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Sinh




Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/01.19.21.2282.01









  


  








Input Form





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