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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 exponential functions > Involving powers of sinh and exp > Involving ep zsinhmu(c z)cosh(a z+b)





http://functions.wolfram.com/01.20.21.1845.01









  


  










Input Form





Integrate[E^(p z) Sinh[c z]^m Cosh[b + a z], z] == ((-I^m) 2^(-1 - m) (E^(2 b + (a + p) z)/(-a - p) + 1/(E^((a - p) z) (a - p))) Binomial[m, m/2] (1 - Mod[m, 2]))/E^b - (2^(-1 - m) Sum[(-1)^k (E^(2 b - (-a + 2 c k - c m - p) z)/ (-a + 2 c k - c m - p) + 1/(E^((a + 2 c k - c m - p) z) (a + 2 c k - c m - p)) + (-1)^m (E^(2 b - (-a - 2 c k + c m - p) z)/ (-a - 2 c k + c m - p) + 1/(E^((a + c (-2 k + m) - p) z) (a + c (-2 k + m) - p)))) Binomial[m, k], {k, 0, Floor[(1/2) (-1 + m)]}])/E^b /; Element[m, Integers] && m > 0










Standard Form





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MathML Form







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</apply> </apply> </apply> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> <ci> k </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> c </ci> <ci> m </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> p </ci> </apply> </apply> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> <ci> k </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> c </ci> <ci> m </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> p </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <plus /> <ci> a </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> <ci> k </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> c </ci> <ci> m </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> p </ci> </apply> </apply> </apply> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <plus /> <ci> a </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> <ci> k </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> c </ci> <ci> m </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> p </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <ci> Binomial </ci> <ci> m </ci> <ci> k </ci> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <in /> <ci> m </ci> <apply> <ci> SuperPlus </ci> <ci> &#8469; </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2002-12-18