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Cosh






Mathematica Notation

Traditional Notation









Elementary Functions > Cosh[z] > Integration > Indefinite integration > Involving functions of the direct function, hyperbolic and trigonometric functions > Involving rational functions of the direct function, hyperbolic and trigonometric functions > Involving sin and rational functions of sinh > Involving sin(d z)(a+b sinh(e z)+c cosh(e z))-n





http://functions.wolfram.com/01.20.21.4764.01









  


  










Input Form





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










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