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Sinh






Mathematica Notation

Traditional Notation









Elementary Functions > Sinh[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving trigonometric and exponential functions > Involving algebraic functions of sin, cos and exp > Involving ep z sinh(d z) (a+b sin(e z)+c cos(e z))beta





http://functions.wolfram.com/01.19.21.1339.01









  


  










Input Form





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










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