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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(d z+e) cosh(c zr+g)





http://functions.wolfram.com/01.20.21.1494.01









  


  








Input Form





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








Standard Form





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MathML Form







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</apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> d </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> d </ci> </apply> <cn type='rational'> 3 <sep /> 2 </cn> </apply> <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