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Sinh




Mathematica Notation

Traditional Notation









Elementary Functions > Sinh[z] > Integration > Indefinite integration > Involving functions of the direct function and trigonometric functions > Involving algebraic functions of the direct function and trigonometric functions > Involving cos > Involving cos(d z)sinh(e z)(a+b sinh(c z))beta





http://functions.wolfram.com/01.19.21.2804.01









  


  








Input Form





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