Hyperbolic cosine integral: Integration (formula 01.20.21.3819)

Cosh

$Mathematica Notation$

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 exp

Involving e^{b z^r+e} cos(a z^r+q) cosh^v(c z^r+g)

http://functions.wolfram.com/01.20.21.3819.01

Input Form

Integrate[E^(b Sqrt[z] + e) Cos[a Sqrt[z] + q] Cosh[c Sqrt[z] + g]^v, z] == (((E^(e - I q + ((-I) a + b) Sqrt[z]) (-1 + ((-I) a + b) Sqrt[z]))/ ((-I) a + b)^2 + (E^(e + I q + (I a + b) Sqrt[z]) (-1 + (I a + b) Sqrt[z]))/(I a + b)^2) Binomial[v, v/2] (1 - Mod[v, 2]))/2^v + Sum[((E^(e - I q - g (-2 s + v) + ((-I) a + b - c (-2 s + v)) Sqrt[z]) (-1 + ((-I) a + b - c (-2 s + v)) Sqrt[z]))/ ((-I) a + b - c (-2 s + v))^2 + (E^(e + I q - g (-2 s + v) + (I a + b - c (-2 s + v)) Sqrt[z]) (-1 + (I a + b - c (-2 s + v)) Sqrt[z]))/(I a + b - c (-2 s + v))^ 2 + (E^(e - I q + g (-2 s + v) + ((-I) a + b + c (-2 s + v)) Sqrt[z]) (-1 + ((-I) a + b + c (-2 s + v)) Sqrt[z]))/ ((-I) a + b + c (-2 s + v))^2 + (E^(e + I q + g (-2 s + v) + (I a + b + c (-2 s + v)) Sqrt[z]) (-1 + (I a + b + c (-2 s + v)) Sqrt[z]))/(I a + b + c (-2 s + v))^2) Binomial[v, s], {s, 0, Floor[(1/2) (-1 + v)]}]/2^v /; 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