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Sinh






Mathematica Notation

Traditional Notation









Elementary Functions > Sinh[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving exponential function and a power function > Involving exp and power > Involving zalpha-1 eb z sinh(c z)





http://functions.wolfram.com/01.19.21.0287.01









  


  










Input Form





Integrate[z^3 E^(b z) Sinh[c z], z] == (1/((b - c)^4 (b + c)^4)) (E^(b z) (c (6 b^5 z^2 - b^6 z^3 + 3 b^4 z (-6 + c^2 z^2) - 3 b^2 c^2 z (-4 + c^2 z^2) - 12 b^3 (-2 + c^2 z^2) + 6 b c^2 (4 + c^2 z^2) + c^4 z (6 + c^2 z^2)) Cosh[c z] + (-3 b^6 z^2 + b^7 z^3 + 3 b^2 c^2 (-12 + c^2 z^2) + 3 b^4 (-2 + c^2 z^2) - 3 c^4 (2 + c^2 z^2) + 3 b^3 c^2 z (4 + c^2 z^2) - b c^4 z (18 + c^2 z^2) + b^5 (6 z - 3 c^2 z^3)) Sinh[c z]))










Standard Form





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MathML Form







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</apply> <ci> b </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 3 </cn> <apply> <power /> <ci> c </ci> <cn type='integer'> 4 </cn> </apply> <apply> <plus /> <apply> <times /> <apply> <power /> <ci> c </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> <apply> <sinh /> <apply> <times /> <ci> c </ci> <ci> z </ci> </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