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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 zr+e) sinh(c zr+f z)





http://functions.wolfram.com/01.19.21.0581.01









  


  










Input Form





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










Standard Form





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MathML Form







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<mrow> <mrow> <mo> - </mo> <mi> b </mi> </mrow> <mo> - </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> c </mi> </mrow> </mrow> </msqrt> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <int /> <bvar> <ci> z </ci> </bvar> <apply> <times /> <apply> <sin /> <apply> <plus /> <apply> <times /> <ci> b </ci> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <ci> e </ci> </apply> </apply> <apply> <sinh /> <apply> <plus /> <apply> <times /> <ci> c </ci> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <ci> f </ci> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <imaginaryi /> <apply> <power /> <apply> <times /> <pi /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <cn 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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