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Sinh




Mathematica Notation

Traditional Notation









Elementary Functions > Sinh[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving trigonometric and exponential functions > Involving cos and exp > Involving ep z cos(b zr)sinh(c z)





http://functions.wolfram.com/01.19.21.1264.01









  


  








Input Form





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








Standard Form





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MathML Form







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