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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 functions > Involving algebraic functions of sin and cos > Involving sinh(d z) (a+b sin2(e z)+c cos2(e z))beta





http://functions.wolfram.com/01.19.21.0873.01









  


  










Input Form





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