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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 algebraic functions of sin and sinh > Involving sinh(e z)cosh(d z)(a+b sin(c z))beta





http://functions.wolfram.com/01.20.21.1900.01









  


  










Input Form





Integrate[Sinh[e z] Cosh[d z] (a + b Sin[c z])^\[Beta], z] == ((1/4) (a + b Sin[c z])^\[Beta] (-((1/(d - e - I c \[Beta])) (E^((d - e) z) AppellF1[-((I (d - e))/c) - \[Beta], -\[Beta], -\[Beta], 1 - (I (d - e))/c - \[Beta], (I b E^(I c z))/(a + Sqrt[a^2 - b^2]), (I b E^(I c z))/(a - Sqrt[a^2 - b^2])])) - (1/(d - e + I c \[Beta])) (E^((-d + e) z) AppellF1[(I (d - e))/c - \[Beta], -\[Beta], -\[Beta], 1 + (I (d - e))/c - \[Beta], (I b E^(I c z))/(a + Sqrt[a^2 - b^2]), (I b E^(I c z))/(a - Sqrt[a^2 - b^2])]) + (1/(d + e - I c \[Beta])) (E^((d + e) z) AppellF1[-((I (d + e))/c) - \[Beta], -\[Beta], -\[Beta], 1 - (I (d + e))/c - \[Beta], (I b E^(I c z))/(a + Sqrt[a^2 - b^2]), (I b E^(I c z))/(a - Sqrt[a^2 - b^2])]) + (1/(d + e + I c \[Beta])) (AppellF1[(I (d + e + I c \[Beta]))/c, -\[Beta], -\[Beta], (c + I (d + e) - c \[Beta])/c, (I b E^(I c z))/(a + Sqrt[a^2 - b^2]), (I b E^(I c z))/(a - Sqrt[a^2 - b^2])]/E^((d + e) z))))/ ((1 + (I b E^(I c z))/(-a + Sqrt[a^2 - b^2]))^\[Beta] (1 - (I b E^(I c z))/(a + Sqrt[a^2 - b^2]))^\[Beta])










Standard Form





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MathML Form







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





2002-12-18