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Cosh




Mathematica Notation

Traditional Notation









Elementary Functions > Cosh[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving hyperbolic and exponential functions > Involving sinh and algebraic functions of exp > Involving ep z(a+b ed z)beta sinh(e z)cosh(c z)





http://functions.wolfram.com/01.20.21.1838.01









  


  








Input Form





Integrate[E^(p z) (a + b E^(d z))^\[Beta] Sinh[e z] Cosh[c z], z] == ((-(1/4)) (a + b E^(d z))^\[Beta] ((E^((c - e + p) z) (c - e - p) Hypergeometric2F1[(c - e + p)/d, -\[Beta], (c + d - e + p)/d, -((b E^(d z))/a)] + E^((-c + e + p) z) (c - e + p) Hypergeometric2F1[(-c + e + p)/d, -\[Beta], (-c + d + e + p)/d, -((b E^(d z))/a)])/((c - e - p) (c - e + p)) + (E^((-c - e + p) z) (-c - e - p) Hypergeometric2F1[(-c - e + p)/d, -\[Beta], (-c + d - e + p)/d, -((b E^(d z))/a)] + E^((c + e + p) z) (-c - e + p) Hypergeometric2F1[(c + e + p)/d, -\[Beta], (c + d + e + p)/d, -((b E^(d z))/a)])/ ((-c - e - p) (-c - e + p))))/(1 + (b E^(d z))/a)^\[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