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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 zr cos(b zr)sinh(c zr)





http://functions.wolfram.com/01.19.21.1273.01









  


  










Input Form





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










Standard Form





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MathML Form







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