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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 cos > Involving cos(a zr) sinh(c zr)





http://functions.wolfram.com/01.19.21.0721.01









  


  










Input Form





Integrate[Cos[b Sqrt[z]] Sinh[c Sqrt[z]], z] == (-I) (((b - I c) Sqrt[z] Cos[(-b + I c) Sqrt[z]] + Sin[(-b + I c) Sqrt[z]])/ (-b + I c)^2 + ((-(b + I c)) Sqrt[z] Cos[(b + I c) Sqrt[z]] + Sin[(b + I c) Sqrt[z]])/(b + I c)^2)










Standard Form





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MathML Form







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</mi> <mo> &#8290; </mo> <mi> c </mi> </mrow> <mo> - </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msqrt> <mi> z </mi> </msqrt> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> c </mi> </mrow> <mo> - </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msqrt> <mi> z </mi> </msqrt> </mrow> <mo> ) </mo> </mrow> </mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> c </mi> </mrow> <mo> - </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mfrac> <mo> + </mo> <mfrac> <mrow> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> + </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> c </mi> </mrow> </mrow> <mtext> </mtext> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msqrt> <mi> z </mi> </msqrt> </mrow> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> + </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> c </mi> </mrow> </mrow> <mtext> </mtext> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msqrt> <mi> z </mi> </msqrt> <mo> &#8290; </mo> <mrow> <mi> cos </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> + </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> c </mi> </mrow> </mrow> <mtext> </mtext> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msqrt> <mi> z </mi> </msqrt> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> + </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> c </mi> </mrow> </mrow> <mtext> </mtext> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <int /> <bvar> <ci> z </ci> </bvar> <apply> <times /> <apply> <cos /> <apply> <times /> <ci> b </ci> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <sinh /> <apply> <times /> <ci> c </ci> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <imaginaryi /> </apply> <apply> <plus /> <apply> <times /> <apply> <plus /> <apply> <times /> <apply> <plus /> <ci> b </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> c </ci> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <cos /> <apply> <times /> <apply> <plus /> <apply> <times /> <imaginaryi /> <ci> c </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> <apply> <sin /> <apply> <times /> <apply> <plus /> <apply> <times /> <imaginaryi /> <ci> c </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </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='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <sin /> <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> <times /> <cn type='integer'> -1 </cn> <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> <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> <power /> <apply> <power /> <apply> <plus /> <ci> b </ci> <apply> <times /> <imaginaryi /> <ci> c </ci> </apply> </apply> <cn type='integer'> 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