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Sinh






Mathematica Notation

Traditional Notation









Elementary Functions > Sinh[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving power function > Involving power > Power arguments





http://functions.wolfram.com/01.19.21.0026.01









  


  










Input Form





Integrate[Sinh[a (z^r)^p], z] == (1/(2 p r)) (z ((-((-a) (z^r)^p)^(-(1/(p r)))) Gamma[1/(p r), (-a) (z^r)^p] + Gamma[1/(p r), a (z^r)^p]/ (a (z^r)^p)^(1/(p r))))










Standard Form





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MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mo> &#8747; </mo> <mrow> <mrow> <mi> sinh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> a </mi> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <msup> <mi> z </mi> <mi> r </mi> </msup> <mo> ) </mo> </mrow> <mi> p </mi> </msup> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> &#8518; </mo> <mi> z </mi> </mrow> </mrow> </mrow> <mo> &#10869; </mo> <mfrac> <mrow> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <msup> <mi> z </mi> <mi> r </mi> </msup> <mo> ) </mo> </mrow> <mi> p </mi> </msup> </mrow> <mo> ) </mo> </mrow> <mrow> <mo> - </mo> <mfrac> <mn> 1 </mn> <mrow> <mi> p </mi> <mo> &#8290; </mo> <mi> r </mi> </mrow> </mfrac> </mrow> </msup> <mo> &#8290; </mo> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mfrac> <mn> 1 </mn> <mrow> <mi> p </mi> <mo> &#8290; </mo> <mi> r </mi> </mrow> </mfrac> <mo> , </mo> <mrow> <mi> a </mi> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <msup> <mi> z </mi> <mi> r </mi> </msup> <mo> ) </mo> </mrow> <mi> p </mi> </msup> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> a </mi> </mrow> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <msup> <mi> z </mi> <mi> r </mi> </msup> <mo> ) </mo> </mrow> <mi> p </mi> </msup> </mrow> <mo> ) </mo> </mrow> <mrow> <mo> - </mo> <mfrac> <mn> 1 </mn> <mrow> <mi> p </mi> <mo> &#8290; </mo> <mi> r </mi> </mrow> </mfrac> </mrow> </msup> <mo> &#8290; </mo> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mfrac> <mn> 1 </mn> <mrow> <mi> p </mi> <mo> &#8290; </mo> <mi> r </mi> </mrow> </mfrac> <mo> , </mo> <mrow> <mrow> <mo> - </mo> <mi> a </mi> </mrow> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <msup> <mi> z </mi> <mi> r </mi> </msup> <mo> ) </mo> </mrow> <mi> p </mi> </msup> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> p </mi> <mo> &#8290; </mo> <mi> r </mi> </mrow> </mfrac> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <int /> <bvar> <ci> z </ci> </bvar> <apply> <sinh /> <apply> <times /> <ci> a </ci> <apply> <power /> <apply> <power /> <ci> z </ci> <ci> r </ci> </apply> <ci> p </ci> </apply> </apply> </apply> </apply> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <apply> <power /> <apply> <times /> <ci> a </ci> <apply> <power /> <apply> <power /> <ci> z </ci> <ci> r </ci> </apply> <ci> p </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <ci> p </ci> <ci> r </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <ci> Gamma </ci> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <ci> p </ci> <ci> r </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <ci> a </ci> <apply> <power /> <apply> <power /> <ci> z </ci> <ci> r </ci> </apply> <ci> p </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> <apply> <power /> <apply> <power /> <ci> z </ci> <ci> r </ci> </apply> <ci> p </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <ci> p </ci> <ci> r </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <ci> Gamma </ci> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <ci> p </ci> <ci> r </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> <apply> <power /> <apply> <power /> <ci> z </ci> <ci> r </ci> </apply> <ci> p </ci> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> p </ci> <ci> r </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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Date Added to functions.wolfram.com (modification date)





2002-12-18