Tangent: Integration (formula 01.08.21.0054)

Tan

$Mathematica Notation$

Elementary Functions

Tan[z]

Integration

Indefinite integration

Involving one direct function and elementary functions

Involving trigonometric functions

Involving algebraic functions of cos

Involving cos(2c z)(a+b cos(2c z))^beta

http://functions.wolfram.com/01.08.21.0054.01

Input Form

Integrate[Cos[2 c z] (a + b Cos[2 c z])^\[Beta] Tan[c z], z] == (1/(2 b c \[Beta] (1 + \[Beta]))) (((a + b Cos[2 c z])^\[Beta] (b (1 + \[Beta]) ((a + b Cos[2 c z])/(a - b))^ \[Beta] Hypergeometric2F1[-\[Beta], -\[Beta], 1 - \[Beta], -(((a - b) Sec[c z]^2)/(2 b))] - \[Beta] (b + b Cos[2 c z] ((a + b Cos[2 c z])/(a - b))^\[Beta] + a (-1 + ((a + b Cos[2 c z])/(a - b))^\[Beta])) (1 + ((a - b) Sec[c z]^2)/(2 b))^\[Beta]))/ (((a + b Cos[2 c z])/(a - b))^\[Beta] (1 + ((a - b) Sec[c z]^2)/(2 b))^ \[Beta]))

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