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Cosh






Mathematica Notation

Traditional Notation









Elementary Functions > Cosh[z] > Integration > Indefinite integration > Involving functions of the direct function, hyperbolic, exponential and trigonometric functions > Involving rational functions of the direct function, hyperbolic, exponential and trigonometric functions > Involving sin, rational functions of sinh and exp > Involving ep zsin(d z)(a sinh2(e z)+b cosh2(e z))-n





http://functions.wolfram.com/01.20.21.4881.01









  


  










Input Form





Integrate[(E^(p z) Sin[d z])/(a Sinh[e z]^2 + b Cosh[e z]^2)^2, z] == (-(1/2)) I ((I E^(((-I) d + 2 e + p) z) ((Sqrt[a] + I Sqrt[b])^2 (a - b) Hypergeometric2F1[1 + ((-I) d + p)/(2 e), 1, 2 + ((-I) d + p)/(2 e), ((a + b) E^(2 e z))/(Sqrt[a] - I Sqrt[b])^2] - (Sqrt[a] - I Sqrt[b])^2 (a - b) Hypergeometric2F1[ 1 + ((-I) d + p)/(2 e), 1, 2 + ((-I) d + p)/(2 e), ((a + b) E^(2 e z))/(Sqrt[a] + I Sqrt[b])^2] - 2 I Sqrt[a] Sqrt[b] ((Sqrt[a] + I Sqrt[b])^2 Hypergeometric2F1[ 1 + ((-I) d + p)/(2 e), 2, 2 + ((-I) d + p)/(2 e), ((a + b) E^(2 e z))/(Sqrt[a] - I Sqrt[b])^2] + (Sqrt[a] - I Sqrt[b])^2 Hypergeometric2F1[1 + ((-I) d + p)/(2 e), 2, 2 + ((-I) d + p)/(2 e), ((a + b) E^(2 e z))/(Sqrt[a] + I Sqrt[b])^ 2])))/(2 a^(3/2) b^(3/2) (a + b) ((-I) d + 2 e + p)) - (I E^((I d + 2 e + p) z) ((Sqrt[a] + I Sqrt[b])^2 (a - b) Hypergeometric2F1[1 + (I d + p)/(2 e), 1, 2 + (I d + p)/(2 e), ((a + b) E^(2 e z))/(Sqrt[a] - I Sqrt[b])^2] - (Sqrt[a] - I Sqrt[b])^2 (a - b) Hypergeometric2F1[1 + (I d + p)/(2 e), 1, 2 + (I d + p)/(2 e), ((a + b) E^(2 e z))/(Sqrt[a] + I Sqrt[b])^ 2] - 2 I Sqrt[a] Sqrt[b] ((Sqrt[a] + I Sqrt[b])^2 Hypergeometric2F1[1 + (I d + p)/(2 e), 2, 2 + (I d + p)/(2 e), ((a + b) E^(2 e z))/(Sqrt[a] - I Sqrt[b])^2] + (Sqrt[a] - I Sqrt[b])^2 Hypergeometric2F1[1 + (I d + p)/(2 e), 2, 2 + (I d + p)/(2 e), ((a + b) E^(2 e z))/(Sqrt[a] + I Sqrt[b])^ 2])))/(2 a^(3/2) b^(3/2) (a + b) (I d + 2 e + p)))










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