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Cosh






Mathematica Notation

Traditional Notation









Elementary Functions > Cosh[z] > Integration > Indefinite integration > Involving functions of the direct function, trigonometric and exponential functions > Involving powers of the direct function, trigonometric and exponential functions > Involving cos and algebraic functions of exp > Involving ep z(a+b ed z)beta cos(e z)coshv(c z)





http://functions.wolfram.com/01.20.21.3825.01









  


  










Input Form





Integrate[E^(p z) (a + b E^(d z))^\[Beta] Cos[e z] Cosh[c z]^v, z] == (2^(-1 - v) (a + b E^(d z))^\[Beta] Binomial[v, v/2] ((-E^(((-I) e + p) z)) (I e + p) Hypergeometric2F1[((-I) e + p)/d, -\[Beta], (d - I e + p)/d, -((b E^(d z))/a)] + E^((I e + p) z) (I e - p) Hypergeometric2F1[(I e + p)/d, -\[Beta], (d + I e + p)/d, -((b E^(d z))/a)]) (1 - Mod[v, 2]))/ (1 + (b E^(d z))/a)^\[Beta]/((I e - p) (I e + p)) + (2^(-1 - v) (a + b E^(d z))^\[Beta] Sum[Binomial[v, s] (((-E^((I e + p - c (2 s - v)) z)) ((-I) e + p + c (2 s - v)) Hypergeometric2F1[ (I e + p - c (2 s - v))/d, -\[Beta], (d + I e + p - c (2 s - v))/ d, -((b E^(d z))/a)] + E^(((-I) e + p + c (2 s - v)) z) ((-I) e - p + c (2 s - v)) Hypergeometric2F1[ ((-I) e + p + c (2 s - v))/d, -\[Beta], (d - I e + p + c (2 s - v))/d, -((b E^(d z))/a)])/ (((-I) e - p + c (2 s - v)) ((-I) e + p + c (2 s - v))) + (E^(((-I) e + p - c (2 s - v)) z) ((-I) e - p - c (2 s - v)) Hypergeometric2F1[((-I) e + p - c (2 s - v))/d, -\[Beta], (d - I e + p - c (2 s - v))/d, -((b E^(d z))/a)] - E^((I e + p + c (2 s - v)) z) ((-I) e + p - c (2 s - v)) Hypergeometric2F1[(I e + p + c (2 s - v))/d, -\[Beta], (d + I e + p + c (2 s - v))/d, -((b E^(d z))/a)])/ (((-I) e - p - c (2 s - v)) ((-I) e + p - c (2 s - v)))), {s, 0, Floor[(1/2) (-1 + v)]}])/(1 + (b E^(d z))/a)^\[Beta] /; Element[v, Integers] && v > 0










Standard Form





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MathML Form







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





2002-12-18