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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 powers of sin and exp > Involving ep zsinmu(c z) coshnu(a z+b)





http://functions.wolfram.com/01.20.21.3764.01









  


  










Input Form





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










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