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Sinh






Mathematica Notation

Traditional Notation









Elementary Functions > Sinh[z] > Integration > Indefinite integration > Involving functions of the direct function and trigonometric functions > Involving algebraic functions of the direct function and trigonometric functions > Involving sin > Involving sin(d z)(a+b sinh2(c z))beta





http://functions.wolfram.com/01.19.21.2799.01









  


  










Input Form





Integrate[Sin[d z] (a + b Sinh[c z]^2)^\[Beta], z] == (-(1/(2 (d^2 + 4 c^2 \[Beta]^2)))) (((a + ((1/4) b (-1 + E^(2 c z))^2)/E^(2 c z))^\[Beta] ((d + 2 I c \[Beta]) AppellF1[-((I d)/(2 c)) - \[Beta], -\[Beta], -\[Beta], 1 - (I d)/(2 c) - \[Beta], (b E^(2 c z))/ (-2 a - 2 Sqrt[a (a - b)] + b), (b E^(2 c z))/ (-2 a + 2 Sqrt[a (a - b)] + b)] + E^(2 I d z) (d - 2 I c \[Beta]) AppellF1[(I d)/(2 c) - \[Beta], -\[Beta], -\[Beta], 1 + (I d)/(2 c) - \[Beta], (b E^(2 c z))/(-2 a - 2 Sqrt[a (a - b)] + b), (b E^(2 c z))/(-2 a + 2 Sqrt[a (a - b)] + b)]))/ (E^(I d z) (1 + (b E^(2 c z))/(2 a + 2 Sqrt[a (a - b)] - b))^\[Beta] (1 - (b E^(2 c z))/(-2 a + 2 Sqrt[a (a - b)] + b))^\[Beta]))










Standard Form





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MathML Form







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</ci> </apply> </apply> <apply> <ci> AppellF1 </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> d </ci> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#946; </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#946; </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#946; </ci> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> d </ci> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#946; </ci> </apply> </apply> <apply> <times /> <ci> b </ci> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> -2 </cn> <ci> a </ci> </apply> <ci> b </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <times /> <ci> a </ci> <apply> <plus /> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <ci> b </ci> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> -2 </cn> <ci> a </ci> </apply> <ci> b </ci> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <times /> <ci> a </ci> <apply> <plus /> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </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