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Cosh




Mathematica Notation

Traditional Notation









Elementary Functions > Cosh[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving hyperbolic and a power functions > Involving sinh and power > Involving zalpha-1sinh(c z+d)cosh(a z+b)





http://functions.wolfram.com/01.20.21.1662.01









  


  








Input Form





Integrate[z^(\[Alpha] - 1) Sinh[d + c z] Cosh[b + a z], z] == ((1/4) z^\[Alpha] ((-((-a + c) z)^\[Alpha]) ((-(a + c)^2) z^2)^\[Alpha] Gamma[\[Alpha], (a - c) z] (Cosh[b] - Sinh[b]) (Cosh[d] + Sinh[d]) + ((a - c) z)^\[Alpha] (((-(a + c)^2) z^2)^\[Alpha] Gamma[\[Alpha], (-a + c) z] (Cosh[b] + Sinh[b]) (Cosh[d] - Sinh[d]) + ((-a + c) z)^\[Alpha] (((-(a + c)) z)^\[Alpha] Gamma[\[Alpha], (a + c) z] (Cosh[b + d] - Sinh[b + d]) - ((a + c) z)^\[Alpha] Gamma[\[Alpha], (-(a + c)) z] (Cosh[b + d] + Sinh[b + d])))))/ (((a - c) z)^\[Alpha] ((-a + c) z)^\[Alpha] ((-(a + c)^2) z^2)^\[Alpha])








Standard Form





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MathML Form







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</ci> </apply> <apply> <power /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <apply> <plus /> <ci> a </ci> <ci> c </ci> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <ci> &#945; </ci> </apply> <apply> <ci> Gamma </ci> <ci> &#945; </ci> <apply> <times /> <apply> <plus /> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> c </ci> </apply> </apply> <ci> z </ci> </apply> </apply> <apply> <plus /> <apply> <cosh /> <ci> b </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <sinh /> <ci> b </ci> </apply> </apply> </apply> <apply> <plus /> <apply> <cosh /> <ci> d </ci> </apply> <apply> <sinh /> <ci> d </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