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Cosh






Mathematica Notation

Traditional Notation









Elementary Functions > Cosh[z] > Integration > Indefinite integration > Involving functions of the direct function, trigonometric and exponential functions > Involving products of the direct function, trigonometric and exponential functions > Involving rational functions of cos and exp > Involving ep zcosh(e z)cosh(d z)/a+b cos2(c z)





http://functions.wolfram.com/01.20.21.3876.01









  


  










Input Form





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










Standard Form





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MathML Form







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<apply> <power /> <apply> <plus /> <ci> a </ci> <ci> b </ci> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> a </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> </apply> <apply> <ci> Hypergeometric2F1 </ci> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <apply> <plus /> <ci> d </ci> <ci> e </ci> <ci> p </ci> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <cn type='integer'> 1 </cn> <apply> <plus /> <cn type='integer'> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <apply> <plus /> <ci> d </ci> <ci> e </ci> <ci> p </ci> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> </apply> <cn type='integer'> -1 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Rule Form





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





2002-12-18