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Cosh




Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/01.20.21.3042.01









  


  








Input Form





Integrate[(a z + b)^\[Beta] E^(p z) Cosh[c z + e]^v, z] == ((-(1/a)) (b + a z)^(1 + \[Beta]) (Binomial[v, v/2] ExpIntegralE[-\[Beta], -((p (b + a z))/a)] (1 - Mod[v, 2]) + Sum[Binomial[v, k] (E^(2 e k - e v + (b c (-2 k + v))/a) (ExpIntegralE[-\[Beta], -(((2 c k + p - c v) (b + a z))/a)] + E^(-4 e k + (2 b c (2 k - v))/a + 2 e v) ExpIntegralE[-\[Beta], -(((p + c (-2 k + v)) (b + a z))/a)])), {k, 0, Floor[(1/2) (-1 + v)]}]))/(2^v E^((b p)/a)) /; 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