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Cosh




Mathematica Notation

Traditional Notation









Elementary Functions > Cosh[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving hyperbolic functions > Involving sinh > Involving sinh(b zr+e) cosh(c zr+f z+g)





http://functions.wolfram.com/01.20.21.1524.01









  


  








Input Form





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








Standard Form





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MathML Form







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z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> f </ci> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <power /> <ci> f </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> e </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> g </ci> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <plus /> <ci> b </ci> <ci> c </ci> </apply> <apply> <power /> <exponentiale /> <apply> <times /> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> c </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> f </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <pi /> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <ci> Erfi </ci> <apply> <times /> <apply> <plus /> <ci> b </ci> <ci> c </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> f </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 /> <cn type='integer'> -1 </cn> <ci> f </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 /> <cn type='integer'> -1 </cn> <ci> f </ci> </apply> <cn type='rational'> 3 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <plus /> <ci> b </ci> <ci> c </ci> </apply> <apply> <power /> <exponentiale /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <ci> e </ci> <ci> g </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <apply> <plus /> <ci> b </ci> <ci> c </ci> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> f </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <pi /> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <ci> Erfi </ci> <apply> <times /> <apply> <plus /> <ci> b </ci> <ci> c </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> f </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 /> <ci> f </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <power /> <ci> f </ci> <cn type='rational'> 3 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <exponentiale /> <apply> <plus /> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <ci> b </ci> <ci> c </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <ci> e </ci> <ci> g </ci> </apply> </apply> <apply> <times /> <ci> f </ci> <ci> z </ci> </apply> </apply> </apply> <apply> <power /> <ci> f </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <exponentiale /> <apply> <plus /> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> c </ci> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> f </ci> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <power /> <ci> f </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </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