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Cosh




Mathematica Notation

Traditional Notation









Elementary Functions > Cosh[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Arguments involving polynomials or algebraic functions and factors involving exponential functions > Involving exp > Involving ab zr+d z cosh(c zr+f z+g)





http://functions.wolfram.com/01.20.21.0495.01









  


  








Input Form





Integrate[a^(b Sqrt[z] + d z) Cosh[c Sqrt[z] + f z + g], z] == -((Sqrt[Pi] Erfi[(-c + b Log[a] + 2 Sqrt[z] (-f + d Log[a]))/ (2 Sqrt[-f + d Log[a]])] (-c + b Log[a]))/ E^((c^2 - 2 b c Log[a] + b^2 Log[a]^2 + 4 (-f + d Log[a]) g)/ (4 (-f + d Log[a]))))/(4 (-f + d Log[a])^(3/2)) + (a^(b Sqrt[z] + d z) E^(-g - c Sqrt[z] - f z))/(2 (-f + d Log[a])) - (Sqrt[Pi] Erfi[(c + b Log[a] + 2 Sqrt[z] (f + d Log[a]))/ (2 Sqrt[f + d Log[a]])] (c + b Log[a]))/ E^((c^2 + 2 b c Log[a] + b^2 Log[a]^2 - 4 (f + d Log[a]) g)/ (4 (f + d Log[a])))/(4 (f + d Log[a])^(3/2)) + (a^(b Sqrt[z] + d z) E^(g + c Sqrt[z] + f z))/(2 (f + d Log[a]))








Standard Form





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MathML Form







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