Secant: Integration (formula 01.11.21.0143)

Sec

$Mathematica Notation$

Elementary Functions

Sec[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^{p z}cos(a z) sec^v( c z)

http://functions.wolfram.com/01.11.21.0143.01

Input Form

Integrate[E^(p z) Cos[a z] Sec[c z]^\[Nu], z] == (1/2) (1 + E^(2 I c z))^\[Nu] ((1/((-I) a + p + I c \[Nu])) (E^(((-I) a + p) z) HypergeometricPFQ[{-(a/(2 c)) - (I p)/(2 c) + \[Nu]/2, \[Nu]}, {1 - a/(2 c) - (I p)/(2 c) + \[Nu]/2}, -E^(2 I c z)]) + (1/(I a + p + I c \[Nu])) (E^((I a + p) z) HypergeometricPFQ[{a/(2 c) - (I p)/(2 c) + \[Nu]/2, \[Nu]}, {1 + a/(2 c) - (I p)/(2 c) + \[Nu]/2}, -E^(2 I c z)])) Sec[c z]^\[Nu]

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)

2002-10-15