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Cosh




Mathematica Notation

Traditional Notation









Elementary Functions > Cosh[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving trigonometric functions > Involving rational functions of sin > Involving cosh(c z)/a+b sin2(d z)





http://functions.wolfram.com/01.20.21.0683.01









  


  








Input Form





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








Standard Form





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MathML Form







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Rule Form





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





2002-12-18