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Cosh




Mathematica Notation

Traditional Notation









Elementary Functions > Cosh[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving hyperbolic and trigonometric functions > Involving rational functions of sinh and sin > Involving sin(e z)cosh(d z)/a+b sinh2(c z)





http://functions.wolfram.com/01.20.21.1904.01









  


  








Input Form





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