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Cos




Mathematica Notation

Traditional Notation









Elementary Functions > Cos[z] > Integration > Indefinite integration > Involving functions of the direct function and exponential function > Involving products of the direct function and exponential function > Involving products of two direct functions and exponential function > Involving ep zrcos(b zr)cos(c z)





http://functions.wolfram.com/01.07.21.1770.01









  


  








Input Form





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








Standard Form





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MathML Form







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