrt[Pi] Erfi[(I b + p - 2 c Sqrt[z])/(2 Sqrt[-c])])/(-c)^(5/2) + (I E^((b + I p)^2/(4 c)) (b + I p) Sqrt[Pi] Erfi[((-I) b + p + 2 c Sqrt[z])/(2 Sqrt[c])])/c^(3/2) - (E^((b - I p)^2/(4 c)) (I b + p) Sqrt[Pi] Erfi[(I b + p + 2 c Sqrt[z])/(2 Sqrt[c])])/c^(3/2))








Standard Form





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MathML Form







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