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Sinh






Mathematica Notation

Traditional Notation









Elementary Functions > Sinh[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving trigonometric and exponential functions > Involving rational functions of cos and exp > Involving ep zcos(e z)sinh(c z)/a+b cos(d z)





http://functions.wolfram.com/01.19.21.1320.01









  


  










Input Form





Integrate[(E^(p z) Cos[e z] Sinh[c z])/(a + b Cos[d z]), z] == (1/4) (-((E^((-c + I d - I e + p) z) ((a + Sqrt[a^2 - b^2]) Hypergeometric2F1[-((I (-c + I d - I e + p))/d), 1, 2 - (I (-c - I e + p))/d, (b E^(I d z))/(-a + Sqrt[a^2 - b^2])] + (-a + Sqrt[a^2 - b^2]) Hypergeometric2F1[ -((I (-c + I d - I e + p))/d), 1, 2 - (I (-c - I e + p))/d, -((b E^(I d z))/(a + Sqrt[a^2 - b^2]))]))/ (b Sqrt[a^2 - b^2] (-c + I d - I e + p))) + (E^((c + I d - I e + p) z) ((a + Sqrt[a^2 - b^2]) Hypergeometric2F1[ -((I (c + I d - I e + p))/d), 1, 2 - (I (c - I e + p))/d, (b E^(I d z))/(-a + Sqrt[a^2 - b^2])] + (-a + Sqrt[a^2 - b^2]) Hypergeometric2F1[-((I (c + I d - I e + p))/d), 1, 2 - (I (c - I e + p))/d, -((b E^(I d z))/(a + Sqrt[a^2 - b^2]))]))/ (b Sqrt[a^2 - b^2] (c + I d - I e + p)) - (E^((-c + I d + I e + p) z) ((a + Sqrt[a^2 - b^2]) Hypergeometric2F1[-((I (-c + I d + I e + p))/d), 1, 2 - (I (-c + I e + p))/d, (b E^(I d z))/(-a + Sqrt[a^2 - b^2])] + (-a + Sqrt[a^2 - b^2]) Hypergeometric2F1[-((I (-c + I d + I e + p))/d), 1, 2 - (I (-c + I e + p))/d, -((b E^(I d z))/ (a + Sqrt[a^2 - b^2]))]))/(b Sqrt[a^2 - b^2] (-c + I d + I e + p)) + (E^((c + I d + I e + p) z) ((a + Sqrt[a^2 - b^2]) Hypergeometric2F1[-((I (c + I d + I e + p))/d), 1, 2 - (I (c + I e + p))/d, (b E^(I d z))/(-a + Sqrt[a^2 - b^2])] + (-a + Sqrt[a^2 - b^2]) Hypergeometric2F1[-((I (c + I d + I e + p))/d), 1, 2 - (I (c + I e + p))/d, -((b E^(I d z))/(a + Sqrt[a^2 - b^2]))]))/ (b Sqrt[a^2 - b^2] (c + I d + I e + p)))










Standard Form





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MathML Form







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<times /> <apply> <power /> <exponentiale /> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> c </ci> </apply> <apply> <times /> <imaginaryi /> <ci> d </ci> </apply> <apply> <times /> <imaginaryi /> <ci> e </ci> </apply> <ci> p </ci> </apply> <ci> z </ci> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <plus /> <ci> a </ci> <apply> <power /> <apply> <plus /> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <ci> Hypergeometric2F1 </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> c </ci> </apply> <apply> <times /> <imaginaryi /> <ci> d </ci> </apply> <apply> <times /> <imaginaryi /> <ci> e </ci> </apply> <ci> p </ci> 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<plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> c </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> e </ci> </apply> </apply> <ci> p </ci> </apply> <apply> <power /> <ci> d </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> b </ci> <apply> <power /> <exponentiale /> <apply> <times /> <imaginaryi /> <ci> d </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <plus /> <ci> a </ci> <apply> <power /> <apply> <plus /> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <ci> b </ci> <apply> <power /> 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Date Added to functions.wolfram.com (modification date)





2002-12-18