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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 and exponential functions > Involving rational functions of sin and exp > Involving ep zsin(e z)cosh(c z)/a+b sin2(d z)





http://functions.wolfram.com/01.20.21.1246.01









  


  








Input Form





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