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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 sin2(e z)+b sin(2 e z)+c cos2(e z))beta





http://functions.wolfram.com/01.19.21.1342.01









  


  










Input Form





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










Standard Form





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MathML Form







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





2002-12-18