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Cosh






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/01.20.21.0578.01









  


  










Input Form





Integrate[Sin[b z^2] Cosh[c z^2 + f z], z] == (-(1/2)) Sqrt[Pi/2] ((1/Sqrt[-b + I c]) (Cos[f^2/(4 (-b + I c))] FresnelS[(I f + 2 (-b + I c) z)/ (Sqrt[-b + I c] Sqrt[2 Pi])] + FresnelC[(I f + 2 (-b + I c) z)/(Sqrt[-b + I c] Sqrt[2 Pi])] Sin[f^2/(4 (-b + I c))]) + (1/Sqrt[-b - I c]) ((-Cos[-(f^2/(4 (-b - I c)))]) FresnelS[(I f + 2 (b + I c) z)/ (Sqrt[-b - I c] Sqrt[2 Pi])] + FresnelC[(I f + 2 (b + I c) z)/(Sqrt[-b - I c] Sqrt[2 Pi])] Sin[-(f^2/(4 (-b - I c)))]))










Standard Form





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MathML Form







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<apply> <power /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <plus /> <apply> <times /> <imaginaryi /> <ci> c </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <power /> <apply> <plus /> <apply> <times /> <imaginaryi /> <ci> c </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </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