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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 functions > Involving sin > Involving sin(b z) sinh(c zr)





http://functions.wolfram.com/01.19.21.0548.01









  


  










Input Form





Integrate[Sin[b z] Sinh[c Sqrt[z]], z] == (-(1/4)) I ((1/(-b)^(3/2)) ((-I) c Sqrt[2 Pi] Cos[c^2/(4 b)] FresnelC[(I c - 2 b Sqrt[z])/(Sqrt[-b] Sqrt[2 Pi])] - I c Sqrt[2 Pi] FresnelS[(I c - 2 b Sqrt[z])/(Sqrt[-b] Sqrt[2 Pi])] Sin[c^2/(4 b)] - 2 Sqrt[-b] Sin[(-I) c Sqrt[z] + b z]) + (1/(-b)^(3/2)) (I c Sqrt[2 Pi] Cos[c^2/(4 b)] FresnelC[(I c + 2 b Sqrt[z])/(Sqrt[-b] Sqrt[2 Pi])] + I c Sqrt[2 Pi] FresnelS[(I c + 2 b Sqrt[z])/(Sqrt[-b] Sqrt[2 Pi])] Sin[c^2/(4 b)] + 2 Sqrt[-b] Sin[I c Sqrt[z] + b z]))










Standard Form





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MathML Form







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